FeatureEstimation.py

+# -*- coding: utf-8 -*-
+"""
+Updated Oct 18 2022
+
+@author: Qianliang Li (glia@dtu.dk)
+
+This script contains the code to estimate the following EEG features:
+    1. Power Spectral Density
+    2. Frontal Theta/Beta Ratio
+    3. Asymmetry
+    4. Peak Alpha Frequency
+    5. 1/f Exponents
+    6. Microstates
+    7. Long-Range Temporal Correlation (DFA Exponent)
+Source localization and functional connectivity
+    8. Imaginary part of Coherence
+    9. Weighted Phase Lag Index
+    10. (Orthogonalized) Power Envelope Correlations
+    11. Granger Causality
+
+It should be run after Preprocessing.py
+
+All features are saved in pandas DataFrame format for the machine learning
+pipeline
+
+Note that the code has not been changed to fit the demonstration dataset,
+thus just running it might introduce some errors.
+The code is provided to show how we performed the feature estimation
+and if you are adapting the code, you should check if it fits your dataset
+e.g. the questionnaire data, sensors and source parcellation etc
+
+The script was written in Spyder. The outline panel can be used to navigate
+the different parts easier (Default shortcut: Ctrl + Shift + O)
+"""
+
+# Set working directory
+import os
+wkdir = "/home/glia/EEG"
+os.chdir(wkdir)
+
+# Load all libraries from the Preamble
+from Preamble import *
+
+# %% Load preprocessed epochs and questionnaire data
+load_path = "./PreprocessedData"
+
+# Get filenames
+files = []
+for r, d, f in os.walk(load_path):
+    for file in f:
+        if ".fif" in file:
+            files.append(os.path.join(r, file))
+files.sort()
+
+# Subject IDs
+Subject_id = [0] * len(files)
+for i in range(len(files)):
+    temp = files[i].split("\\")
+    temp = temp[-1].split("_")
+    Subject_id[i] = int(temp[0])
+
+n_subjects = len(Subject_id)
+
+# Load Final epochs
+final_epochs = [0]*n_subjects
+for n in range(n_subjects):
+    final_epochs[n] = mne.read_epochs(fname = os.path.join(files[n]),
+                    verbose=0)
+
+# Load dropped epochs - used for gap idx in microstates
+bad_subjects = [12345] # list with subjects that were excluded due to too many dropped epochs/chs
+Drop_epochs_df = pd.read_pickle("./Preprocessing/dropped_epochs.pkl")
+
+good_subject_df_idx = [not i in bad_subjects for i in Drop_epochs_df["Subject_ID"]]
+Drop_epochs_df = Drop_epochs_df.loc[good_subject_df_idx,:]
+Drop_epochs_df = Drop_epochs_df.sort_values(by=["Subject_ID"]).reset_index(drop=True)
+
+### Load questionnaire data
+# For the purposes of this demonstration I will make a dummy dataframe
+# The original code imported csv files with questionnaire data and group status
+final_qdf = pd.DataFrame({"Subject_ID":Subject_id,
+                          "Age":[23,26],
+                          "Gender":[0,0],
+                          "Group_status":[0,1],
+                          "PCL_total":[33,56],
+                          "Q1":[1.2, 2.3],
+                          "Q2":[1.7, 1.5],
+                          "Qn":[2.1,1.0]})
+
+# Define cases as >= 44 total PCL
+# Type: numpy array with subject id
+cases = np.array(final_qdf["Subject_ID"][final_qdf["PCL_total"]>=44])
+n_groups = 2
+Groups = ["CTRL", "PTSD"]
+
+# Define folder for saving features
+Feature_savepath = "./Features/"
+Stat_savepath = "./Statistics/"
+Model_savepath = "./Model/"
+
+# %% Power spectrum features
+Freq_Bands = {"delta": [1.25, 4.0],
+              "theta": [4.0, 8.0],
+              "alpha": [8.0, 13.0],
+              "beta": [13.0, 30.0],
+              "gamma": [30.0, 49.0]}
+ch_names = final_epochs[0].info["ch_names"]
+n_channels = final_epochs[0].info["nchan"]
+
+# Pre-allocate memory
+power_bands = [0]*len(final_epochs)
+
+def power_band_estimation(n):
+    # Get index for eyes open and eyes closed
+    EC_index = final_epochs[n].events[:,2] == 1
+    EO_index = final_epochs[n].events[:,2] == 2
+    
+    # Calculate the power spectral density
+    psds, freqs = psd_multitaper(final_epochs[n], fmin = 1, fmax = 50) # output (epochs, channels, freqs)
+    
+    temp_power_band = []
+    
+    for fmin, fmax in Freq_Bands.values():
+        # Calculate the power each frequency band
+        psds_band = psds[:, :, (freqs >= fmin) & (freqs < fmax)].sum(axis=-1)
+        # Calculate the mean for each eye status
+        psds_band_eye = np.array([psds_band[EC_index,:].mean(axis=0),
+                                      psds_band[EO_index,:].mean(axis=0)])
+        # Append for each freq band
+        temp_power_band.append(psds_band_eye)
+        # Output: List with the 5 bands, and each element is a 2D array with eye status as 1st dimension and channels as 2nd dimension
+    
+    # The list is reshaped and absolute and relative power are calculated
+    abs_power_band = np.reshape(temp_power_band, (5, 2, n_channels))
+    abs_power_band = 10.*np.log10(abs_power_band) # Convert to decibel scale
+    
+    rel_power_band = np.reshape(temp_power_band, (5, 2, n_channels))
+    rel_power_band = rel_power_band/np.sum(rel_power_band, axis=0, keepdims=True)
+    # each eye condition and channel have been normalized to power in all 5 frequencies for that given eye condition and channel
+    
+    # Make one list in 1 dimension
+    abs_power_values = np.concatenate(np.concatenate(abs_power_band, axis=0), axis=0)
+    rel_power_values = np.concatenate(np.concatenate(rel_power_band, axis=0), axis=0)
+    ## Output: First the channels, then the eye status and finally the frequency bands are concatenated
+    ## E.g. element 26 is 3rd channel, eyes open, first frequency band
+    #assert abs_power_values[26] == abs_power_band[0,1,2]
+    #assert abs_power_values[47] == abs_power_band[0,1,23] # +21 channels to last
+    #assert abs_power_values[50] == abs_power_band[1,0,2] # once all channels have been changed then the freq is changed and eye status
+    
+    # Get result
+    res = np.concatenate([abs_power_values,rel_power_values],axis=0)
+    return n, res
+
+with concurrent.futures.ProcessPoolExecutor() as executor:
+    for n, result in executor.map(power_band_estimation, range(len(final_epochs))): # Function and arguments
+        power_bands[n] = result
+
+# Combine all data into one dataframe
+# First the columns are prepared
+n_subjects = len(Subject_id)
+
+# The group status (PTSD/CTRL) is made using the information about the cases
+Group_status = np.array(["CTRL"]*n_subjects)
+Group_status[np.array([i in cases for i in Subject_id])] = "PTSD"
+
+# A variable that codes the channels based on A/P localization is also made
+Frontal_chs = ["Fp1", "Fpz", "Fp2", "AFz", "Fz", "F3", "F4", "F7", "F8"]
+Central_chs = ["Cz", "C3", "C4", "T7", "T8", "FT7", "FC3", "FCz", "FC4", "FT8", "TP7", "CP3", "CPz", "CP4", "TP8"]
+Posterior_chs = ["Pz", "P3", "P4", "P7", "P8", "POz", "O1", "O2", "Oz"]
+
+Brain_region_labels = ["Frontal","Central","Posterior"]
+Brain_region = np.array(ch_names, dtype = "<U9")
+Brain_region[np.array([i in Frontal_chs for i in ch_names])] = Brain_region_labels[0]
+Brain_region[np.array([i in Central_chs for i in ch_names])] = Brain_region_labels[1]
+Brain_region[np.array([i in Posterior_chs for i in ch_names])] = Brain_region_labels[2]
+
+# A variable that codes the channels based on M/L localization
+Left_chs = ["Fp1", "F3", "F7", "FC3", "FT7", "C3", "T7", "CP3", "TP7", "P3", "P7", "O1"]
+Right_chs = ["Fp2", "F4", "F8", "FC4", "FT8", "C4", "T8", "CP4", "TP8", "P4", "P8", "O2"]
+Mid_chs = ["Fpz", "AFz", "Fz", "FCz", "Cz", "CPz", "Pz", "POz", "Oz"]
+
+Brain_side = np.array(ch_names, dtype = "<U5")
+Brain_side[np.array([i in Left_chs for i in ch_names])] = "Left"
+Brain_side[np.array([i in Right_chs for i in ch_names])] = "Right"
+Brain_side[np.array([i in Mid_chs for i in ch_names])] = "Mid"
+
+# Eye status is added
+eye_status = list(final_epochs[0].event_id.keys())
+n_eye_status = len(eye_status)
+
+# Frequency bands
+freq_bands_name = list(Freq_Bands.keys())
+n_freq_bands = len(freq_bands_name)
+
+# Quantification (Abs/Rel)
+quant_status = ["Absolute", "Relative"]
+n_quant_status = len(quant_status)
+
+# The dataframe is made by combining all the unlisted pds values
+# Each row correspond to a different channel. It is reset after all channel names have been used
+# Each eye status element is repeated n_channel times, before it is reset
+# Each freq_band element is repeated n_channel * n_eye_status times, before it is reset
+# Each quantification status element is repeated n_channel * n_eye_status * n_freq_bands times, before it is reset
+power_df = pd.DataFrame(data = {"Subject_ID": [ele for ele in Subject_id for i in range(n_eye_status*n_quant_status*n_freq_bands*n_channels)],
+                                "Group_status": [ele for ele in Group_status for i in range(n_eye_status*n_quant_status*n_freq_bands*n_channels)],
+                                "Channel": ch_names*(n_eye_status*n_quant_status*n_freq_bands*n_subjects),
+                                "Brain_region": list(Brain_region)*(n_eye_status*n_quant_status*n_freq_bands*n_subjects),
+                                "Brain_side": list(Brain_side)*(n_eye_status*n_quant_status*n_freq_bands*n_subjects),
+                                "Eye_status": [ele for ele in eye_status for i in range(n_channels)]*n_quant_status*n_freq_bands*n_subjects,
+                                "Freq_band": [ele for ele in freq_bands_name for i in range(n_channels*n_eye_status)]*n_quant_status*n_subjects,
+                                "Quant_status": [ele for ele in quant_status for i in range(n_channels*n_eye_status*n_freq_bands)]*n_subjects,
+                                "PSD": list(np.concatenate(power_bands, axis=0))
+                                })
+# Absolute power is in decibels (10*log10(power))
+
+# Fix Freq_band categorical order
+power_df["Freq_band"] = power_df["Freq_band"].astype("category").\
+            cat.reorder_categories(list(Freq_Bands.keys()), ordered=True)
+# Fix Brain_region categorical order
+power_df["Brain_region"] = power_df["Brain_region"].astype("category").\
+            cat.reorder_categories(Brain_region_labels, ordered=True)
+
+# Save the dataframe
+power_df.to_pickle(os.path.join(Feature_savepath,"Power_df.pkl"))
+
+
+# %% Theta-beta ratio
+# Frontal theta/beta ratio has been implicated in cognitive control of attention
+power_df = pd.read_pickle(os.path.join(Feature_savepath,"Power_df.pkl"))
+
+eye_status = list(final_epochs[0].event_id)
+n_eye_status = len(eye_status)
+
+# Subset frontal absolute power
+power_df_sub1 = power_df[(power_df["Quant_status"] == "Absolute")&
+                         (power_df["Brain_region"] == "Frontal")]
+
+# Calculate average frontal power
+frontal_theta_mean_subject = power_df_sub1[power_df_sub1["Freq_band"] == "theta"].\
+    groupby(["Subject_ID","Group_status","Eye_status"]).mean().reset_index()
+frontal_beta_mean_subject = power_df_sub1[power_df_sub1["Freq_band"] == "beta"].\
+    groupby(["Subject_ID","Group_status","Eye_status"]).mean().reset_index()
+
+# Convert from dB to raw power
+frontal_theta_mean_subject["PSD"] = 10**(frontal_theta_mean_subject["PSD"]/10)
+frontal_beta_mean_subject["PSD"] = 10**(frontal_beta_mean_subject["PSD"]/10)
+
+# Calculate mean for each group and take ratio for whole group
+# To confirm trend observed in PSD plots
+mean_group_f_theta = frontal_theta_mean_subject.iloc[:,1:].groupby(["Group_status","Eye_status"]).mean()
+mean_group_f_beta = frontal_beta_mean_subject.iloc[:,1:].groupby(["Group_status","Eye_status"]).mean()
+mean_group_f_theta_beta_ratio = mean_group_f_theta/mean_group_f_beta
+
+# Calculate ratio for each subject
+frontal_theta_beta_ratio = frontal_theta_mean_subject.copy()
+frontal_theta_beta_ratio["PSD"] = frontal_theta_mean_subject["PSD"]/frontal_beta_mean_subject["PSD"]
+
+# Take the natural log of ratio 
+frontal_theta_beta_ratio["PSD"] = np.log(frontal_theta_beta_ratio["PSD"])
+
+# Rename and save feature
+frontal_theta_beta_ratio.rename(columns={"PSD":"TBR"},inplace=True)
+# Add dummy variable for re-using plot code
+dummy_variable = ["Frontal Theta Beta Ratio"]*frontal_theta_beta_ratio.shape[0]
+frontal_theta_beta_ratio.insert(3, "Measurement", dummy_variable )
+
+frontal_theta_beta_ratio.to_pickle(os.path.join(Feature_savepath,"fTBR_df.pkl"))
+
+# %% Frequency bands asymmetry
+# Defined as ln(right) - ln(left)
+# Thus we should only work with the absolute values and undo the dB transformation
+# Here I avg over all areas. I.e. mean((ln(F4)-ln(F3),(ln(F8)-ln(F7),(ln(Fp2)-ln(Fp1))) for frontal
+ROI = ["Frontal", "Central", "Posterior"]
+qq = "Absolute" # only calculate asymmetry for absolute
+# Pre-allocate memory
+asymmetry = np.zeros(shape=(len(np.unique(power_df["Subject_ID"])),
+                             len(np.unique(power_df["Eye_status"])),
+                             len(list(Freq_Bands.keys())),
+                             len(ROI)))
+
+def calculate_asymmetry(i):
+    ii = np.unique(power_df["Subject_ID"])[i]
+    temp_asymmetry = np.zeros(shape=(len(np.unique(power_df["Eye_status"])),
+                             len(list(Freq_Bands.keys())),
+                             len(ROI)))
+    for e in range(len(np.unique(power_df["Eye_status"]))):
+        ee = np.unique(power_df["Eye_status"])[e]
+        for f in range(len(list(Freq_Bands.keys()))):
+            ff = list(Freq_Bands.keys())[f]
+            
+            # Get the specific part of the df
+            temp_power_df = power_df[(power_df["Quant_status"] == qq) &
+                                     (power_df["Eye_status"] == ee) &
+                                     (power_df["Subject_ID"] == ii) &
+                                     (power_df["Freq_band"] == ff)].copy()
+            
+            # Convert from dB to raw power
+            temp_power_df.loc[:,"PSD"] = np.array(10**(temp_power_df["PSD"]/10))
+            
+            # Calculate the power asymmetry
+            for r in range(len(ROI)):
+                rr = ROI[r]
+                temp_power_roi_df = temp_power_df[(temp_power_df["Brain_region"] == rr)&
+                                                  ~(temp_power_df["Brain_side"] == "Mid")]
+                # Sort using channel names to make sure F8-F7 and not F4-F7 etc.
+                temp_power_roi_df = temp_power_roi_df.sort_values("Channel").reset_index(drop=True)
+                # Get the log power
+                R_power = temp_power_roi_df[(temp_power_roi_df["Brain_side"] == "Right")]["PSD"]
+                ln_R_power = np.log(R_power) # get log power
+                L_power = temp_power_roi_df[(temp_power_roi_df["Brain_side"] == "Left")]["PSD"]
+                ln_L_power = np.log(L_power) # get log power
+                # Pairwise subtraction followed by averaging
+                asymmetry_value = np.mean(np.array(ln_R_power) - np.array(ln_L_power))
+                # Save it to the array
+                temp_asymmetry[e,f,r] = asymmetry_value
+    # Print progress
+    print("{} out of {} finished testing".format(i+1,n_subjects))
+    return i, temp_asymmetry
+
+with concurrent.futures.ProcessPoolExecutor() as executor:
+    for i, res in executor.map(calculate_asymmetry, range(len(np.unique(power_df["Subject_ID"])))): # Function and arguments
+        asymmetry[i,:,:,:] = res
+
+# Prepare conversion of array to df using flatten
+n_subjects = len(Subject_id)
+
+# The group status (PTSD/CTRL) is made using the information about the cases
+Group_status = np.array(["CTRL"]*n_subjects)
+Group_status[np.array([i in cases for i in Subject_id])] = "PTSD"
+
+# Eye status is added
+eye_status = list(final_epochs[0].event_id.keys())
+n_eye_status = len(eye_status)
+
+# Frequency bands
+freq_bands_name = list(Freq_Bands.keys())
+n_freq_bands = len(freq_bands_name)
+
+# ROIs
+n_ROI = len(ROI)
+
+# Make the dataframe                
+asymmetry_df = pd.DataFrame(data = {"Subject_ID": [ele for ele in Subject_id for i in range(n_eye_status*n_freq_bands*n_ROI)],
+                                     "Group_status": [ele for ele in Group_status for i in range(n_eye_status*n_freq_bands*n_ROI)],
+                                     "Eye_status": [ele for ele in eye_status for i in range(n_freq_bands*n_ROI)]*(n_subjects),
+                                     "Freq_band": [ele for ele in freq_bands_name for i in range(n_ROI)]*(n_subjects*n_eye_status),
+                                     "ROI": list(ROI)*(n_subjects*n_eye_status*n_freq_bands),
+                                     "Asymmetry_score": asymmetry.flatten(order="C")
+                                     })
+# Flatten with order=C means that it first goes through last axis,
+# then repeat along 2nd last axis, and then repeat along 3rd last etc
+
+# Asymmetry numpy to pandas conversion check
+random_point=321
+asymmetry_df.iloc[random_point]
+
+i = np.where(np.unique(power_df["Subject_ID"]) == asymmetry_df.iloc[random_point]["Subject_ID"])[0]
+e = np.where(np.unique(power_df["Eye_status"]) == asymmetry_df.iloc[random_point]["Eye_status"])[0]
+f = np.where(np.array(list(Freq_Bands.keys())) == asymmetry_df.iloc[random_point]["Freq_band"])[0]
+r = np.where(np.array(ROI) == asymmetry_df.iloc[random_point]["ROI"])[0]
+
+assert asymmetry[i,e,f,r] == asymmetry_df.iloc[random_point]["Asymmetry_score"]
+
+# Save the dataframe
+asymmetry_df.to_pickle(os.path.join(Feature_savepath,"asymmetry_df.pkl"))
+
+# %% Using FOOOF
+# Peak alpha frequency (PAF) and 1/f exponent (OOF)
+# Using the FOOOF algorithm (Fitting oscillations and one over f)
+# Published by Donoghue et al, 2020 in Nature Neuroscience
+# To start, FOOOF takes the freqs and power spectra as input
+n_channels = final_epochs[0].info["nchan"]
+ch_names = final_epochs[0].info["ch_names"]
+sfreq = final_epochs[0].info["sfreq"]
+Freq_Bands = {"delta": [1.25, 4.0],
+              "theta": [4.0, 8.0],
+              "alpha": [8.0, 13.0],
+              "beta": [13.0, 30.0],
+              "gamma": [30.0, 49.0]}
+n_freq_bands = len(Freq_Bands)
+
+# From visual inspection there seems to be problem if PSD is too steep at the start
+# To overcome this problem, we try multiple start freq
+OOF_r2_thres = 0.95 # a high threshold as we allow for overfitting
+PAF_r2_thres = 0.90 # a more lenient threshold for PAF, as it is usually still captured even if fit for 1/f is not perfect
+freq_start_it_range = [2,3,4,5,6]
+freq_end = 40 # Stop freq at 40Hz to not be influenced by the Notch Filter
+
+eye_status = list(final_epochs[0].event_id.keys())
+n_eye_status = len(eye_status)
+
+PAF_data = np.zeros((n_subjects,n_eye_status,n_channels,3)) # CF, power, band_width
+OOF_data = np.zeros((n_subjects,n_eye_status,n_channels,2)) # offset and exponent
+
+def FOOOF_estimation(i):
+    PAF_data0 = np.zeros((n_eye_status,n_channels,3)) # CF, power, band_width
+    OOF_data0 = np.zeros((n_eye_status,n_channels,2)) # offset and exponent
+    # Get Eye status
+    eye_idx = [final_epochs[i].events[:,2] == 1, final_epochs[i].events[:,2] == 2] # EC and EO
+    # Calculate the power spectral density
+    psd, freqs = psd_multitaper(final_epochs[i], fmin = 1, fmax = 50) # output (epochs, channels, freqs)
+    # Retrieve psds for the 2 conditions and calculate mean across epochs
+    psds = []
+    for e in range(n_eye_status):
+        # Get the epochs for specific eye condition
+        temp_psd = psd[eye_idx[e],:,:]
+        # Calculate the mean across epochs
+        temp_psd = np.mean(temp_psd, axis=0)
+        # Save
+        psds.append(temp_psd)
+    # Try multiple start freq
+    PAF_data00 = np.zeros((n_eye_status,n_channels,len(freq_start_it_range),3)) # CF, power, band_width
+    OOF_data00 = np.zeros((n_eye_status,n_channels,len(freq_start_it_range),2)) # offset and exponent
+    r2s00 = np.zeros((n_eye_status,n_channels,len(freq_start_it_range)))
+    for e in range(n_eye_status):
+        psds_avg = psds[e]
+        for f in range(len(freq_start_it_range)):
+            # Initiate FOOOF group for analysis of multiple PSD
+            fg = fooof.FOOOFGroup()
+            # Set the frequency range to fit the model
+            freq_range = [freq_start_it_range[f], freq_end] # variable freq start to 49Hz
+            # Fit to each source PSD separately, but in parallel
+            fg.fit(freqs,psds_avg,freq_range,n_jobs=1)
+            # Extract aperiodic parameters
+            aps = fg.get_params('aperiodic_params')
+            # Extract peak parameters
+            peaks = fg.get_params('peak_params')
+            # Extract goodness-of-fit metrics
+            r2s = fg.get_params('r_squared')
+            # Save OOF and r2s
+            OOF_data00[e,:,f] = aps
+            r2s00[e,:,f] = r2s
+            # Find the alpha peak with greatest power
+            for c in range(n_channels):
+                peaks0 = peaks[peaks[:,3] == c]
+                # Subset the peaks within the alpha band
+                in_alpha_band = (peaks0[:,0] >= Freq_Bands["alpha"][0]) & (peaks0[:,0] <= Freq_Bands["alpha"][1])
+                if sum(in_alpha_band) > 0: # Any alpha peaks?
+                    # Choose the peak with the highest power
+                    max_alpha_idx = np.argmax(peaks0[in_alpha_band,1])
+                    # Save results
+                    PAF_data00[e,c,f] = peaks0[in_alpha_band][max_alpha_idx,:-1]
+                else:
+                    # No alpha peaks
+                    PAF_data00[e,c,f] = [np.nan]*3
+    # Check criterias
+    good_fits_OOF = (r2s00 > OOF_r2_thres) & (OOF_data00[:,:,:,1] > 0) # r^2 > 0.95 and exponent > 0
+    good_fits_PAF = (r2s00 > PAF_r2_thres) & (np.isfinite(PAF_data00[:,:,:,0])) # r^2 > 0.90 and detected peak in alpha band
+    # Save the data or NaN if criterias were not fulfilled
+    for e in range(n_eye_status):
+        for c in range(n_channels):
+            if sum(good_fits_OOF[e,c]) == 0: # no good OOF estimation
+                OOF_data0[e,c] = [np.nan]*2
+            else: # Save OOF associated with greatest r^2 that fulfilled criterias
+                OOF_data0[e,c] = OOF_data00[e,c,np.argmax(r2s00[e,c,good_fits_OOF[e,c]])]
+            if sum(good_fits_PAF[e,c]) == 0: # no good PAF estimation
+                PAF_data0[e,c] = [np.nan]*3
+            else: # Save PAF associated with greatest r^2 that fulfilled criterias
+                PAF_data0[e,c] = PAF_data00[e,c,np.argmax(r2s00[e,c,good_fits_PAF[e,c]])]
+    print("Finished {} out of {} subjects".format(i+1,n_subjects))
+    return i, PAF_data0, OOF_data0
+
+# Get current time
+c_time1 = time.localtime()
+c_time1 = time.strftime("%a %d %b %Y %H:%M:%S", c_time1)
+print(c_time1)
+
+with concurrent.futures.ProcessPoolExecutor() as executor:
+    for i, PAF_result, OOF_result in executor.map(FOOOF_estimation, range(n_subjects)): # Function and arguments
+        PAF_data[i] = PAF_result
+        OOF_data[i] = OOF_result
+
+# Save data
+with open(Feature_savepath+"PAF_data_arr.pkl", "wb") as file:
+    pickle.dump(PAF_data, file)
+with open(Feature_savepath+"OOF_data_arr.pkl", "wb") as file:
+    pickle.dump(OOF_data, file)
+
+# Get current time
+c_time2 = time.localtime()
+c_time2 = time.strftime("%a %d %b %Y %H:%M:%S", c_time2)
+print("Started", c_time1, "\nFinished",c_time2)
+
+# Convert to Pandas dataframe (only keep mean parameter for PAF)
+# The dimensions will each be a column with numbers and the last column will be the actual values
+ori = PAF_data[:,:,:,0]
+arr = np.column_stack(list(map(np.ravel, np.meshgrid(*map(np.arange, ori.shape), indexing="ij"))) + [ori.ravel()])
+PAF_data_df = pd.DataFrame(arr, columns = ["Subject_ID", "Eye_status", "Channel", "Value"])
+# Change from numerical coding to actual values
+
+index_values = [Subject_id,eye_status,ch_names]
+temp_df = PAF_data_df.copy() # make temp df to not sequential overwrite what is changed
+for col in range(len(index_values)):
+    col_name = PAF_data_df.columns[col]
+    for shape in range(ori.shape[col]):
+        temp_df.loc[PAF_data_df.iloc[:,col] == shape,col_name]\
+        = index_values[col][shape]
+PAF_data_df = temp_df # replace original df 
+
+# Add group status
+Group_status = np.array(["CTRL"]*len(PAF_data_df["Subject_ID"]))
+Group_status[np.array([i in cases for i in PAF_data_df["Subject_ID"]])] = "PTSD"
+# Add to dataframe
+PAF_data_df.insert(3, "Group_status", Group_status)
+
+# Global peak alpha
+PAF_data_df_global = PAF_data_df.groupby(["Subject_ID", "Group_status", "Eye_status"]).mean().reset_index() # by default pandas mean skip nan
+# Add dummy variable for re-using plot code
+dummy_variable = ["Global Peak Alpha Frequency"]*PAF_data_df_global.shape[0]
+PAF_data_df_global.insert(3, "Measurement", dummy_variable )
+
+# Regional peak alpha
+# A variable that codes the channels based on A/P localization is also made
+Frontal_chs = ["Fp1", "Fpz", "Fp2", "AFz", "Fz", "F3", "F4", "F7", "F8"]
+Central_chs = ["Cz", "C3", "C4", "T7", "T8", "FT7", "FC3", "FCz", "FC4", "FT8", "TP7", "CP3", "CPz", "CP4", "TP8"]
+Posterior_chs = ["Pz", "P3", "P4", "P7", "P8", "POz", "O1", "O2", "Oz"]
+
+Brain_region = np.array(ch_names, dtype = "<U9")
+Brain_region[np.array([i in Frontal_chs for i in ch_names])] = "Frontal"
+Brain_region[np.array([i in Central_chs for i in ch_names])] = "Central"
+Brain_region[np.array([i in Posterior_chs for i in ch_names])] = "Posterior"
+
+PAF_data_df.insert(4, "Brain_region", list(Brain_region)*int(PAF_data_df.shape[0]/len(Brain_region)))
+
+# Save the dataframes
+PAF_data_df.to_pickle(os.path.join(Feature_savepath,"PAF_data_FOOOF_df.pkl"))
+PAF_data_df_global.to_pickle(os.path.join(Feature_savepath,"PAF_data_FOOOF_global_df.pkl"))
+
+# Convert to Pandas dataframe (only keep exponent parameter for OOF)
+# The dimensions will each be a column with numbers and the last column will be the actual values
+ori = OOF_data[:,:,:,1]
+arr = np.column_stack(list(map(np.ravel, np.meshgrid(*map(np.arange, ori.shape), indexing="ij"))) + [ori.ravel()])
+PAF_data_df = pd.DataFrame(arr, columns = ["Subject_ID", "Eye_status", "Channel", "Value"])
+# Change from numerical coding to actual values
+
+index_values = [Subject_id,eye_status,ch_names]
+temp_df = PAF_data_df.copy() # make temp df to not sequential overwrite what is changed
+for col in range(len(index_values)):
+    col_name = PAF_data_df.columns[col]
+    for shape in range(ori.shape[col]):
+        temp_df.loc[PAF_data_df.iloc[:,col] == shape,col_name]\
+        = index_values[col][shape]
+OOF_data_df = temp_df # replace original df 
+
+# Add group status
+Group_status = np.array(["CTRL"]*len(OOF_data_df["Subject_ID"]))
+Group_status[np.array([i in cases for i in OOF_data_df["Subject_ID"]])] = "PTSD"
+# Add to dataframe
+OOF_data_df.insert(3, "Group_status", Group_status)
+
+# Regional OOF
+OOF_data_df.insert(4, "Brain_region", list(Brain_region)*int(PAF_data_df.shape[0]/len(Brain_region)))
+
+# Save the dataframes
+OOF_data_df.to_pickle(os.path.join(Feature_savepath,"OOF_data_FOOOF_df.pkl"))
+
+# %% Microstate analysis
+# The function takes the data as a numpy array (n_t, n_ch)
+# The data is already re-referenced to common average
+# Variables for the clustering function are extracted
+sfreq = final_epochs[0].info["sfreq"]
+eye_status = list(final_epochs[0].event_id.keys())
+n_eye_status = len(eye_status)
+ch_names = final_epochs[0].info["ch_names"]
+n_channels = len(ch_names)
+locs = np.zeros((n_channels,2)) # xy coordinates of the electrodes
+for c in range(n_channels):
+    locs[c] = final_epochs[0].info["chs"][c]["loc"][0:2]
+
+# The epochs are transformed to numpy arrays
+micro_data = []
+EC_micro_data = []
+EO_micro_data = []
+for i in range(n_subjects):
+    # Transform data to correct shape
+    micro_data.append(final_epochs[i].get_data()) # get data
+    arr_shape = micro_data[i].shape # get shape
+    micro_data[i] = micro_data[i].swapaxes(1,2) # swap ch and time axis
+    micro_data[i] = micro_data[i].reshape(arr_shape[0]*arr_shape[2],arr_shape[1]) # reshape by combining epochs and times
+    # Get indices for eyes open and closed
+    EC_index = final_epochs[i].events[:,2] == 1
+    EO_index = final_epochs[i].events[:,2] == 2
+    # Repeat with 4s * sample frequency to correct for concatenation of times and epochs
+    EC_index = np.repeat(EC_index,4*sfreq)
+    EO_index = np.repeat(EO_index,4*sfreq)
+    # Save data where it is divided into eye status
+    EC_micro_data.append(micro_data[i][EC_index])
+    EO_micro_data.append(micro_data[i][EO_index])
+
+# Global explained variance and Cross-validation criterion is used to determine number of microstates
+# First all data is concatenated to find the optimal number of maps for all data
+micro_data_all = np.vstack(micro_data)
+
+# Determine the number of clusters
+# I use a slightly modified kmeans function which returns the cv_min
+global_gev = []
+cv_criterion = []
+for n_maps in range(2,7):
+    maps, L, gfp_peaks, gev, cv_min = kmeans_return_all(micro_data_all, n_maps)
+    global_gev.append(np.sum(gev))
+    cv_criterion.append(cv_min)
+# Save run results
+cluster_results = np.array([global_gev,cv_criterion])
+np.save("Microstate_n_cluster_test_results.npy", cluster_results) # (gev/cv_crit, n_maps from 2 to 6)
+
+#cluster_results = np.load("Microstate_n_cluster_test_results.npy")
+#global_gev = cluster_results[0,:]
+#cv_criterion = cluster_results[1,:]
+
+# Evaluate best n_maps
+plt.figure()
+plt.plot(np.linspace(2,6,len(cv_criterion)),(cv_criterion/np.sum(cv_criterion)), label="CV Criterion")
+plt.plot(np.linspace(2,6,len(cv_criterion)),(global_gev/np.sum(global_gev)), label="GEV")
+plt.legend()
+plt.ylabel("Normalized to total")
+# The lower CV the better.
+# But the higher GEV the better.
+# Based on the plots and the recommendation by vong Wegner & Laufs 2018
+# we used 4 microstates
+
+# In order to compare between groups, I fix the microstates by clustering on data from both groups
+# Due to instability of maps when running multiple times, I increased n_maps from 4 to 6
+n_maps = 4
+mode = ["aahc", "kmeans", "kmedoids", "pca", "ica"][1]
+
+# K-means is stochastic, thus I run it multiple times in order to find the maps with highest GEV
+# Each K-means is run 5 times and best map is chosen. But I do this 10 times more, so in total 50 times!
+n_run = 10
+# Pre-allocate memory
+microstate_cluster_results = []
+
+# Parallel processing can only be implemented by ensuring different seeds
+# Otherwise the iteration would be the same.
+# However the k-means already use parallel processing so making outer loop with
+# concurrent processes make it use too many processors
+# Get current time
+c_time1 = time.localtime()
+c_time1 = time.strftime("%a %d %b %Y %H:%M:%S", c_time1)
+print(c_time1)
+
+for r in range(n_run):
+    maps = [0]*2
+    m_labels = [0]*2
+    gfp_peaks = [0]*2
+    gev = [0]*2
+    # Eyes closed
+    counter = 0
+    maps_, x_, gfp_peaks_, gev_ = clustering(
+        np.vstack(np.array(EC_micro_data)), sfreq, ch_names, locs, mode, n_maps, doplot=False) # doplot=True is bugged
+    maps[counter] = maps_
+    m_labels[counter] = x_
+    gfp_peaks[counter] = gfp_peaks_
+    gev[counter] = gev_
+    counter += 1
+    # Eyes open
+    maps_, x_, gfp_peaks_, gev_ = clustering(
+        np.vstack(np.array(EO_micro_data)), sfreq, ch_names, locs, mode, n_maps, doplot=False) # doplot=True is bugged
+    maps[counter] = maps_
+    m_labels[counter] = x_
+    gfp_peaks[counter] = gfp_peaks_
+    gev[counter] = gev_
+    counter += 1
+    
+    microstate_cluster_results.append([maps, m_labels, gfp_peaks, gev])
+    print("Finished {} out of {}".format(r+1, n_run))
+
+# Get current time
+c_time2 = time.localtime()
+c_time2 = time.strftime("%a %d %b %Y %H:%M:%S", c_time2)
+print("Started", c_time1, "\nFinished",c_time2)
+
+# Save the results
+with open(Feature_savepath+"Microstate_4_maps_10x5_k_means_results.pkl", "wb") as file:
+    pickle.dump(microstate_cluster_results, file)
+
+# # Load
+# with open(Feature_savepath+"Microstate_4_maps_10x5_k_means_results.pkl", "rb") as file:
+#     microstate_cluster_results = pickle.load(file)
+
+# Find the best maps (Highest GEV across all the K-means clusters)
+EC_total_gevs = np.sum(np.vstack(np.array(microstate_cluster_results)[:,3,0]), axis=1) # (runs, maps/labels/gfp/gev, ec/eo)
+EO_total_gevs = np.sum(np.vstack(np.array(microstate_cluster_results)[:,3,1]), axis=1)
+Best_EC_idx = np.argmax(EC_total_gevs)
+Best_EO_idx = np.argmax(EO_total_gevs)
+# Update the variables for the best maps
+maps = [microstate_cluster_results[Best_EC_idx][0][0],microstate_cluster_results[Best_EO_idx][0][1]]
+m_labels = [microstate_cluster_results[Best_EC_idx][1][0],microstate_cluster_results[Best_EO_idx][1][1]]
+gfp_peaks = [microstate_cluster_results[Best_EC_idx][2][0],microstate_cluster_results[Best_EO_idx][2][1]]
+gev = [microstate_cluster_results[Best_EC_idx][3][0],microstate_cluster_results[Best_EO_idx][3][1]]
+
+# Plot the maps
+plt.style.use('default')
+labels = ["EC", "EO"]
+for i in range(len(labels)):    
+    fig, axarr = plt.subplots(1, n_maps, figsize=(20,5))
+    fig.patch.set_facecolor('white')
+    for imap in range(n_maps):
+        mne.viz.plot_topomap(maps[i][imap,:], pos = final_epochs[0].info, axes = axarr[imap]) # plot
+        axarr[imap].set_title("GEV: {:.2f}".format(gev[i][imap]), fontsize=16, fontweight="bold") # title
+    fig.suptitle("Microstates: {}".format(labels[i]), fontsize=20, fontweight="bold")
+
+# Manual re-order the maps
+# Due the random initiation of K-means this have to be modified every time clusters are made!
+# Assign map labels (e.g. 0, 2, 1, 3)
+order = [0]*2
+order[0] = [3,0,1,2] # EC
+order[1] = [3,1,0,2] # EO
+for i in range(len(order)):
+    maps[i] = maps[i][order[i],:] # re-order maps
+    gev[i] = gev[i][order[i]] # re-order GEV
+    # Make directory to find and replace map labels
+    dic0 = {value:key for key, value in enumerate(order[i])}
+    m_labels[i][:] = [dic0.get(n, n) for n in m_labels[i]] # re-order labels
+
+# The maps seems to be correlated both negatively and positively (see spatial correlation plots)
+# Thus the sign of the map does not really reflect which areas are positive or negative (absolute)
+# But more which areas are different during each state (relatively)
+# I can therefore change the sign of the map for the visualizaiton
+sign_swap = [[1,-1,1,1],[1,1,1,-1]]
+for i in range(len(order)):
+    for m in range(n_maps):
+        maps[i][m] *= sign_swap[i][m]
+
+# Plot the maps and save
+save_path = "/home/glia/Analysis/Figures/Microstates/"
+labels = ["EC", "EO"]
+for i in range(len(labels)):    
+    fig, axarr = plt.subplots(1, n_maps, figsize=(20,5))
+    fig.patch.set_facecolor('white')
+    for imap in range(n_maps):
+        mne.viz.plot_topomap(maps[i][imap,:], pos = final_epochs[0].info, axes = axarr[imap]) # plot
+        axarr[imap].set_title("GEV: {:.2f}".format(gev[i][imap]), fontsize=16, fontweight="bold") # title
+    fig.suptitle("Microstates: {} - Total GEV: {:.2f}".format(labels[i],sum(gev[i])), fontsize=20, fontweight="bold")
+    # Save the figure
+    fig.savefig(os.path.join(save_path,str("Microstates_{}".format(labels[i]) + ".png")))
+
+# Calculate spatial correlation between maps and actual data points (topography)
+# The sign of the map is changed so the correlation is positive
+# By default the code looks for highest spatial correlation (regardless of sign)
+# Thus depending on random initiation point the map might be opposite
+plt.style.use('ggplot')
+def spatial_correlation(data, maps):
+    n_t = data.shape[0]
+    n_ch = data.shape[1]
+    data = data - data.mean(axis=1, keepdims=True)
+
+    # GFP peaks
+    gfp = np.std(data, axis=1)
+    gfp_peaks = locmax(gfp)
+    gfp_values = gfp[gfp_peaks]
+    gfp2 = np.sum(gfp_values**2) # normalizing constant in GEV
+    n_gfp = gfp_peaks.shape[0]
+
+    # Spatial correlation
+    C = np.dot(data, maps.T)
+    C /= (n_ch*np.outer(gfp, np.std(maps, axis=1)))
+    L = np.argmax(C**2, axis=1) # C is squared here which means the maps do no retain information about the sign of the correlation
+    
+    return C
+
+C_EC = spatial_correlation(np.vstack(np.array(EC_micro_data)), maps[0])
+C_EO = spatial_correlation(np.vstack(np.array(EO_micro_data)), maps[1])
+C = [C_EC, C_EO]
+
+# Plot the distribution of spatial correlation for each label and each map
+labels = ["EC", "EO"]
+for i in range(len(labels)):
+    fig, axarr = plt.subplots(n_maps, n_maps, figsize=(16,16))
+    for Lmap in range(n_maps):
+        for Mmap in range(n_maps):
+            sns.distplot(C[i][m_labels[i] == Lmap,Mmap], ax = axarr[Lmap,Mmap])
+            axarr[Lmap,Mmap].set_xlabel("Spatial correlation")
+    plt.suptitle("Distribution of spatial correlation_{}".format(labels[i]), fontsize=20, fontweight="bold")
+    # Add common x and y axis labels by making one big axis
+    fig.add_subplot(111, frameon=False)
+    plt.tick_params(labelcolor="none", top="off", bottom="off", left="off", right="off") # hide tick labels and ticks
+    plt.grid(False) # remove global grid
+    plt.xlabel("Microstate number", labelpad=20)
+    plt.ylabel("Label number", labelpad=10)
+    fig.savefig(os.path.join(save_path,str("Microstates_Spatial_Correlation_Label_State_{}".format(labels[i]) + ".png")))
+
+# Plot the distribution of spatial correlation for all data and each map
+labels = ["EC", "EO"]
+for i in range(len(labels)):
+    fig, axarr = plt.subplots(1,n_maps, figsize=(20,5))
+    for imap in range(n_maps):
+        sns.distplot(C[i][:,imap], ax = axarr[imap])
+        plt.xlabel("Spatial correlation")
+    plt.suptitle("Distribution of spatial correlation", fontsize=20, fontweight="bold")
+    # Add common x and y axis labels by making one big axis
+    fig.add_subplot(111, frameon=False)
+    plt.tick_params(labelcolor="none", top="off", bottom="off", left="off", right="off") # hide tick labels and ticks
+    plt.grid(False) # remove global grid
+    plt.xlabel("Microstate number", labelpad=20)
+    plt.ylabel("Label number")
+
+# Prepare for calculation of transition matrix
+# I modified the function, so it takes the list argument gap_index
+# gap_index should have the indices right before gaps in data
+
+# Gaps: Between dropped epochs, trials (eo/ec) and subjects
+# The between subjects gaps is removed by dividing the data into subjects
+n_trials = 5
+n_epoch_length = final_epochs[0].get_data().shape[2]
+
+micro_labels = []
+micro_subject_EC_idx = [0]
+micro_subject_EO_idx = [0]
+gaps_idx = []
+gaps_trials_idx = []
+for i in range(n_subjects):
+    # Get indices for subject
+    micro_subject_EC_idx.append(micro_subject_EC_idx[i]+EC_micro_data[i].shape[0])
+    temp_EC = m_labels[0][micro_subject_EC_idx[i]:micro_subject_EC_idx[i+1]]
+    # Get labels for subject i EO
+    micro_subject_EO_idx.append(micro_subject_EO_idx[i]+EO_micro_data[i].shape[0])
+    temp_EO = m_labels[1][micro_subject_EO_idx[i]:micro_subject_EO_idx[i+1]]
+    # Save
+    micro_labels.append([temp_EC,temp_EO]) # (subject, eye)
+    
+    # Get indices with gaps
+    # Dropped epochs are first considered
+    # Each epoch last 4s, which correspond to 2000 samples and a trial is 15 epochs - dropped epochs
+    # Get epochs for each condition
+    EC_drop_epochs = Drop_epochs_df.iloc[i,1:][Drop_epochs_df.iloc[i,1:] <= 75].to_numpy()
+    EO_drop_epochs = Drop_epochs_df.iloc[i,1:][(Drop_epochs_df.iloc[i,1:] >= 75)&
+                                            (Drop_epochs_df.iloc[i,1:] <= 150)].to_numpy()
+    # Get indices for the epochs for EC that were dropped and correct for changing index due to drop
+    EC_drop_epochs_gaps_idx = []
+    counter = 0
+    for d in range(len(EC_drop_epochs)):
+        drop_epoch_number = EC_drop_epochs[d]
+        Drop_epoch_idx = (drop_epoch_number-counter)*n_epoch_length # counter subtracted as the drop index is before dropped
+        EC_drop_epochs_gaps_idx.append(Drop_epoch_idx-1) # -1 for point just before gap
+        counter += 1
+    # Negative index might occur if the first epochs were removed. This index is not needed for transition matrix
+    if len(EC_drop_epochs_gaps_idx) > 0:
+        for d in range(len(EC_drop_epochs_gaps_idx)): # check all, e.g. if epoch 0,1,2,3 are dropped then all should be caught
+            if EC_drop_epochs_gaps_idx[0] == -1:
+                EC_drop_epochs_gaps_idx = EC_drop_epochs_gaps_idx[1:len(EC_drop_epochs)]
+    
+    # Get indices for the epochs for EO that were dropped and correct for changing index due to drop
+    EO_drop_epochs_gaps_idx = []
+    counter = 0
+    for d in range(len(EO_drop_epochs)):
+        drop_epoch_number = EO_drop_epochs[d]-75
+        Drop_epoch_idx = (drop_epoch_number-counter)*n_epoch_length # counter subtracted as the drop index is before dropped
+        EO_drop_epochs_gaps_idx.append(Drop_epoch_idx-1) # -1 for point just before gap
+        counter += 1
+    # Negative index might occur if the first epoch was removed. This index is not needed for transition matrix
+    if len(EO_drop_epochs_gaps_idx) > 0:
+        for d in range(len(EO_drop_epochs_gaps_idx)): # check all, e.g. if epoch 0,1,2,3 are dropped then all should be caught
+            if EO_drop_epochs_gaps_idx[0] == -1:
+                EO_drop_epochs_gaps_idx = EO_drop_epochs_gaps_idx[1:len(EO_drop_epochs)]
+    
+    # Gaps between trials
+    Trial_indices = [0, 15, 30, 45, 60, 75] # all the indices for start and end of the 5 trials
+    EC_trial_gaps_idx = []
+    EO_trial_gaps_idx = []
+    counter_EC = 0
+    counter_EO = 0
+    for t in range(len(Trial_indices)-2): # -2 as start and end is not used in transition matrix
+        temp_drop = EC_drop_epochs[(EC_drop_epochs >= Trial_indices[t])&
+                            (EC_drop_epochs < Trial_indices[t+1])]
+        # Correct the trial id for any potential drops within that trial
+        counter_EC += len(temp_drop)
+        trial_idx_corrected_for_drops = 15*(t+1)-counter_EC
+        EC_trial_gaps_idx.append((trial_idx_corrected_for_drops*n_epoch_length)-1) # multiply id with length of epoch and subtract 1
+        
+        temp_drop = EO_drop_epochs[(EO_drop_epochs >= Trial_indices[t]+75)&
+                            (EO_drop_epochs < Trial_indices[t+1]+75)]
+        # Correct the trial id for any potential drops within that trial
+        counter_EO += len(temp_drop)
+        trial_idx_corrected_for_drops = 15*(t+1)-counter_EO
+        EO_trial_gaps_idx.append((trial_idx_corrected_for_drops*n_epoch_length)-1) # multiply id with length of epoch and subtract 1
+    
+    # Concatenate all drop indices
+    gaps_idx.append([np.unique(np.sort(EC_drop_epochs_gaps_idx+EC_trial_gaps_idx)),
+                    np.unique(np.sort(EO_drop_epochs_gaps_idx+EO_trial_gaps_idx))])
+    # Make on with trial gaps only for use in LRTC analysis
+    gaps_trials_idx.append([EC_trial_gaps_idx,EO_trial_gaps_idx])
+
+# Save the gap idx files
+np.save("Gaps_idx.npy",np.array(gaps_idx))
+np.save("Gaps_trials_idx.npy",np.array(gaps_trials_idx))
+
+# %% Calculate microstate features
+# Symbol distribution (also called ratio of time covered RTT)
+# Transition matrix
+# Shannon entropy
+EC_p_hat = p_empirical(m_labels[0], n_maps)
+EO_p_hat = p_empirical(m_labels[1], n_maps)
+# Sanity check: Overall between EC and EO
+
+microstate_time_data = np.zeros((n_subjects,n_eye_status,n_maps))
+microstate_transition_data = np.zeros((n_subjects,n_eye_status,n_maps,n_maps))
+microstate_entropy_data = np.zeros((n_subjects,n_eye_status))
+for i in range(n_subjects):
+    # Calculate ratio of time covered
+    temp_EC_p_hat = p_empirical(micro_labels[i][0], n_maps)
+    temp_EO_p_hat = p_empirical(micro_labels[i][1], n_maps)
+    # Calculate transition matrix
+    temp_EC_T_hat = T_empirical(micro_labels[i][0], n_maps, gaps_idx[i][0])
+    temp_EO_T_hat = T_empirical(micro_labels[i][1], n_maps, gaps_idx[i][1])
+    # Calculate Shannon entropy
+    temp_EC_h_hat = H_1(micro_labels[i][0], n_maps)
+    temp_EO_h_hat = H_1(micro_labels[i][1], n_maps)
+    
+    # Save the data
+    microstate_time_data[i,0,:] = temp_EC_p_hat
+    microstate_time_data[i,1,:] = temp_EO_p_hat
+    microstate_transition_data[i,0,:,:] = temp_EC_T_hat
+    microstate_transition_data[i,1,:,:] = temp_EO_T_hat
+    microstate_entropy_data[i,0] = temp_EC_h_hat/max_entropy(n_maps) # ratio of max entropy
+    microstate_entropy_data[i,1] = temp_EO_h_hat/max_entropy(n_maps) # ratio of max entropy
+
+# Save transition data
+np.save(Feature_savepath+"microstate_transition_data.npy", microstate_transition_data)
+# Convert transition data to dataframe for further processing with other features
+# Transition matrix should be read as probability of row to column
+microstate_transition_data_arr =\
+     microstate_transition_data.reshape((n_subjects,n_eye_status,n_maps*n_maps)) # flatten 4 x 4 matrix to 1D
+transition_info = ["M1->M1", "M1->M2", "M1->M3", "M1->M4",
+                   "M2->M1", "M2->M2", "M2->M3", "M2->M4",
+                   "M3->M1", "M3->M2", "M3->M3", "M3->M4",
+                   "M4->M1", "M4->M2", "M4->M3", "M4->M4"]
+
+arr = np.column_stack(list(map(np.ravel, np.meshgrid(*map(np.arange, microstate_transition_data_arr.shape), indexing="ij"))) + [microstate_transition_data_arr.ravel()])
+microstate_transition_data_df = pd.DataFrame(arr, columns = ["Subject_ID", "Eye_status", "Transition", "Value"])
+# Change from numerical coding to actual values
+eye_status = list(final_epochs[0].event_id.keys())
+
+index_values = [Subject_id,eye_status,transition_info]
+for col in range(len(index_values)):
+    col_name = microstate_transition_data_df.columns[col]
+    for shape in reversed(range(microstate_transition_data_arr.shape[col])): # notice this is the shape of original numpy array. Not shape of DF
+        microstate_transition_data_df.loc[microstate_transition_data_df.iloc[:,col] == shape,col_name]\
+        = index_values[col][shape]
+
+# Add group status
+Group_status = np.array(["CTRL"]*len(microstate_transition_data_df["Subject_ID"]))
+Group_status[np.array([i in cases for i in microstate_transition_data_df["Subject_ID"]])] = "PTSD"
+# Add to dataframe
+microstate_transition_data_df.insert(2, "Group_status", Group_status)
+
+# Save df
+microstate_transition_data_df.to_pickle(os.path.join(Feature_savepath,"microstate_transition_data_df.pkl"))
+
+# Convert time covered data to Pandas dataframe
+# The dimensions will each be a column with numbers and the last column will be the actual values
+arr = np.column_stack(list(map(np.ravel, np.meshgrid(*map(np.arange, microstate_time_data.shape), indexing="ij"))) + [microstate_time_data.ravel()])
+microstate_time_df = pd.DataFrame(arr, columns = ["Subject_ID", "Eye_status", "Microstate", "Value"])
+# Change from numerical coding to actual values
+eye_status = list(final_epochs[0].event_id.keys())
+microstates = [1,2,3,4]
+
+index_values = [Subject_id,eye_status,microstates]
+for col in range(len(index_values)):
+    col_name = microstate_time_df.columns[col]
+    for shape in reversed(range(microstate_time_data.shape[col])): # notice this is the shape of original numpy array. Not shape of DF
+        microstate_time_df.loc[microstate_time_df.iloc[:,col] == shape,col_name]\
+        = index_values[col][shape]
+# Reversed in inner loop is used to avoid sequencial data being overwritten.
+# E.g. if 0 is renamed to 1, then the next loop all 1's will be renamed to 2
+
+# Add group status
+Group_status = np.array(["CTRL"]*len(microstate_time_df["Subject_ID"]))
+Group_status[np.array([i in cases for i in microstate_time_df["Subject_ID"]])] = "PTSD"
+# Add to dataframe
+microstate_time_df.insert(2, "Group_status", Group_status)
+
+# Save df
+microstate_time_df.to_pickle(os.path.join(Feature_savepath,"microstate_time_df.pkl"))
+
+# Transition data - mean
+# Get index for groups
+PTSD_idx = np.array([i in cases for i in Subject_id])
+CTRL_idx = np.array([not i in cases for i in Subject_id])
+n_groups = 2
+
+microstate_transition_data_mean = np.zeros((n_groups,n_eye_status,n_maps,n_maps))
+microstate_transition_data_mean[0,:,:,:] = np.mean(microstate_transition_data[PTSD_idx,:,:,:], axis=0)
+microstate_transition_data_mean[1,:,:,:] = np.mean(microstate_transition_data[CTRL_idx,:,:,:], axis=0)
+
+# Convert entropy data to Pandas dataframe
+# The dimensions will each be a column with numbers and the last column will be the actual values
+arr = np.column_stack(list(map(np.ravel, np.meshgrid(*map(np.arange, microstate_entropy_data.shape), indexing="ij"))) + [microstate_entropy_data.ravel()])
+microstate_entropy_df = pd.DataFrame(arr, columns = ["Subject_ID", "Eye_status", "Value"])
+# Change from numerical coding to actual values
+eye_status = list(final_epochs[0].event_id.keys())
+
+index_values = [Subject_id,eye_status]
+for col in range(len(index_values)):
+    col_name = microstate_entropy_df.columns[col]
+    for shape in reversed(range(microstate_entropy_data.shape[col])): # notice this is the shape of original numpy array. Not shape of DF
+        microstate_entropy_df.loc[microstate_entropy_df.iloc[:,col] == shape,col_name]\
+        = index_values[col][shape]
+# Reversed in inner loop is used to avoid sequencial data being overwritten.
+# E.g. if 0 is renamed to 1, then the next loop all 1's will be renamed to 2
+
+# Add group status
+Group_status = np.array(["CTRL"]*len(microstate_entropy_df["Subject_ID"]))
+Group_status[np.array([i in cases for i in microstate_entropy_df["Subject_ID"]])] = "PTSD"
+# Add to dataframe
+microstate_entropy_df.insert(2, "Group_status", Group_status)
+# Add dummy variable for re-using plot code
+dummy_variable = ["Entropy"]*len(Group_status)
+microstate_entropy_df.insert(3, "Measurement", dummy_variable)
+
+# Save df
+microstate_entropy_df.to_pickle(os.path.join(Feature_savepath,"microstate_entropy_df.pkl"))
+
+# %% Long-range temporal correlations (LRTC)
+"""
+See Hardstone et al, 2012
+Hurst exponent estimation steps:
+    1. Preprocess
+    2. Band-pass filter for frequency band of interest
+    3. Hilbert transform to obtain amplitude envelope
+    4. Perform DFA
+        4.1 Compute cumulative sum of time series to create signal profile
+        4.2 Define set of window sizes (see below)
+        4.3 Remove the linear trend using least-squares for each window
+        4.4 Calculate standard deviation for each window and take the mean
+        4.5 Plot fluctuation function (Standard deviation) as function
+            for all window sizes, on double logarithmic scale
+        4.6 The DFA exponent alpha correspond to Hurst exponent
+            f(L) = sd = L^alpha (with alpha as linear coefficient in log plot)
+
+If 0 < alpha < 0.5: The process exhibits anti-correlations
+If 0.5 < alpha < 1: The process exhibits positive correlations
+If alpha = 0.5: The process is indistinguishable from a random process
+If 1.0 < alpha < 2.0: The process is non-stationary. H = alpha - 1
+
+Window sizes should be equally spaced on a logarithmic scale
+Sizes should be at least 4 samples and up to 10% of total signal length
+Filters can influence neighboring samples, thus filters should be tested
+on white noise to estimate window sizes that are unaffected by filters
+
+filter_length=str(2*1/fmin)+"s" # cannot be used with default transition bandwidth
+
+"""
+# From simulations with white noise I determined window size thresholds for the 5 frequency bands:
+thresholds = [7,7,7,6.5,6.5]
+# And their corresponding log step sizes
+with open("LRTC_log_win_sizes.pkl", "rb") as filehandle:
+    log_win_sizes = pickle.load(filehandle)
+
+# Variables for the the different conditions
+# Sampling frequency
+sfreq = final_epochs[0].info["sfreq"]
+# Channels
+ch_names = final_epochs[0].info["ch_names"]
+n_channels = len(ch_names)
+# Frequency
+Freq_Bands = {"delta": [1.25, 4.0],
+              "theta": [4.0, 8.0],
+              "alpha": [8.0, 13.0],
+              "beta": [13.0, 30.0],
+              "gamma": [30.0, 49.0]}
+n_freq_bands = len(Freq_Bands)
+# Eye status
+eye_status = list(final_epochs[0].event_id.keys())
+n_eye_status = len(eye_status)
+
+### Estimating Hurst exponent for the data
+# The data should be re-referenced to common average (Already done)
+
+# Data are transformed to numpy arrays
+# Then divided into EO and EC and further into each of the 5 trials
+# So DFA is estimated for each trial separately, which was concluded from simulations
+gaps_trials_idx = np.load("Gaps_trials_idx.npy") # re-used from microstate analysis
+n_trials = 5
+
+H_data = []
+for i in range(n_subjects):
+    # Transform data to correct shape
+    temp_arr = final_epochs[i].get_data() # get data
+    arr_shape = temp_arr.shape # get shape
+    temp_arr = temp_arr.swapaxes(1,2) # swap ch and time axis
+    temp_arr = temp_arr.reshape(arr_shape[0]*arr_shape[2],arr_shape[1]) # reshape by combining epochs and times
+    # Get indices for eyes open and closed
+    EC_index = final_epochs[i].events[:,2] == 1
+    EO_index = final_epochs[i].events[:,2] == 2
+    # Repeat with 4s * sample frequency to correct for concatenation of times and epochs
+    EC_index = np.repeat(EC_index,4*sfreq)
+    EO_index = np.repeat(EO_index,4*sfreq)
+    # Divide into eye status
+    EC_data = temp_arr[EC_index]
+    EO_data = temp_arr[EO_index]
+    # Divide into trials
+    EC_gap_idx = np.array([0]+list(gaps_trials_idx[i,0])+[len(EC_data)])
+    EO_gap_idx = np.array([0]+list(gaps_trials_idx[i,1])+[len(EO_data)])
+    
+    EC_trial_data = []
+    EO_trial_data = []
+    for t in range(n_trials):
+        EC_trial_data.append(EC_data[EC_gap_idx[t]:EC_gap_idx[t+1]])
+        EO_trial_data.append(EO_data[EO_gap_idx[t]:EO_gap_idx[t+1]])
+        
+    # Save data
+    H_data.append([EC_trial_data,EO_trial_data]) # output [subject][eye][trial][time,ch]
+
+# Calculate H for each subject, eye status, trial, freq and channel
+H_arr = np.zeros((n_subjects,n_eye_status,n_trials,n_channels,n_freq_bands))
+w_len = [len(ele) for ele in log_win_sizes]
+DFA_arr = np.empty((n_subjects,n_eye_status,n_trials,n_channels,n_freq_bands,2,np.max(w_len)))
+DFA_arr[:] = np.nan
+
+# Get current time
+c_time1 = time.localtime()
+c_time1 = time.strftime("%a %d %b %Y %H:%M:%S", c_time1)
+print("Started",c_time1)
+
+# Nolds are already using all cores so multiprocessing with make it slower
+# Warning occurs when R2 is estimated during detrending - but R2 is not used
+warnings.simplefilter("ignore")
+for i in range(n_subjects):
+    # Pre-allocate memory
+    DFA_temp = np.empty((n_eye_status,n_trials,n_channels,n_freq_bands,2,np.max(w_len)))
+    DFA_temp[:] = np.nan
+    H_temp = np.empty((n_eye_status,n_trials,n_channels,n_freq_bands))
+    for e in range(n_eye_status):
+        for trial in range(n_trials):
+            for c in range(n_channels):
+                # Get the data
+                signal = H_data[i][e][trial][:,c]
+                
+                counter = 0 # prepare counter
+                for fmin, fmax in Freq_Bands.values():
+                    # Filter for each freq band
+                    signal_filtered = mne.filter.filter_data(signal, sfreq=sfreq, verbose=0,
+                                                  l_freq=fmin, h_freq=fmax)
+                    # Hilbert transform
+                    analytic_signal = scipy.signal.hilbert(signal_filtered)
+                    # Get Amplitude envelope
+                    # np.abs is the same as np.linalg.norm, i.e. the length for complex input which is the amplitude
+                    ampltude_envelope = np.abs(analytic_signal)
+                    # Perform DFA using predefined window sizes from simulation
+                    a, dfa_data = nolds.dfa(ampltude_envelope,
+                                            nvals=np.exp(log_win_sizes[counter]).astype("int"),
+                                            debug_data=True)
+                    # Save DFA results
+                    DFA_temp[e,trial,c,counter,:,0:w_len[counter]] = dfa_data[0:2]
+                    H_temp[e,trial,c,counter] = a
+                    # Update counter
+                    counter += 1
+
+    # Print run status
+    print("Finished {} out of {}".format(i+1,n_subjects))
+    # Save the results
+    H_arr[i] = H_temp
+    DFA_arr[i] = DFA_temp
+
+warnings.simplefilter("default")
+
+# Get current time
+c_time2 = time.localtime()
+c_time2 = time.strftime("%a %d %b %Y %H:%M:%S", c_time2)
+print("Started", c_time1, "\nCurrent Time",c_time2)
+
+# Save the DFA analysis data 
+np.save(Feature_savepath+"DFA_arr.npy", DFA_arr)
+np.save(Feature_savepath+"H_arr.npy", H_arr)
+
+# Load
+DFA_arr = np.load(Feature_savepath+"DFA_arr.npy")
+H_arr = np.load(Feature_savepath+"H_arr.npy")
+
+# Average the Hurst Exponent across trials
+H_arr = np.mean(H_arr, axis=2)
+
+# Convert to Pandas dataframe (Hurst exponent)
+# The dimensions will each be a column with numbers and the last column will be the actual values
+arr = np.column_stack(list(map(np.ravel, np.meshgrid(*map(np.arange, H_arr.shape), indexing="ij"))) + [H_arr.ravel()])
+H_data_df = pd.DataFrame(arr, columns = ["Subject_ID", "Eye_status", "Channel", "Freq_band", "Value"])
+# Change from numerical coding to actual values
+eye_status = list(final_epochs[0].event_id.keys())
+ch_name = final_epochs[0].info["ch_names"]
+
+index_values = [Subject_id,eye_status,ch_name,list(Freq_Bands.keys())]
+for col in range(len(index_values)):
+    col_name = H_data_df.columns[col]
+    for shape in range(H_arr.shape[col]): # notice this is the shape of original numpy array. Not shape of DF
+        H_data_df.loc[H_data_df.iloc[:,col] == shape,col_name]\
+        = index_values[col][shape]
+
+# Add group status
+Group_status = np.array(["CTRL"]*len(H_data_df["Subject_ID"]))
+Group_status[np.array([i in cases for i in H_data_df["Subject_ID"]])] = "PTSD"
+# Add to dataframe
+H_data_df.insert(2, "Group_status", Group_status)
+
+# Fix Freq_band categorical order
+H_data_df["Freq_band"] = H_data_df["Freq_band"].astype("category").\
+            cat.reorder_categories(list(Freq_Bands.keys()), ordered=True)
+
+# Global Hurst exponent
+H_data_df_global = H_data_df.groupby(["Subject_ID", "Eye_status", "Freq_band"]).mean().reset_index() # by default pandas mean skip nan
+# Add group status (cannot use group_by as each subject only have 1 group, not both)
+Group_status = np.array(["CTRL"]*len(H_data_df_global["Subject_ID"]))
+Group_status[np.array([i in cases for i in H_data_df_global["Subject_ID"]])] = "PTSD"
+# Add to dataframe
+H_data_df_global.insert(2, "Group_status", Group_status)
+# Add dummy variable for re-using plot code
+dummy_variable = ["Global Hurst Exponent"]*H_data_df_global.shape[0]
+H_data_df_global.insert(3, "Measurement", dummy_variable )
+
+# Save the data
+H_data_df.to_pickle(os.path.join(Feature_savepath,"H_data_df.pkl"))
+H_data_df_global.to_pickle(os.path.join(Feature_savepath,"H_data_global_df.pkl"))
+
+# %% Source localization of sensor data
+# Using non-interpolated channels
+# Even interpolated channels during preprocessing and visual inspection
+# are dropped
+
+# Prepare epochs for estimation of source connectivity
+source_epochs = [0]*n_subjects
+for i in range(n_subjects):
+    source_epochs[i] = final_epochs[i].copy()
+
+### Make forward solutions
+# A forward solution is first made for all individuals with no dropped channels
+# Afterwards individual forward solutions are made for subjects with bad
+# channels that were interpolated in preprocessing and these are dropped
+# First forward operator is computed using a template MRI for each dataset
+fs_dir = "/home/glia/MNE-fsaverage-data/fsaverage"
+subjects_dir = os.path.dirname(fs_dir)
+trans = "fsaverage"
+src = os.path.join(fs_dir, "bem", "fsaverage-ico-5-src.fif")
+bem = os.path.join(fs_dir, "bem", "fsaverage-5120-5120-5120-bem-sol.fif")
+
+# Read the template sourcespace
+sourcespace = mne.read_source_spaces(src)
+
+temp_idx = 0 # Index with subject that had no bad channels
+subject_eeg = source_epochs[temp_idx].copy()
+subject_eeg.set_eeg_reference(projection=True) # needed for inverse modelling
+# Make forward solution
+fwd = mne.make_forward_solution(subject_eeg.info, trans=trans, src=src,
+                            bem=bem, eeg=True, mindist=5.0, n_jobs=1)
+# Save forward operator
+fname_fwd = "./Source_fwd/fsaverage-fwd.fif"
+mne.write_forward_solution(fname_fwd, fwd, overwrite=True)
+
+# A specific forward solution is also made for each subject with bad channels
+with open("./Preprocessing/bad_ch.pkl", "rb") as file:
+   bad_ch = pickle.load(file)
+
+All_bad_ch = bad_ch
+All_drop_epochs = dropped_epochs_df
+All_dropped_ch = []
+
+Bad_ch_idx = [idx for idx, item in enumerate(All_bad_ch) if item != 0]
+Bad_ch_subjects = All_drop_epochs["Subject_ID"][Bad_ch_idx]
+# For each subject with bad channels, drop the channels and make forward operator
+for n in range(len(Bad_ch_subjects)):
+    Subject = Bad_ch_subjects.iloc[n]
+    try:
+        Subject_idx = Subject_id.index(Subject)
+        # Get unique bad channels
+        Bad_ch0 = All_bad_ch[Bad_ch_idx[n]]
+        Bad_ch1 = []
+        for i2 in range(len(Bad_ch0)):
+            if type(Bad_ch0[i2]) == list:
+                for i3 in range(len(Bad_ch0[i2])):
+                    Bad_ch1.append(Bad_ch0[i2][i3])
+            elif type(Bad_ch0[i2]) == str:
+                Bad_ch1.append(Bad_ch0[i2])
+        Bad_ch1 = np.unique(Bad_ch1)
+        # Drop the bad channels
+        source_epochs[Subject_idx].drop_channels(Bad_ch1)
+        # Save the overview of dropped channels
+        All_dropped_ch.append([Subject,Subject_idx,Bad_ch1])
+        # Make forward operator
+        subject_eeg = source_epochs[Subject_idx].copy()
+        subject_eeg.set_eeg_reference(projection=True) # needed for inverse modelling
+        # Make forward solution
+        fwd = mne.make_forward_solution(subject_eeg.info, trans=trans, src=src,
+                                    bem=bem, eeg=True, mindist=5.0, n_jobs=1)
+        # Save forward operator
+        fname_fwd = "./Source_fwd/fsaverage_{}-fwd.fif".format(Subject)
+        mne.write_forward_solution(fname_fwd, fwd, overwrite=True)
+    except:
+        print(Subject,"was already dropped")
+
+with open("./Preprocessing/All_datasets_bad_ch.pkl", "wb") as filehandle:
+    pickle.dump(All_dropped_ch, filehandle)
+
+
+# %% Load forward operators
+# Re-use for all subjects without dropped channels
+fname_fwd = "./Source_fwd/fsaverage-fwd.fif"
+fwd = mne.read_forward_solution(fname_fwd)
+
+fwd_list = [fwd]*n_subjects
+
+# Use specific forward solutions for subjects with dropped channels
+with open("./Preprocessing/All_datasets_bad_ch.pkl", "rb") as file:
+   All_dropped_ch = pickle.load(file)
+
+for i in range(len(All_dropped_ch)):
+    Subject = All_dropped_ch[i][0]
+    Subject_idx = All_dropped_ch[i][1]
+    fname_fwd = "./Source_fwd/fsaverage_{}-fwd.fif".format(Subject)
+    fwd = mne.read_forward_solution(fname_fwd)
+    fwd_list[Subject_idx] = fwd
+
+# Check the correct number of channels are present in fwd
+random_point = int(np.random.randint(0,len(All_dropped_ch)-1,1))
+assert len(fwds[All_dropped_ch[random_point][1]].ch_names) == source_epochs[All_dropped_ch[random_point][1]].info["nchan"]
+
+# %% Make parcellation
+# After mapping to source space, I end up with 20484 vertices
+# but I wanted to map to fewer sources and not many more
+# Thus I need to perform parcellation
+# Get labels for FreeSurfer "aparc" cortical parcellation (example with 74 labels/hemi - Destriuex)
+labels_aparc = mne.read_labels_from_annot("fsaverage", parc="aparc.a2009s",
+                                    subjects_dir=subjects_dir)
+labels_aparc = labels_aparc[:-2] # remove unknowns
+
+labels_aparc_names = [label.name for label in labels_aparc]
+
+# Manually adding the 31 ROIs (14-lh/rh + 3 in midline) from Toll et al, 2020
+# Making fuction to take subset of a label
+def label_subset(label, subset, name="ROI_name"):
+    label_subset = mne.Label(label.vertices[subset], label.pos[subset,:],
+                         label.values[subset], label.hemi,
+                         name = "{}-{}".format(name,label.hemi),
+                         subject = label.subject, color = None)
+    return label_subset
+
+### Visual area 1 (V1 and somatosensory cortex BA1-3)
+label_filenames = ["lh.V1.label", "rh.V1.label",
+                   "lh.BA1.label", "rh.BA1.label",
+                   "lh.BA2.label", "rh.BA2.label",
+                   "lh.BA3a.label", "rh.BA3a.label",
+                   "lh.BA3b.label", "rh.BA3b.label"]
+labels0 = [0]*len(label_filenames)
+for i, filename in enumerate(label_filenames):
+    labels0[i] = mne.read_label(os.path.join(fs_dir, "label", filename), subject="fsaverage")
+# Add V1 to final label variable
+labels = labels0[:2]
+# Rename to remove redundant hemi information
+labels[0].name = "V1-{}".format(labels[0].hemi)
+labels[1].name = "V1-{}".format(labels[1].hemi)
+# Assign a color
+labels[0].color = matplotlib.colors.to_rgba("salmon")
+labels[1].color = matplotlib.colors.to_rgba("salmon")
+# Combine Brodmann Areas for SMC. Only use vertices ones to avoid duplication error
+SMC_labels = labels0[2:]
+for hem in range(2):
+    SMC_p1 = SMC_labels[hem]
+    for i in range(1,len(SMC_labels)//2):
+        SMC_p2 = SMC_labels[hem+2*i]
+        p2_idx = np.isin(SMC_p2.vertices, SMC_p1.vertices, invert=True)
+        SMC_p21 = label_subset(SMC_p2, p2_idx, "SMC")
+        SMC_p1 = SMC_p1.__add__(SMC_p21)
+    SMC_p1.name = SMC_p21.name
+    # Assign a color
+    SMC_p1.color = matplotlib.colors.to_rgba("orange")
+    labels.append(SMC_p1)
+
+### Inferior frontal junction
+# Located at junction between inferior frontal and inferior precentral sulcus
+label_aparc_names0 = ["S_front_inf","S_precentral-inf-part"]
+temp_labels = []
+for i in range(len(label_aparc_names0)):
+    labels_aparc_idx = [labels_aparc_names.index(l) for l in labels_aparc_names if l.startswith(label_aparc_names0[i])]
+    for i2 in range(len(labels_aparc_idx)):
+        temp_labels.append(labels_aparc[labels_aparc_idx[i2]].copy())
+
+pos1 = temp_labels[0].pos
+pos2 = temp_labels[2].pos
+distm = scipy.spatial.distance.cdist(pos1,pos2)
+# Find the closest points between the 2 ROIs
+l1_idx = np.unique(np.where(distm<np.quantile(distm, 0.001))[0]) # q chosen to correspond to around 10% of ROI
+l2_idx = np.unique(np.where(distm<np.quantile(distm, 0.0005))[1]) # q chosen to correspond to around 10% of ROI
+
+IFJ_label_p1 = label_subset(temp_labels[0], l1_idx, "IFJ")
+IFJ_label_p2 = label_subset(temp_labels[2], l2_idx, "IFJ")
+# Combine the 2 parts
+IFJ_label = IFJ_label_p1.__add__(IFJ_label_p2)
+IFJ_label.name = IFJ_label_p1.name
+# Assign a color
+IFJ_label.color = matplotlib.colors.to_rgba("chartreuse")
+# Append to final list
+labels.append(IFJ_label)
+
+# Do the same for the right hemisphere
+pos1 = temp_labels[1].pos
+pos2 = temp_labels[3].pos
+distm = scipy.spatial.distance.cdist(pos1,pos2)
+# Find the closest points between the 2 ROIs
+l1_idx = np.unique(np.where(distm<np.quantile(distm, 0.00075))[0]) # q chosen to correspond to around 10% of ROI
+l2_idx = np.unique(np.where(distm<np.quantile(distm, 0.0005))[1]) # q chosen to correspond to around 10% of ROI
+IFJ_label_p1 = label_subset(temp_labels[1], l1_idx, "IFJ")
+IFJ_label_p2 = label_subset(temp_labels[3], l2_idx, "IFJ")
+# Combine the 2 parts
+IFJ_label = IFJ_label_p1.__add__(IFJ_label_p2)
+IFJ_label.name = IFJ_label_p1.name
+# Assign a color
+IFJ_label.color = matplotlib.colors.to_rgba("chartreuse")
+# Append to final list
+labels.append(IFJ_label)
+
+### Intraparietal sulcus
+label_aparc_names0 = ["S_intrapariet_and_P_trans"]
+labels_aparc_idx = [labels_aparc_names.index(l) for l in labels_aparc_names if l.startswith(label_aparc_names0[0])]
+for i in range(len(labels_aparc_idx)):
+    labels.append(labels_aparc[labels_aparc_idx[i]].copy())
+    labels[-1].name = "IPS-{}".format(labels[-1].hemi)
+
+### Frontal eye field as intersection between middle frontal gyrus and precentral gyrus
+label_aparc_names0 = ["G_front_middle","G_precentral"]
+temp_labels = []
+for i in range(len(label_aparc_names0)):
+    labels_aparc_idx = [labels_aparc_names.index(l) for l in labels_aparc_names if l.startswith(label_aparc_names0[i])]
+    for i2 in range(len(labels_aparc_idx)):
+        temp_labels.append(labels_aparc[labels_aparc_idx[i2]].copy())
+
+# Take 10% of middle frontal gyrus closest to precentral gyrus (most posterior)
+temp_label0 = temp_labels[0]
+G_fm_y = temp_label0.pos[:,1]
+thres_G_fm_y = np.sort(G_fm_y)[len(G_fm_y)//10]
+idx_p1 = np.where(G_fm_y<thres_G_fm_y)[0]
+FEF_label_p1 = label_subset(temp_label0, idx_p1, "FEF")
+# Take 10% closest for precentral gyrus (most anterior)
+temp_label0 = temp_labels[2]
+# I cannot only use y (anterior/posterior) but also need to restrict z-position
+G_pre_cen_z = temp_label0.pos[:,2]
+thres_G_pre_cen_z = 0.04 # visually inspected threshold
+G_pre_cen_y = temp_label0.pos[:,1]
+thres_G_pre_cen_y = np.sort(G_pre_cen_y[G_pre_cen_z>thres_G_pre_cen_z])[-len(G_pre_cen_y)//10] # notice - for anterior
+idx_p2 = np.where((G_pre_cen_y>thres_G_pre_cen_y) & (G_pre_cen_z>thres_G_pre_cen_z))[0]
+FEF_label_p2 = label_subset(temp_label0, idx_p2, "FEF")
+# Combine the 2 parts
+FEF_label = FEF_label_p1.__add__(FEF_label_p2)
+FEF_label.name = FEF_label_p1.name
+# Assign a color
+FEF_label.color = matplotlib.colors.to_rgba("aqua")
+# Append to final list
+labels.append(FEF_label)
+
+# Do the same for the right hemisphere
+temp_label0 = temp_labels[1]
+G_fm_y = temp_label0.pos[:,1]
+thres_G_fm_y = np.sort(G_fm_y)[len(G_fm_y)//10]
+idx_p1 = np.where(G_fm_y<thres_G_fm_y)[0]
+FEF_label_p1 = label_subset(temp_label0, idx_p1, "FEF")
+
+temp_label0 = temp_labels[3]
+G_pre_cen_z = temp_label0.pos[:,2]
+thres_G_pre_cen_z = 0.04 # visually inspected threshold
+G_pre_cen_y = temp_label0.pos[:,1]
+thres_G_pre_cen_y = np.sort(G_pre_cen_y[G_pre_cen_z>thres_G_pre_cen_z])[-len(G_pre_cen_y)//10] # notice - for anterior
+idx_p2 = np.where((G_pre_cen_y>thres_G_pre_cen_y) & (G_pre_cen_z>thres_G_pre_cen_z))[0]
+FEF_label_p2 = label_subset(temp_label0, idx_p2, "FEF")
+# Combine the 2 parts
+FEF_label = FEF_label_p1.__add__(FEF_label_p2)
+FEF_label.name = FEF_label_p1.name
+# Assign a color
+FEF_label.color = matplotlib.colors.to_rgba("aqua")
+# Append to final list
+labels.append(FEF_label)
+
+### Supplementary eye fields
+# Located at caudal end of frontal gyrus and upper part of paracentral sulcus
+label_aparc_names0 = ["G_and_S_paracentral","G_front_sup"]
+temp_labels = []
+for i in range(len(label_aparc_names0)):
+    labels_aparc_idx = [labels_aparc_names.index(l) for l in labels_aparc_names if l.startswith(label_aparc_names0[i])]
+    for i2 in range(len(labels_aparc_idx)):
+        temp_labels.append(labels_aparc[labels_aparc_idx[i2]].copy())
+
+pos1 = temp_labels[0].pos
+pos2 = temp_labels[2].pos
+distm = scipy.spatial.distance.cdist(pos1,pos2)
+# Find the closest points between the 2 ROIs
+l1_idx = np.unique(np.where(distm<np.quantile(distm, 0.0005))[0]) # q chosen to correspond to around 15% of ROI
+l2_idx = np.unique(np.where(distm<np.quantile(distm, 0.005))[1]) # q chosen to correspond to around 10% of ROI
+# Notice that superior frontal gyrus is around 4 times bigger than paracentral
+len(l1_idx)/pos1.shape[0]
+len(l2_idx)/pos2.shape[0]
+# Only use upper part
+z_threshold = 0.06 # visually inspected
+l1_idx = l1_idx[pos1[l1_idx,2] > z_threshold]
+l2_idx = l2_idx[pos2[l2_idx,2] > z_threshold]
+
+SEF_label_p1 = label_subset(temp_labels[0], l1_idx, "SEF")
+SEF_label_p2 = label_subset(temp_labels[2], l2_idx, "SEF")
+# Combine the 2 parts
+SEF_label = SEF_label_p1.__add__(SEF_label_p2)
+SEF_label.name = SEF_label_p1.name
+# Assign a color
+SEF_label.color = matplotlib.colors.to_rgba("royalblue")
+# Append to final list
+labels.append(SEF_label)
+
+# Do the same for the right hemisphere
+pos1 = temp_labels[1].pos
+pos2 = temp_labels[3].pos
+distm = scipy.spatial.distance.cdist(pos1,pos2)
+# Find the closest points between the 2 ROIs
+l1_idx = np.unique(np.where(distm<np.quantile(distm, 0.0005))[0]) # q chosen to correspond to around 15% of ROI
+l2_idx = np.unique(np.where(distm<np.quantile(distm, 0.005))[1]) # q chosen to correspond to around 10% of ROI
+# Notice that superior frontal gyrus is around 4 times bigger than paracentral
+len(l1_idx)/pos1.shape[0]
+len(l2_idx)/pos2.shape[0]
+# Only use upper part
+z_threshold = 0.06 # visually inspected
+l1_idx = l1_idx[pos1[l1_idx,2] > z_threshold]
+l2_idx = l2_idx[pos2[l2_idx,2] > z_threshold]
+
+SEF_label_p1 = label_subset(temp_labels[1], l1_idx, "SEF")
+SEF_label_p2 = label_subset(temp_labels[3], l2_idx, "SEF")
+# Combine the 2 parts
+SEF_label = SEF_label_p1.__add__(SEF_label_p2)
+SEF_label.name = SEF_label_p1.name
+# Assign a color
+SEF_label.color = matplotlib.colors.to_rgba("royalblue")
+# Append to final list
+labels.append(SEF_label)
+
+### Posterior cingulate cortex
+label_aparc_names0 = ["G_cingul-Post-dorsal", "G_cingul-Post-ventral"]
+temp_labels = []
+for i in range(len(label_aparc_names0)):
+    labels_aparc_idx = [labels_aparc_names.index(l) for l in labels_aparc_names if l.startswith(label_aparc_names0[i])]
+    for i2 in range(len(labels_aparc_idx)):
+        temp_labels.append(labels_aparc[labels_aparc_idx[i2]].copy())
+labels0 = []
+for hem in range(2):
+    PCC_p1 = temp_labels[hem]
+    for i in range(1,len(temp_labels)//2):
+        PCC_p2 = temp_labels[hem+2*i]
+        PCC_p1 = PCC_p1.__add__(PCC_p2)
+    PCC_p1.name = "PCC-{}".format(PCC_p1.hemi)
+    labels0.append(PCC_p1)
+# Combine the 2 hemisphere in 1 label
+labels.append(labels0[0].__add__(labels0[1]))
+
+### Medial prefrontal cortex
+# From their schematic it looks like rostral 1/4 of superior frontal gyrus
+label_aparc_names0 = ["G_front_sup"]
+temp_labels = []
+for i in range(len(label_aparc_names0)):
+    labels_aparc_idx = [labels_aparc_names.index(l) for l in labels_aparc_names if l.startswith(label_aparc_names0[i])]
+    for i2 in range(len(labels_aparc_idx)):
+        temp_labels0 = labels_aparc[labels_aparc_idx[i2]].copy()
+        temp_labels0 = temp_labels0.split(4, subjects_dir=subjects_dir)[3]
+        temp_labels0.name = "mPFC-{}".format(temp_labels0.hemi)
+        temp_labels.append(temp_labels0)
+# Combine the 2 hemisphere in 1 label
+labels.append(temp_labels[0].__add__(temp_labels[1]))
+
+### Angular gyrus
+label_aparc_names0 = ["G_pariet_inf-Angular"]
+for i in range(len(label_aparc_names0)):
+    labels_aparc_idx = [labels_aparc_names.index(l) for l in labels_aparc_names if l.startswith(label_aparc_names0[i])]
+    for i2 in range(len(labels_aparc_idx)):
+        temp_labels = labels_aparc[labels_aparc_idx[i2]].copy()
+        temp_labels.name = "ANG-{}".format(temp_labels.hemi)
+        labels.append(temp_labels)
+
+### Posterior middle frontal gyrus
+label_aparc_names0 = ["G_front_middle"]
+for i in range(len(label_aparc_names0)):
+    labels_aparc_idx = [labels_aparc_names.index(l) for l in labels_aparc_names if l.startswith(label_aparc_names0[i])]
+    for i2 in range(len(labels_aparc_idx)):
+        temp_labels = labels_aparc[labels_aparc_idx[i2]].copy()
+        temp_labels = temp_labels.split(2, subjects_dir=subjects_dir)[0]
+        temp_labels.name = "PMFG-{}".format(temp_labels.hemi)
+        labels.append(temp_labels)
+
+### Inferior parietal lobule
+# From their parcellation figure seems to be rostral angular gyrus and posterior supramarginal gyrus
+label_aparc_names0 = ["G_pariet_inf-Angular","G_pariet_inf-Supramar"]
+temp_labels = []
+for i in range(len(label_aparc_names0)):
+    labels_aparc_idx = [labels_aparc_names.index(l) for l in labels_aparc_names if l.startswith(label_aparc_names0[i])]
+    for i2 in range(len(labels_aparc_idx)):
+        temp_labels.append(labels_aparc[labels_aparc_idx[i2]].copy())
+# Split angular in 2 and get rostral part
+temp_labels[0] = temp_labels[0].split(2, subjects_dir=subjects_dir)[1]
+temp_labels[1] = temp_labels[1].split(2, subjects_dir=subjects_dir)[1]
+# Split supramarginal in 2 and get posterior part
+temp_labels[2] = temp_labels[2].split(2, subjects_dir=subjects_dir)[0]
+temp_labels[3] = temp_labels[3].split(2, subjects_dir=subjects_dir)[0]
+
+for hem in range(2):
+    PCC_p1 = temp_labels[hem]
+    for i in range(1,len(temp_labels)//2):
+        PCC_p2 = temp_labels[hem+2*i]
+        PCC_p1 = PCC_p1.__add__(PCC_p2)
+    PCC_p1.name = "IPL-{}".format(PCC_p1.hemi)
+    labels.append(PCC_p1)
+
+### Orbital gyrus
+# From their figure it seems to correspond to orbital part of inferior frontal gyrus
+label_aparc_names0 = ["G_front_inf-Orbital"]
+for i in range(len(label_aparc_names0)):
+    labels_aparc_idx = [labels_aparc_names.index(l) for l in labels_aparc_names if l.startswith(label_aparc_names0[i])]
+    for i2 in range(len(labels_aparc_idx)):
+        temp_labels = labels_aparc[labels_aparc_idx[i2]].copy()
+        temp_labels.name = "ORB-{}".format(temp_labels.hemi)
+        labels.append(temp_labels)
+
+### Middle temporal gyrus
+# From their figure it seems to only be 1/4 of MTG at the 2nd to last caudal part
+label_aparc_names0 = ["G_temporal_middle"]
+for i in range(len(label_aparc_names0)):
+    labels_aparc_idx = [labels_aparc_names.index(l) for l in labels_aparc_names if l.startswith(label_aparc_names0[i])]
+    for i2 in range(len(labels_aparc_idx)):
+        temp_labels = labels_aparc[labels_aparc_idx[i2]].copy()
+        temp_labels = temp_labels.split(4, subjects_dir=subjects_dir)[1]
+        temp_labels.name = "MTG-{}".format(temp_labels.hemi)
+        labels.append(temp_labels)
+
+### Anterior middle frontal gyrus
+label_aparc_names0 = ["G_front_middle"]
+for i in range(len(label_aparc_names0)):
+    labels_aparc_idx = [labels_aparc_names.index(l) for l in labels_aparc_names if l.startswith(label_aparc_names0[i])]
+    for i2 in range(len(labels_aparc_idx)):
+        temp_labels = labels_aparc[labels_aparc_idx[i2]].copy()
+        temp_labels = temp_labels.split(2, subjects_dir=subjects_dir)[1]
+        temp_labels.name = "AMFG-{}".format(temp_labels.hemi)
+        labels.append(temp_labels)
+
+### Insula
+label_aparc_names0 = ["G_Ins_lg_and_S_cent_ins","G_insular_short"]
+temp_labels = []
+for i in range(len(label_aparc_names0)):
+    labels_aparc_idx = [labels_aparc_names.index(l) for l in labels_aparc_names if l.startswith(label_aparc_names0[i])]
+    for i2 in range(len(labels_aparc_idx)):
+        temp_labels.append(labels_aparc[labels_aparc_idx[i2]].copy())
+for hem in range(2):
+    PCC_p1 = temp_labels[hem]
+    for i in range(1,len(temp_labels)//2):
+        PCC_p2 = temp_labels[hem+2*i]
+        PCC_p1 = PCC_p1.__add__(PCC_p2)
+    PCC_p1.name = "INS-{}".format(PCC_p1.hemi)
+    labels.append(PCC_p1)
+
+### (Dorsal) Anterior Cingulate Cortex
+label_aparc_names0 = ["G_and_S_cingul-Ant"]
+temp_labels = []
+for i in range(len(label_aparc_names0)):
+    labels_aparc_idx = [labels_aparc_names.index(l) for l in labels_aparc_names if l.startswith(label_aparc_names0[i])]
+    for i2 in range(len(labels_aparc_idx)):
+        temp_labels.append(labels_aparc[labels_aparc_idx[i2]].copy())
+        temp_labels[-1].name = "ACC-{}".format(temp_labels[-1].hemi)
+# Combine the 2 hemisphere in 1 label
+labels.append(temp_labels[0].__add__(temp_labels[1]))
+
+### Supramarginal Gyrus
+label_aparc_names0 = ["G_pariet_inf-Supramar"]
+for i in range(len(label_aparc_names0)):
+    labels_aparc_idx = [labels_aparc_names.index(l) for l in labels_aparc_names if l.startswith(label_aparc_names0[i])]
+    for i2 in range(len(labels_aparc_idx)):
+        temp_labels = labels_aparc[labels_aparc_idx[i2]].copy()
+        temp_labels.name = "SUP-{}".format(temp_labels.hemi)
+        labels.append(temp_labels)
+
+print("{} ROIs have been defined".format(len(labels)))
+
+# # Visualize positions
+# fig = plt.figure()
+# ax = fig.add_subplot(111, projection="3d")
+# for i in range(0,3):
+#     temp_pos = temp_labels[i].pos
+#     ax.scatter(temp_pos[:,0],temp_pos[:,1],temp_pos[:,2], marker="o", alpha=0.1)
+# # Add to plot
+# ax.scatter(labels[-1].pos[:,0],labels[-1].pos[:,1],labels[-1].pos[:,2], marker="o")
+
+# # Visualize the labels
+# # temp_l = labels_aparc[labels_aparc_idx[0]]
+# temp_l = labels[-2]
+# l_stc = stc[100].in_label(temp_l)
+# l_stc.vertices
+
+# l_stc.plot(**surfer_kwargs)
+
+# Save the annotation file
+with open("custom_aparc2009_Li_et_al_2022.pkl", "wb") as file:
+    pickle.dump(labels, file)
+
+# %% Calculate orthogonalized power envelope connectivity in source space
+# In non-interpolated channels
+# Updated 22/1 - 2021 to use delta = 1/81 and assumption
+# about non-correlated and equal variance noise covariance matrix for channels
+
+# Load
+with open("custom_aparc2009_Li_et_al_2022.pkl", "rb") as file:
+    labels = pickle.load(file)
+label_names = [label.name for label in labels]
+
+# Define function to estimate PEC
+def PEC_estimation(x, freq_bands, sfreq=200):
+    """
+    This function takes a source timeseries signal x and performs:
+        1. Bandpass filtering
+        2. Hilbert transform to yield analytical signal
+        3. Compute all to all connectivity by iteratively computing for each pair
+            a. Orthogonalization
+            b. Computing power envelopes by squaring the signals |x|^2
+            c. Log-transform to enhance normality
+            d. Pearson's correlation between each pair
+            e. Fisher's r-to-z transform to enhance normality
+    The code has been optimized by inspiration from MNE-Python's function:
+    mne.connectivity.enelope_correlation.
+    
+    In MNE-python version < 0.22 there was a bug, but after the fix in 0.22
+    the mne function is equivalent to my implementation, although they don't
+    use epsilon but gives same result with a RuntimeWarning about log(0)
+    
+    IMPORTANT NOTE:
+        Filtering introduce artifacts for first and last timepoint
+    The values are very low, more than 1e-12 less than the others
+    If they are not removed, then they will heavily influence Pearson's
+    correlation as it is outlier sensitive
+    
+    Inputs:
+        x - The signal in source space as np.array with shape (ROIs,Timepoints)
+        freq_bands - The frequency bands of interest as a dictionary e.g.
+                     {"alpha": [8.0, 13.0], "beta": [13.0, 30.0]}
+        sfreq - The sampling frequency in Hertz
+    
+    Output:
+        The pairwise connectivity matrix
+    """
+    n_roi, n_timepoints = x.shape
+    n_freq_bands = len(freq_bands)
+    
+    epsilon = 1e-100 # small value to prevent log(0) errors
+    
+    # Filter the signal in the different freq bands
+    PEC_con0 = np.zeros((n_roi,n_roi,n_freq_bands))
+    for fname, frange in freq_bands.items():
+        fmin, fmax = [float(interval) for interval in frange]
+        signal_filtered = mne.filter.filter_data(x, sfreq, fmin, fmax,
+                                          fir_design="firwin", verbose=0)
+        # Filtering on finite signals will yield very low values for first
+        # and last timepoint, which can create outliers. E.g. 1e-29 compared to 1e-14
+        # Outlier sensitive methods, like Pearson's correlation, is therefore
+        # heavily affected and this systematic error is removed by removing
+        # the first and last timepoint
+        signal_filtered = signal_filtered[:,1:-1]
+        
+        # Hilbert transform
+        analytic_signal = scipy.signal.hilbert(signal_filtered)
+        # I will use x and y to keep track of orthogonalization
+        x0 = analytic_signal
+        # Get power envelope
+        x0_mag = np.abs(x0)
+        # Get scaled conjugate used for orthogonalization estimation
+        x0_conj_scaled = x0.conj()
+        x0_conj_scaled /= x0_mag
+        # Take square power envelope
+        PEx = np.square(x0_mag)
+        # Take log transform
+        lnPEx = np.log(PEx+epsilon)
+        # Remove mean for Pearson correlation calculation
+        lnPEx_nomean = lnPEx - np.mean(lnPEx, axis=-1, keepdims=True) # normalize each roi timeseries
+        # Get std for Pearson correlation calculation
+        lnPEx_std = np.std(lnPEx, axis=-1)
+        lnPEx_std[lnPEx_std == 0] = 1 # Prevent std = 0 problems
+        # Prepare con matrix
+        con0 = np.zeros((n_roi,n_roi))
+        for roi_r, y0 in enumerate(x0): # for each y0
+            # Calculate orthogonalized signal y with respect to x for all x
+            # Using y_ort = imag(y*x_conj/|x|)
+            # I checked the formula in temp_v3 and it works as intended
+            # I want to orthogonalize element wise for each timepoint
+            y0_ort = (y0*x0_conj_scaled).imag
+            # Here y0_ort.shape = (n_roi, n_timepoints)
+            # So y is current roi and the first axis gives each x it is orthogonalized to
+            # Take the abs to get power envelope
+            y0_ort = np.abs(y0_ort)
+            # Prevent log(0) error when calculating y_ort on y
+            y0_ort[roi_r] = 1. # this will be 0 zero after mean subtraction
+            # Take square power envelope
+            PEy = np.square(y0_ort) # squared power envelope
+            # Take log transform
+            lnPEy = np.log(PEy+epsilon)
+            # Remove mean for pearson correlation calculation
+            lnPEy_nomean = lnPEy - np.mean(lnPEy, axis=-1, keepdims=True)
+            # Get std for Pearson correlation calculation
+            lnPEy_std = np.std(lnPEy, axis=-1)
+            lnPEy_std[lnPEy_std == 0] = 1.
+            # Pearson correlation is expectation of X_nomean * Y_nomean for each time-series divided with standard deviations
+            PEC = np.mean(lnPEx_nomean*lnPEy_nomean, axis=-1)
+            PEC /= lnPEx_std
+            PEC /= lnPEy_std
+            con0[roi_r] = PEC
+        # The con0 connectivity matrix should be read as correlation between
+        # orthogonalized y (row number) and x (column number)
+        # It is not symmetrical, as cor(roi2_ort, roi1) is not cor(roi1_ort, roi2)
+        # To make it symmetrical the average of the absolute correlation
+        # of the 2 possibilities for each pair are taken
+        con0 = np.abs(con0)
+        con0 = (con0.T+con0)/2.
+        # Fisher's z transform - which is equivalent to arctanh
+        con0 = np.arctanh(con0)
+        # The diagonal is not 0 as I wanted to avoid numerical errors with log(0)
+        # and used a small epsilon value. Thus the diagonal is explicitly set to 0
+        
+        # Save to array
+        PEC_con0[:,:,list(freq_bands.keys()).index(fname)] = con0
+    return PEC_con0
+
+# Prepare variables
+Freq_Bands = {"delta": [1.25, 4.0],
+              "theta": [4.0, 8.0],
+              "alpha": [8.0, 13.0],
+              "beta": [13.0, 30.0],
+              "gamma": [30.0, 49.0]}
+n_freq_bands = len(Freq_Bands)
+n_roi = len(labels)
+
+# Get current time
+c_time1 = time.localtime()
+c_time1 = time.strftime("%a %d %b %Y %H:%M:%S", c_time1)
+print(c_time1)
+
+# PEC analysis
+PEC_data_list = [0]*n_subjects
+STCs_list = [0]*n_subjects
+
+# Using inverse operator as generator interferes with concurrent processes
+# If I run it for multiple subjects I run out of ram
+# Thus concurrent processes are used inside the for loop
+def PEC_analysis(input_args): # iterable epoch number and corresponding ts
+    i2, ts = input_args
+    # Estimate PEC
+    PEC_con0 = PEC_estimation(ts, Freq_Bands, sfreq)
+    print("Finished {} out of {} epochs".format(i2+1,n_epochs))
+    return i2, PEC_con0, ts
+
+for i in range(n_subjects):
+    n_epochs, n_ch, n_timepoints = source_epochs[i].get_data().shape
+    # Use different forward solutions depending on number of channels
+    cur_subject_id = Subject_id[i]
+    fwd = fwds[i]
+    
+    # Using assumption about equal variance and no correlations I make a diagonal matrix
+    # Using the default option for 0.2µV std for EEG data
+    noise_cov = mne.make_ad_hoc_cov(source_epochs[i].info, None)
+    
+    # Make inverse operator
+    # Using default depth parameter = 0.8 and free orientation (loose = 1)
+    inverse_operator = mne.minimum_norm.make_inverse_operator(source_epochs[i].info,
+                                                              fwd, noise_cov,
+                                                              loose = 1, depth = 0.8,
+                                                              verbose = 0)
+    src_inv = inverse_operator["src"]
+    # Compute inverse solution and retrieve time series for each label
+    # Preallocate memory
+    label_ts = np.full((n_epochs,len(labels),n_timepoints),np.nan)
+    # Define regularization
+    snr = 9 # Zhang et al, 2020 used delta = 1/81, which is inverse SNR and correspond to lambda2
+    # A for loop is used for each label due to memory issues when doing all labels at the same time
+    for l in range(len(labels)):
+        stc = mne.minimum_norm.apply_inverse_epochs(source_epochs[i],inverse_operator,
+                                                    lambda2 = 1/(snr**2),
+                                                    label = labels[l],
+                                                    pick_ori = "vector",
+                                                    return_generator=False,
+                                                    method = "MNE", verbose = 0)
+        # Use PCA to reduce the 3 orthogonal directions to 1 principal direction with max power
+        # There can be ambiguity about the orientation, thus the one that
+        # is pointing most "normal", i.e. closest 90 degrees to the skull is used
+        stc_pca = [0]*len(stc)
+        for ep in range(n_epochs):
+            stc_pca[ep], pca_dir = stc[ep].project(directions="pca", src=src_inv)
+        # Get mean time series for the whole label
+        temp_label_ts = mne.extract_label_time_course(stc_pca, labels[l], src_inv, mode="mean_flip",
+                                         return_generator=False, verbose=0)
+        # Save to array
+        label_ts[:,l,:] = np.squeeze(np.array(temp_label_ts))
+        print("Finished estimating STC for {} out of {} ROIs".format(l+1,len(labels)))
+    
+    # Free up memory
+    del stc
+
+    # Prepare variables
+    sfreq=source_epochs[i].info["sfreq"]
+    n_epochs = len(source_epochs[i])
+    # Estimate the pairwise PEC for each epoch
+    PEC_con_subject = np.zeros((n_epochs,n_roi,n_roi,n_freq_bands))
+    stcs0 = np.zeros((n_epochs,n_roi,int(sfreq)*4)) # 4s epochs
+    # Make list of arguments to pass into PEC_analysis using the helper func
+    args = []
+    for i2 in range(n_epochs):
+        args.append((i2,label_ts[i2]))
+    
+    with concurrent.futures.ProcessPoolExecutor(max_workers=16) as executor:
+        for i2, PEC_result, stc_result in executor.map(PEC_analysis, args): # Function and arguments
+            PEC_con_subject[i2] = PEC_result
+            stcs0[i2] = stc_result
+    
+    # Save to list
+    PEC_data_list[i] = PEC_con_subject # [subject](epoch,ch,ch,freq)
+    STCs_list[i] = stcs0 # [subject][epoch,roi,timepoint]
+    
+    # Print progress
+    print("Finished {} out of {} subjects".format(i+1,n_subjects))
+
+# Get current time
+c_time2 = time.localtime()
+c_time2 = time.strftime("%a %d %b %Y %H:%M:%S", c_time2)
+print("Started", c_time1, "\nFinished",c_time2)
+
+with open(Feature_savepath+"PEC_each_epoch_drop_interpol_ch_fix_snr.pkl", "wb") as file:
+    pickle.dump(PEC_data_list, file)
+with open(Feature_savepath+"STCs_each_epoch_drop_interpol_ch_fix_snr.pkl", "wb") as file:
+    pickle.dump(STCs_list, file)
+
+# # # Load
+# with open(Feature_savepath+"PEC_each_epoch_drop_interpol_ch_fix_snr.pkl", "rb") as file:
+#     PEC_data_list = pickle.load(file)
+
+# # Load
+# with open(Feature_savepath+"STCs_each_epoch_drop_interpol_ch_fix_snr.pkl", "rb") as file:
+#     STCs_list = pickle.load(file)
+
+# Average over eye status
+eye_status = list(source_epochs[0].event_id.keys())
+n_eye_status = len(eye_status)
+pec_data = np.zeros((n_subjects,n_eye_status,n_roi,n_roi,n_freq_bands))
+for i in range(n_subjects):
+    # Get indices for eyes open and closed
+    EC_index = source_epochs[i].events[:,2] == 1
+    EO_index = source_epochs[i].events[:,2] == 2
+    # Average over the indices and save to array
+    pec_data[i,0] = np.mean(PEC_data_list[i][EC_index], axis=0)
+    pec_data[i,1] = np.mean(PEC_data_list[i][EO_index], axis=0)
+    # Only use the lower diagonal as the diagonal should be 0 (or very small due to numerical errors)
+    # And it is symmetric
+    for f in range(n_freq_bands):
+        pec_data[i,0,:,:,f] = np.tril(pec_data[i,0,:,:,f],k=-1)
+        pec_data[i,1,:,:,f] = np.tril(pec_data[i,1,:,:,f],k=-1)
+
+# Also save as dataframe format for feature selection
+# Convert to Pandas dataframe
+# The dimensions will each be a column with numbers and the last column will be the actual values
+arr = np.column_stack(list(map(np.ravel, np.meshgrid(*map(np.arange, pec_data.shape), indexing="ij"))) + [pec_data.ravel()])
+pec_data_df = pd.DataFrame(arr, columns = ["Subject_ID", "Eye_status", "chx", "chy", "Freq_band", "Value"])
+# Change from numerical coding to actual values
+eye_status = list(source_epochs[0].event_id.keys())
+freq_bands_name = list(Freq_Bands.keys())
+label_names = [label.name for label in labels]
+
+index_values = [Subject_id,eye_status,label_names,label_names,freq_bands_name]
+for col in range(len(index_values)):
+    col_name = pec_data_df.columns[col]
+    for shape in range(pec_data.shape[col]): # notice not dataframe but the array
+        pec_data_df.loc[pec_data_df.iloc[:,col] == shape,col_name]\
+        = index_values[col][shape]
+
+# Add group status
+Group_status = np.array(["CTRL"]*len(pec_data_df["Subject_ID"]))
+Group_status[np.array([i in cases for i in pec_data_df["Subject_ID"]])] = "PTSD"
+# Add to dataframe
+pec_data_df.insert(3, "Group_status", Group_status)
+
+# Remove all diagonal and upper-matrix entries by removing zeros
+pec_data_df = pec_data_df.iloc[pec_data_df["Value"].to_numpy().nonzero()]
+
+# Save df
+pec_data_df.to_pickle(os.path.join(Feature_savepath,"pec_data_drop_interpol_ch_df.pkl"))
+
+# %% Sparse clustering of PEC for subtyping PTSD group
+# They did it for both eye status together, so all data in one matrix
+# Load PEC df
+# pec_data_df = pd.read_pickle(os.path.join(Feature_savepath,"pec_data_df.pkl"))
+pec_data_df = pd.read_pickle(os.path.join(Feature_savepath,"pec_data_drop_interpol_ch_df.pkl"))
+
+# Convert to wide format
+# Make function to add measurement column for indexing
+def add_measurement_column(df, measurement = "Text"):
+    dummy_variable = [measurement]*df.shape[0]
+    df.insert(1, "Measurement", dummy_variable)
+    return df
+# Make function to convert column tuple to string
+def convertTupleHeader(header):
+    header = list(header)
+    str = "_".join(header)
+    return str
+
+# Prepare overall dataframe
+PEC_df = pd.DataFrame(Subject_id, columns = ["Subject_ID"])
+# Add PEC
+pec_data_df = add_measurement_column(pec_data_df, "PEC")
+temp_df = pec_data_df.pivot_table(index="Subject_ID",columns=["Measurement",
+                                    "Eye_status", "chx", "chy",
+                                    "Freq_band"], dropna=True,
+                               values="Value").reset_index(drop=True)
+# check NaN is properly dropped and subject index is correct
+assert pec_data_df.shape[0] == np.prod(temp_df.shape)
+test1 = pec_data_df.iloc[np.random.randint(n_subjects),:]
+assert test1["Value"] ==\
+    temp_df[test1[1]][test1[2]][test1[3]][test1[5]][test1[6]][Subject_id.index(test1[0])]
+# Fix column names
+temp_df.columns = [convertTupleHeader(temp_df.columns[i]) for i in range(len(temp_df.columns))]
+
+PEC_df = pd.concat([PEC_df,temp_df], axis=1)
+
+# Add group status
+Groups = ["CTRL", "PTSD"]
+Group_status = np.array([0]*PEC_df.shape[0]) # CTRL = 0
+Group_status[np.array([i in cases for i in PEC_df["Subject_ID"]])] = 1 # PTSD = 1
+PEC_df.insert(1, "Group_status", Group_status)
+
+# Only use PTSD patient group
+PEC_df2 = PEC_df.loc[PEC_df["Group_status"]==1,:]
+
+Subject_info_cols = ["Subject_ID","Group_status"]
+
+# Use gridsearch and permutations to estimate gap statistic and use it to 
+# determine number of clusters and sparsity s
+# I will use 100 permutations and test 2 to 6 clusters as Zhang 2020
+# Error when trying to determine Gap statistic for 1 cluster? Also in R package
+max_clusters = 6
+n_sparsity_feat = 20
+perm_res = []
+for k in range(1,max_clusters):
+    # Cannot permute with 1 cluster
+    n_clusters = k+1
+    x = np.array(PEC_df2.copy().drop(Subject_info_cols, axis=1))
+    perm = pysparcl.cluster.permute_modified(x, k=n_clusters, verbose=True,
+                                             nvals=n_sparsity_feat, nperms=100)
+    perm_res.append(perm)
+
+# Save the results
+with open(Feature_savepath+"PEC_drop_interpol_ch_kmeans_perm.pkl", "wb") as file:
+    pickle.dump(perm_res, file)
+
+# # Load
+# with open(Feature_savepath+"PEC_drop_interpol_ch_kmeans_perm.pkl", "rb") as file:
+#     perm_res = pickle.load(file)
+
+# Convert results to array
+perm_res_arr = np.zeros((len(perm_res)*n_sparsity_feat,4))
+for i in range(len(perm_res)):
+    _, gaps, sdgaps, wbounds, _ = perm_res[i].values()
+    for i2 in range(n_sparsity_feat):
+        perm_res_arr[20*i+i2,0] = i+2 # cluster size
+        perm_res_arr[20*i+i2,1] = gaps[i2] # gap statistic
+        perm_res_arr[20*i+i2,2] = sdgaps[i2] # gap statistic std
+        perm_res_arr[20*i+i2,3] = wbounds[i2] # sparsity feature s
+
+# For each sparsity s, determine best k using one-standard-error criterion
+# Meaning the cluster and sparsity is chosen for the smallest value of k for a fixed s
+# that fulfill Gap(k) >= Gap(k+1)-std(k+1)
+def one_standard_deviation_search(gaps, std):
+    best_gaps = np.argmax(gaps)
+    current_gaps = gaps[best_gaps]
+    current_std = std[best_gaps]
+    current_gaps_idx = best_gaps
+    while (gaps[current_gaps_idx-1] >= current_gaps - current_std):
+        if current_gaps_idx == 0:
+            break
+        else:
+            current_gaps_idx -= 1
+            current_gaps = gaps[current_gaps_idx]
+            current_std = std[current_gaps_idx]
+    out = current_gaps, current_std, current_gaps_idx
+    return out
+
+best_ks = np.zeros((n_sparsity_feat, 2))
+all_s = np.unique(perm_res_arr[:,3])
+plt.figure(figsize=(12,12))
+for i2 in range(n_sparsity_feat):
+    current_s = all_s[i2]
+    gaps = perm_res_arr[perm_res_arr[:,3] == current_s,1]
+    std = perm_res_arr[perm_res_arr[:,3] == current_s,2]
+    _, _, idx = one_standard_deviation_search(gaps, std)
+    # Save to array
+    best_ks[i2,0] = current_s
+    best_ks[i2,1] = perm_res_arr[perm_res_arr[:,3] == current_s,0][idx]
+    # Plot gap
+    plt.errorbar(perm_res_arr[perm_res_arr[:,3] == current_s,0].astype("int"),
+             gaps, yerr=std, capsize=5, label = np.round(current_s,3))
+plt.title("Gap statistic for different fixed s")
+plt.legend(loc=1)
+plt.xlabel("Number of clusters")
+plt.ylabel("Gap statistic")
+
+best_k = int(scipy.stats.mode(best_ks[:,1])[0])
+
+# Determine s using fixed k as lowest s within 1 std of max gap statistic
+# According to Witten & Tibshirani, 2010
+best_gaps_idx = np.argmax(perm_res_arr[perm_res_arr[:,0] == best_k,1])
+best_gaps = perm_res_arr[perm_res_arr[:,0] == best_k,1][best_gaps_idx]
+best_gaps_std = perm_res_arr[perm_res_arr[:,0] == best_k,2][best_gaps_idx]
+one_std_crit = perm_res_arr[perm_res_arr[:,0] == best_k,1]>=best_gaps-best_gaps_std
+
+best_s = np.array([perm_res_arr[perm_res_arr[:,0] == best_k,3][one_std_crit][0]])
+
+# Perform clustering with k clusters
+x = np.array(PEC_df2.copy().drop(Subject_info_cols, axis=1))
+sparcl = pysparcl.cluster.kmeans(x, k=best_k, wbounds=best_s)[0]
+
+# Save the results
+with open(Feature_savepath+"PEC_drop_interpol_ch_sparse_kmeans.pkl", "wb") as file:
+    pickle.dump(sparcl, file)
+
+# Get overview of the features chosen and summarize feature type with countplot
+nonzero_idx = sparcl["ws"].nonzero()
+sparcl_features = PEC_df2.copy().drop(Subject_info_cols, axis=1).columns[nonzero_idx]
+
+# Prepare variables
+Freq_Bands = {"delta": [1.25, 4.0],
+              "theta": [4.0, 8.0],
+              "alpha": [8.0, 13.0],
+              "beta": [13.0, 30.0],
+              "gamma": [30.0, 49.0]}
+n_freq_bands = len(Freq_Bands)
+eye_status = list(source_epochs[0].event_id.keys())
+n_eye_status = len(eye_status)
+
+sparcl_feat = []
+sparcl_feat_counts = []
+for e in range(n_eye_status):
+    ee = eye_status[e]
+    for f in range(n_freq_bands):
+        ff = list(Freq_Bands.keys())[f]
+        temp_feat = sparcl_features[sparcl_features.str.contains(("_"+ee))]
+        temp_feat = temp_feat[temp_feat.str.contains(("_"+ff))]
+        # Save to list
+        sparcl_feat.append(temp_feat)
+        sparcl_feat_counts.append(["{}_{}".format(ee,ff), len(temp_feat)])
+
+# Convert the list to dataframe to use in countplot
+sparcl_feat_counts_df = pd.DataFrame(columns=["Eye_status", "Freq_band"])
+for i in range(len(sparcl_feat_counts)):
+    # If this feature type does not exist, then skip it
+    if sparcl_feat_counts[i][1] == 0:
+        continue
+    ee, ff = sparcl_feat_counts[i][0].split("_")
+    counts = sparcl_feat_counts[i][1]
+    temp_df = pd.DataFrame({"Eye_status":np.repeat(ee,counts),
+                            "Freq_band":np.repeat(ff,counts)})
+    sparcl_feat_counts_df = sparcl_feat_counts_df.append(temp_df, ignore_index=True)
+
+# Fix Freq_band categorical order
+cat_type = pd.CategoricalDtype(categories=list(Freq_Bands.keys()), ordered=True)
+sparcl_feat_counts_df["Freq_band"] = sparcl_feat_counts_df["Freq_band"].astype(cat_type)
+
+plt.figure(figsize=(8,8))
+g = sns.countplot(y="Freq_band", hue="Eye_status", data=sparcl_feat_counts_df)
+plt.title("PEC Sparse K-means features")
+plt.xlabel("Number of non-zero weights")
+plt.ylabel("Frequency Band")
+
+# %% Functional connectivity in source space
+# MNE implementation of PLV and wPLI is phase across trials(epochs), e.g. for ERPs
+# I'll use my own manually implemented PLV and wPLI across time and then average across epochs
+# Notice that the new MNE-connectivity library now also takes phase across time
+
+sfreq = final_epochs[0].info["sfreq"]
+# error when using less than 5 cycles for spectrum estimation
+# 1Hz too low with epoch length of 4, thus I changed the fmin to 1.25 for delta
+Freq_Bands = {"delta": [1.25, 4.0],
+              "theta": [4.0, 8.0],
+              "alpha": [8.0, 13.0],
+              "beta": [13.0, 30.0],
+              "gamma": [30.0, 49.0]}
+n_freq_bands = len(Freq_Bands)
+freq_centers = np.array([2.5,6,10.5,21.5,40])
+# Convert to tuples for the mne function
+fmin=tuple([list(Freq_Bands.values())[f][0] for f in range(len(Freq_Bands))])
+fmax=tuple([list(Freq_Bands.values())[f][1] for f in range(len(Freq_Bands))])
+
+# Make linspace array for morlet waves
+freq_centers = np.arange(fmin[0],fmax[-1]+0.25,0.25)
+# Prepare Morlets
+morlets = mne.time_frequency.tfr.morlet(sfreq,freq_centers,n_cycles=3)
+
+# Make freqs array for indexing
+freqs0 = [0]*n_freq_bands
+for f in range(n_freq_bands):
+    freqs0[f] = freq_centers[(freq_centers>=fmin[f]) & (freq_centers<=fmax[f])]
+
+# The in-built connectivity function gives an (n_channel, n_channel, freqs output
+# For loop over subject ID and eye status is implemented
+n_subjects = len(Subject_id)
+eye_status = list(final_epochs[0].event_id.keys())
+n_eye_status = len(eye_status)
+ch_names = final_epochs[0].info["ch_names"]
+
+# Load source labels
+with open("custom_aparc2009_Li_et_al_2022.pkl", "rb") as file:
+    labels = pickle.load(file)
+label_names = [label.name for label in labels]
+n_sources = len(label_names)
+
+# Connectivity methods
+connectivity_methods = ["coh","imcoh","plv","wpli"]
+n_con_methods=len(connectivity_methods)
+
+# Number of pairwise ch connections
+n_ch_connections = scipy.special.comb(n_sources,2, exact=True, repetition=False)
+
+# Load source time series
+with open(Feature_savepath+"STCs_each_epoch_drop_interpol_ch_fix_snr.pkl", "rb") as file:
+    STCs_list = pickle.load(file)
+
+# I made my own slightly-optimized PLV & WPLI function
+# Version 2 based on Filter + Hilbert instead of Morlets
+def calculate_PLV_WPLI_across_time(data):
+    n_ch, n_time0 = data.shape
+    x = data.copy()
+    # Filter the signal in the different freq bands
+    con_array0 = np.zeros((2,n_ch,n_ch,n_freq_bands))
+    # con_array0[con_array0==0] = np.nan
+    for fname, frange in Freq_Bands.items():
+        fmin, fmax = [float(interval) for interval in frange]
+        signal_filtered = mne.filter.filter_data(x, sfreq, fmin, fmax,
+                                          fir_design="firwin", verbose=0)
+        # Filtering on finite signals will yield very low values for first
+        # and last timepoint, which can create outliers. E.g. 1e-29 compared to 1e-14
+        # This systematic error is removed by removing the first and last timepoint
+        signal_filtered = signal_filtered[:,1:-1]
+        # Hilbert transform to get complex signal
+        analytic_signal = scipy.signal.hilbert(signal_filtered)
+        # Calculate for the lower diagnonal only as it is symmetric
+        for ch_r in range(n_ch):
+            for ch_c in range(n_ch):
+                if ch_r>ch_c:
+                    # =========================================================================
+                    # PLV over time correspond to mean across time of the absolute value of
+                    # the circular length of the relative phases. So PLV will be 1 if
+                    # the phases of 2 signals maintain a constant lag
+                    # In equational form: PLV = 1/N * |sum(e^i(phase1-phase2))|
+                    # In code: abs(mean(exp(1i*phase_diff)))
+                    # =========================================================================
+                    # The real part correspond to the amplitude and the imaginary part can be used to calculate the phase
+                    phase_diff = np.angle(analytic_signal[ch_r])-np.angle(analytic_signal[ch_c])
+                    # Convert phase difference to complex part i(phase1-phase2)
+                    phase_diff_im = 0*phase_diff+1j*phase_diff
+                    # Take the exponential, then the mean followed by absolute value
+                    PLV = np.abs(np.mean(np.exp(phase_diff_im)))
+                    # Save to array
+                    con_array0[0,ch_r,ch_c,list(Freq_Bands.keys()).index(fname)] = PLV
+                    # =========================================================================
+                    # PLI over time correspond to the sign of the sine of relative phase
+                    # differences. So PLI will be 1 if one signal is always leading or
+                    # lagging behind the other signal. But it is insensitive to changes in
+                    # relative phase, as long as it is the same signal that leads.
+                    # If 2 signals are almost in phase, they might shift between lead/lag
+                    # due to small fluctuations from noise. This would lead to unstable
+                    # estimation of "phase" synchronisation.
+                    # The wPLI tries to correct for this by weighting the PLI with the
+                    # magnitude of the lag, to attenuate noise sources giving rise to
+                    # near zero phase lag "synchronization"
+                    # In equational form: WPLI = |E{|phase_diff|*sign(phase_diff)}| / E{|phase_diff|}
+                    # =========================================================================
+                    # Calculate the magnitude of phase differences
+                    phase_diff_mag = np.abs(np.sin(phase_diff))
+                    # Calculate the signed phase difference (PLI)
+                    sign_phase_diff = np.sign(np.sin(phase_diff))
+                    # Calculate the nominator (abs and average across time)
+                    WPLI_nominator = np.abs(np.mean(phase_diff_mag*sign_phase_diff))
+                    # Calculate denominator for normalization
+                    WPLI_denom = np.mean(phase_diff_mag)
+                    # Calculate WPLI
+                    WPLI = WPLI_nominator/WPLI_denom
+                    # Save to array
+                    con_array0[1,ch_r,ch_c,list(Freq_Bands.keys()).index(fname)] = WPLI
+    return con_array0
+
+# Pre-allocatate memory
+con_data = np.zeros((n_con_methods,n_subjects,n_eye_status,n_sources,n_sources,n_freq_bands))
+n_epochs_matrix = np.zeros((n_subjects,n_eye_status))
+
+# Get current time
+c_time = time.localtime()
+c_time = time.strftime("%H:%M:%S", c_time)
+print(c_time)
+
+def connectivity_estimation(i):
+    con_data0 = np.zeros((n_con_methods,n_eye_status,n_sources,n_sources,n_freq_bands))
+    con_data0[con_data0==0] = np.nan
+    n_epochs_matrix0 = np.zeros((n_eye_status))
+    for e in range(n_eye_status):
+        ee = eye_status[e]
+        eye_idx = final_epochs[i].events[:,2] == e+1 # EC = 1 and EO = 2
+        # Get source time series
+        temp_STC = STCs_list[i][eye_idx]
+        # Calculate the coherence and ImgCoh for the given subject and eye status
+        con, freqs, times, n_epochs, n_tapers = spectral_connectivity(
+            temp_STC, method=connectivity_methods[0:2],
+            mode="multitaper", sfreq=sfreq, fmin=fmin, fmax=fmax,
+            faverage=True, verbose=0)
+        # Save the results in array
+        con_data0[0,e,:,:,:] = con[0] # coherence
+        con_data0[1,e,:,:,:] = np.abs(con[1]) # Absolute value of ImgCoh to reflect magnitude of ImgCoh
+        
+        # Calculate PLV and wPLI for each epoch and then average
+        n_epochs0 = temp_STC.shape[0]
+        con_data1 = np.zeros((len(connectivity_methods[2:]),n_epochs0,n_sources,n_sources,n_freq_bands))
+        for epoch in range(n_epochs0):
+            # First the data is retrieved and epoch axis dropped
+            temp_data = temp_STC[epoch,:,:]
+            # PLV and WPLI value is calculated across timepoints in each freq band
+            PLV_WPLI_con = calculate_PLV_WPLI_across_time(temp_data)
+            # Save results
+            con_data1[0,epoch,:,:,:] = PLV_WPLI_con[0] # phase locking value
+            con_data1[1,epoch,:,:,:] = PLV_WPLI_con[1] # weighted phase lag index
+        # Take average across epochs for PLV and wPLI
+        con_data2 = np.mean(con_data1,axis=1)
+        # Save to final array
+        con_data0[2,e,:,:,:] = con_data2[0] # phase locking value
+        con_data0[3,e,:,:,:] = con_data2[1] # weighted phase lag index
+        n_epochs_matrix0[e] = n_epochs
+    
+    print("{} out of {} finished".format(i+1,n_subjects))
+    return i, con_data0, n_epochs_matrix0
+
+with concurrent.futures.ProcessPoolExecutor(max_workers=16) as executor:
+    for i, con_result, n_epochs_mat in executor.map(connectivity_estimation, range(n_subjects)): # Function and arguments
+        con_data[:,i,:,:,:,:] = con_result
+        n_epochs_matrix[i] = n_epochs_mat
+
+# Get current time
+c_time = time.localtime()
+c_time = time.strftime("%H:%M:%S", c_time)
+print(c_time)
+
+# Save the results
+np.save(Feature_savepath+"Source_drop_interpol_ch_connectivity_measures_data.npy", con_data) # (con_measure,subject,eye,ch,ch,freq)
+
+# Also save as dataframe format for feature selection
+# Convert to Pandas dataframe
+# The dimensions will each be a column with numbers and the last column will be the actual values
+arr = np.column_stack(list(map(np.ravel, np.meshgrid(*map(np.arange, con_data.shape), indexing="ij"))) + [con_data.ravel()])
+con_data_df = pd.DataFrame(arr, columns = ["Con_measurement", "Subject_ID", "Eye_status", "chx", "chy", "Freq_band", "Value"])
+# Change from numerical coding to actual values
+eye_status = list(final_epochs[0].event_id.keys())
+freq_bands_name = list(Freq_Bands.keys())
+
+index_values = [connectivity_methods,Subject_id,eye_status,label_names,label_names,freq_bands_name]
+for col in range(len(index_values)):
+    col_name = con_data_df.columns[col]
+    for shape in range(con_data.shape[col]): # notice not dataframe but the array
+        con_data_df.loc[con_data_df.iloc[:,col] == shape,col_name]\
+        = index_values[col][shape]
+
+# Add group status
+Group_status = np.array(["CTRL"]*len(con_data_df["Subject_ID"]))
+Group_status[np.array([i in cases for i in con_data_df["Subject_ID"]])] = "PTSD"
+# Add to dataframe
+con_data_df.insert(3, "Group_status", Group_status)
+
+# Remove all diagonal and upper-matrix entries
+con_data_df = con_data_df.iloc[con_data_df["Value"].to_numpy().nonzero()]
+
+# Save df
+con_data_df.to_pickle(os.path.join(Feature_savepath,"con_data_source_drop_interpol_df.pkl"))
+
+# %% Estimate Granger's Causality in source space
+# Load source labels
+with open("custom_aparc2009_Li_et_al_2022.pkl", "rb") as file:
+    labels = pickle.load(file)
+label_names = [label.name for label in labels]
+n_sources = len(label_names)
+
+# Load source time series
+with open(Feature_savepath+"STCs_each_epoch_drop_interpol_ch_fix_snr.pkl", "rb") as file:
+    STCs_list = pickle.load(file)
+
+# Granger's causality might be influenced by volume conduction, thus working with CSD might be beneficial
+# But since I already used source modelling to alleviate this problem I will not apply CSD
+# Barrett et al, 2012 also do not apply CSD on source GC
+
+# GC assumes stationarity, thus I will test for stationarity using ADF test
+# The null hypothesis of ADF is that it has unit root, i.e. is non-stationary
+# I will test how many can reject the null hypothesis, i.e. are stationary
+
+# Due to the low numerical values in STC the ADF test is unstable, thus I multiply it to be around 1e0
+
+stationary_test_arr = [0]*n_subjects
+n_tests = [0]*n_subjects
+for i in range(n_subjects):
+    # Get data
+    data_arr = STCs_list[i]
+    # Get shape
+    n_epochs, n_channels, n_timepoints = data_arr.shape
+    # Create array for indices to print out progress
+    ep_progress_idx = np.arange(n_epochs//5,n_epochs,n_epochs//5)
+    # Calculate number of tests performed for each subject
+    n_tests[i] = n_epochs*n_channels
+    # Prepare empty array (with 2's as 0 and 1 will be used)
+    stationary_test_arr0 = np.zeros((n_epochs,n_channels))+2 # make array of 2's
+    for ep in range(n_epochs):
+        for c in range(n_channels):
+            ADF = adfuller(data_arr[ep,c,:]*1e14) # multilying with a constant does not change ADF, but helps against numerical instability
+            p_value = ADF[1]
+            if p_value < 0.05:
+                stationary_test_arr0[ep,c] = True # Stationary set to 1
+            else:
+                stationary_test_arr0[ep,c] = False # Non-stationary set to 0
+        # Print partial progress
+        if len(np.where(ep_progress_idx==ep)[0]) > 0:
+            print("Finished epoch number: {} out of {}".format(ep,n_epochs))
+    # Indices that were not tested
+    no_test_idx = np.where(stationary_test_arr0==2)[0]
+    if len(no_test_idx) > 0:
+        print("An unexpected error occurred and {} was not tested".format(no_test_idx))
+    # Save to list
+    stationary_test_arr[i] = stationary_test_arr0
+    # Print progress
+    print("Finished subject {} out of {}".format(i+1,n_subjects))
+
+with open(Stat_savepath+"Source_drop_interpol_GC_stationarity_tests.pkl", "wb") as filehandle:
+    # The data is stored as binary data stream
+    pickle.dump(stationary_test_arr, filehandle)
+
+# I used a threshold of 0.05
+# This means that on average I would expect 5% false positives among the tests that showed significance for stationarity
+ratio_stationary = [0]*n_subjects
+for i in range(n_subjects):
+    # Ratio of tests that showed stationarity
+    ratio_stationary[i] = np.sum(stationary_test_arr[i])/n_tests[i]
+
+print("Ratio of stationary time series: {0:.3f}".format(np.mean(ratio_stationary))) # 88%
+
+# The pre-processing have already ensured that most of the data fulfills the stationarity assumption.
+
+# Divide the data into eyes closed and open
+ch_names = label_names
+n_channels = len(ch_names)
+
+STC_eye_data = []
+for i in range(n_subjects):
+    # Get index for eyes open and eyes closed
+    EC_index = final_epochs[i].events[:,2] == 1
+    EO_index = final_epochs[i].events[:,2] == 2
+    # Get the data
+    EC_epoch_data = STCs_list[i][EC_index,:,:] # eye index
+    EO_epoch_data = STCs_list[i][EO_index,:,:]
+    # Save to list
+    STC_eye_data.append([EC_epoch_data, EO_epoch_data])
+
+# Make each epoch a TimeSeries object
+# Input for TimeSeries is: (ch, time)
+eye_status = list(final_epochs[0].event_id.keys())
+n_eye_status = len(eye_status)
+sfreq = final_epochs[0].info["sfreq"]
+
+Timeseries_data = []
+for i in range(n_subjects):
+    temp_list1 = []
+    for e in range(n_eye_status):
+        temp_list2 = []
+        n_epochs = STC_eye_data[i][e].shape[0]
+        for ep in range(n_epochs):
+            # Convert to TimeSeries
+            time_series = nts.TimeSeries(STC_eye_data[i][e][ep,:,:], sampling_rate=sfreq)
+            # Save the object
+            temp_list2.append(time_series)
+        # Save the timeseries across eye status
+        temp_list1.append(temp_list2)
+    # Save the timeseries across subjects
+    Timeseries_data.append(temp_list1) # output [subject][eye][epoch](ch,time)
+
+# Test multiple specified model orders of AR models, each combination has its own model
+m_orders = np.linspace(1,25,25) # the model orders tested
+m_orders = np.round(m_orders)
+n_timepoints = len(Timeseries_data[0][0][0])
+n_ch_combinations = scipy.special.comb(n_channels,2, exact=True, repetition=False)
+
+# To reduce computation time I only test representative epochs (1 from each 1 min session)
+# There will be 5 epochs from eyes closed and 5 from eyes open
+n_rep_epoch = 5
+# The subjects have different number of epochs due to dropped epochs
+gaps_trials_idx = np.load("Gaps_trials_idx.npy") # time_points between sessions
+# I convert the gap time points to epoch number used as representative epoch
+epoch_idx = np.zeros((n_subjects,n_eye_status,n_rep_epoch), dtype=int) # prepare array
+epoch_idx[:,:,0:4] = np.round(gaps_trials_idx/n_timepoints,0)-8 # take random epoch from sessions 1 to 4
+epoch_idx[:,:,4] = np.round(gaps_trials_idx[:,:,3]/n_timepoints,0)+5 # take random epoch from session 5
+
+# Checking if all epoch idx exists
+for i in range(n_subjects):
+    EC_index = final_epochs[i].events[:,2] == 1
+    EO_index = final_epochs[i].events[:,2] == 2
+    assert np.sum(EC_index) >= epoch_idx[i,0,4]
+    assert np.sum(EO_index) >= epoch_idx[i,1,4]
+
+# Prepare model order estimation
+AIC_arr = np.zeros((len(m_orders),n_subjects,n_eye_status,n_rep_epoch,n_ch_combinations))
+BIC_arr = np.zeros((len(m_orders),n_subjects,n_eye_status,n_rep_epoch,n_ch_combinations))
+
+def GC_model_order_est(i):
+    AIC_arr0 = np.zeros((len(m_orders),n_eye_status,n_rep_epoch,n_ch_combinations))
+    BIC_arr0 = np.zeros((len(m_orders),n_eye_status,n_rep_epoch,n_ch_combinations))
+    for e in range(n_eye_status):
+        n_epochs = STC_eye_data[i][e].shape[0]
+        N_total = n_timepoints*n_epochs # total number of datapoints for specific eye condition
+        for ep in range(n_rep_epoch):
+            epp = epoch_idx[i,e,ep]
+            for o in range(len(m_orders)):
+                order = int(m_orders[o])
+                # Make the Granger Causality object
+                GCA1 = nta.GrangerAnalyzer(Timeseries_data[i][e][epp-1], order=order,
+                                           n_freqs=2000)
+                for c in range(n_ch_combinations):
+                    # Retrieve error covariance matrix for all combinations
+                    ecov = np.array(list(GCA1.error_cov.values()))
+                    # Calculate AIC
+                    AIC = ntsu.akaike_information_criterion(ecov[c,:,:], p = n_channels,
+                                                            m=order, Ntotal=N_total)
+                    # Calculate BIC
+                    BIC = ntsu.bayesian_information_criterion(ecov[c,:,:], p = n_channels,
+                                                              m=order, Ntotal=N_total)
+                    # Save the information criterions
+                    AIC_arr0[o,e,ep,c] = AIC
+                    BIC_arr0[o,e,ep,c] = BIC
+
+    print("{} out of {} finished testing".format(i+1,n_subjects))
+    return i, AIC_arr0, BIC_arr0
+
+# Get current time
+c_time1 = time.localtime()
+c_time1 = time.strftime("%a %d %b %Y %H:%M:%S", c_time1)
+print(c_time1)
+
+with concurrent.futures.ProcessPoolExecutor() as executor:
+    for i, AIC_result, BIC_result in executor.map(GC_model_order_est, range(n_subjects)): # Function and arguments
+        AIC_arr[:,i] = AIC_result
+        BIC_arr[:,i] = BIC_result
+
+# Get current time
+c_time2 = time.localtime()
+c_time2 = time.strftime("%a %d %b %Y %H:%M:%S", c_time2)
+print("Started", c_time1, "\nCurrent Time",c_time2)
+
+# Save the AIC and BIC results
+np.save(Feature_savepath+"AIC_Source_drop_interpol_GC_model_order.npy", AIC_arr) # (m. order, subject, eye, epoch, combination)
+np.save(Feature_savepath+"BIC_Source_drop_interpol_GC_model_order.npy", BIC_arr) # (m. order, subject, eye, epoch, combination)
+
+# Load data
+AIC_arr = np.load(Feature_savepath+"AIC_Source_drop_interpol_GC_model_order.npy")
+BIC_arr = np.load(Feature_savepath+"BIC_Source_drop_interpol_GC_model_order.npy")
+
+# Average across all subjects, eye status, epochs and combinations
+plt.figure(figsize=(8,6))
+plt.plot(m_orders, np.nanmean(AIC_arr, axis=(1,2,3,4)), label="AIC")
+plt.plot(m_orders, np.nanmean(BIC_arr, axis=(1,2,3,4)), label="BIC")
+plt.title("Average information criteria value")
+plt.xlabel("Model order (Lag)")
+plt.legend()
+
+np.sum(np.isnan(AIC_arr))/AIC_arr.size # around 0.07% NaN due to non-convergence
+np.sum(np.isnan(BIC_arr))/BIC_arr.size # around 0.07% NaN due to non-convergence
+
+# If we look at each subject
+mean_subject_AIC = np.nanmean(AIC_arr, axis=(2,3,4))
+
+plt.figure(figsize=(8,6))
+for i in range(n_subjects):
+    plt.plot(m_orders, mean_subject_AIC[:,i])
+plt.title("Average AIC for each subject")
+plt.xlabel("Model order (Lag)")
+
+mean_subject_BIC = np.nanmean(BIC_arr, axis=(2,3,4))
+plt.figure(figsize=(8,6))
+for i in range(n_subjects):
+    plt.plot(m_orders, mean_subject_BIC[:,i])
+plt.title("Average BIC for each subject")
+plt.xlabel("Model order (Lag)")
+
+# We see that for many cases in BIC, it does not converge. Monotonic increasing!
+
+# We can look at the distribution of chosen order for each time series analyzed
+# I.e. I will find the minima in model order for each model
+AIC_min_arr = np.argmin(AIC_arr, axis=0)
+BIC_min_arr = np.argmin(BIC_arr, axis=0)
+
+# Plot the distributions of the model order chosen
+plt.figure(figsize=(8,6))
+sns.distplot(AIC_min_arr.reshape(-1)+1, kde=False, norm_hist=True,
+             bins=np.linspace(0.75,30.25,60), label="AIC")
+plt.ylabel("Frequency density")
+plt.xlabel("Model order")
+plt.title("AIC Model Order Estimation")
+
+plt.figure(figsize=(8,6))
+sns.distplot(BIC_min_arr.reshape(-1)+1, kde=False, norm_hist=True, color="blue",
+             bins=np.linspace(0.75,30.25,60), label="BIC")
+plt.ylabel("Frequency density")
+plt.xlabel("Model order")
+plt.title("BIC Model Order Estimation")
+# It is clear from the BIC model that most have model order 1
+# which reflect their monotonic increasing nature without convergence
+# Thus I will only use AIC
+
+# There is a bias variance trade-off with model order [Stokes & Purdon, 2017]
+# Lower order is associated with higher bias and higher order with variance
+# I will choose the model order that is chosen the most (i.e. majority voting)
+AR_order = int(np.nanquantile(AIC_min_arr.reshape(-1), q=0.5))
+# Order = 5
+
+# Calculate Granger Causality for each subject, eye and epoch
+Freq_Bands = {"delta": [1.25, 4.0],
+              "theta": [4.0, 8.0],
+              "alpha": [8.0, 13.0],
+              "beta": [13.0, 30.0],
+              "gamma": [30.0, 49.0]}
+n_freq_bands = len(Freq_Bands)
+
+# Pre-allocate memory
+GC_data = np.zeros((2,n_subjects,n_eye_status,n_channels,n_channels,n_freq_bands))
+
+def GC_analysis(i):
+    GC_data0 = np.zeros((2,n_eye_status,n_channels,n_channels,n_freq_bands))
+    for e in range(n_eye_status):
+        n_epochs = STC_eye_data[i][e].shape[0]
+        # Make temporary array to save GC for each epoch
+        temp_GC_data = np.zeros((2,n_epochs,n_channels,n_channels,n_freq_bands))
+        for ep in range(n_epochs):
+            # Fit the AR model
+            GCA = nta.GrangerAnalyzer(Timeseries_data[i][e][ep], order=AR_order,
+                                       n_freqs=int(800)) # n_Freq=800 correspond to step of 0.25Hz, the same as multitaper for power estimation
+            for f in range(n_freq_bands):
+                # Define lower and upper band
+                f_lb = list(Freq_Bands.values())[f][0]
+                f_ub = list(Freq_Bands.values())[f][1]
+                # Get index corresponding to the frequency bands of interest
+                freq_idx_G = np.where((GCA.frequencies >= f_lb) * (GCA.frequencies < f_ub))[0]
+                # Calculcate Granger causality quantities
+                g_xy = np.mean(GCA.causality_xy[:, :, freq_idx_G], -1) # avg on last dimension
+                g_yx = np.mean(GCA.causality_yx[:, :, freq_idx_G], -1) # avg on last dimension
+                # Transpose to use same format as con_measurement and save
+                temp_GC_data[0,ep,:,:,f] = np.transpose(g_xy)
+                temp_GC_data[1,ep,:,:,f] = np.transpose(g_yx)
+        
+        # Average over epochs for each person, eye condition, direction and frequency band
+        temp_GC_epoch_mean = np.nanmean(temp_GC_data, axis=1) # sometimes Log(Sxx/xx_auto_component) is nan
+        # Save to array
+        GC_data0[:,e,:,:,:] = temp_GC_epoch_mean
+        
+    print("{} out of {} finished analyzing".format(i+1,n_subjects))
+    return i, GC_data0
+
+# Get current time
+c_time1 = time.localtime()
+c_time1 = time.strftime("%a %d %b %Y %H:%M:%S", c_time1)
+print(c_time1)
+
+with concurrent.futures.ProcessPoolExecutor() as executor:
+    for i, GC_result in executor.map(GC_analysis, range(n_subjects)): # Function and arguments
+        GC_data[:,i] = GC_result
+        
+# Get current time
+c_time2 = time.localtime()
+c_time2 = time.strftime("%a %d %b %Y %H:%M:%S", c_time2)
+print("Started", c_time1, "\nCurrent Time",c_time2)
+
+# Output: GC_data (g_xy/g_yx, subject, eye, chx, chy, freq)
+# Notice that for g_xy ([0,...]) it means "chy" Granger causes "chx"
+# and for g_yx ([1,...]) it means "chx" Granger causes "chy"
+# This is due to the transposing which flipped the results on to the lower-part of the diagonal
+
+# Save the Granger_Causality data
+np.save(Feature_savepath+"Source_drop_interpol_GrangerCausality_data.npy", GC_data)
+
+# Theoretically negative GC values should be impossible, but in practice
+# they can still occur due to problems with model fitting (see Stokes & Purdon, 2017)
+print("{:.3f}% negative GC values".\
+      format(np.sum(GC_data[~np.isnan(GC_data)]<0)/np.sum(~np.isnan(GC_data))*100)) # 0.08% negative values
+# These values cannot be interpreted, but seems to occur mostly for true non-causal connections
+# Hence I set them to 0
+with np.errstate(invalid="ignore"): # invalid number refers to np.nan, which will be set to False for comparisons
+    GC_data[(GC_data<0)] = 0
+
+# Save as dataframe for further processing with other features
+# Convert to Pandas dataframe
+# The dimensions will each be a column with numbers and the last column will be the actual values
+arr = np.column_stack(list(map(np.ravel, np.meshgrid(*map(np.arange, GC_data.shape), indexing="ij"))) + [GC_data.ravel()])
+GC_data_df = pd.DataFrame(arr, columns = ["GC_direction", "Subject_ID", "Eye_status", "chx", "chy", "Freq_band", "Value"])
+# Change from numerical coding to actual values
+eye_status = list(final_epochs[0].event_id.keys())
+freq_bands_name = list(Freq_Bands.keys())
+GC_directions_info = ["chy -> chx", "chx -> chy"]
+
+index_values = [GC_directions_info,Subject_id,eye_status,ch_names,ch_names,freq_bands_name]
+for col in range(len(index_values)):
+    col_name = GC_data_df.columns[col]
+    for shape in range(GC_data.shape[col]): # notice not dataframe but the array
+        GC_data_df.loc[GC_data_df.iloc[:,col] == shape,col_name]\
+        = index_values[col][shape]
+
+# Add group status
+Group_status = np.array(["CTRL"]*len(GC_data_df["Subject_ID"]))
+Group_status[np.array([i in cases for i in GC_data_df["Subject_ID"]])] = "PTSD"
+# Add to dataframe
+GC_data_df.insert(3, "Group_status", Group_status)
+
+# Remove all nan (including diagonal and upper-matrix entries)
+GC_data_df = GC_data_df.iloc[np.invert(np.isnan(GC_data_df["Value"].to_numpy()))]
+
+# Swap ch values for GC_direction chy -> chx (so it is always chx -> chy)
+tempchy = GC_data_df[GC_data_df["GC_direction"] == "chy -> chx"]["chy"] # save chy
+GC_data_df.loc[GC_data_df["GC_direction"] == "chy -> chx","chy"] =\
+             GC_data_df.loc[GC_data_df["GC_direction"] == "chy -> chx","chx"] # overwrite old chy
+GC_data_df.loc[GC_data_df["GC_direction"] == "chy -> chx","chx"] = tempchy # overwrite chx
+
+# Drop the GC_direction column
+GC_data_df = GC_data_df.drop("GC_direction", axis=1)
+
+# Save df
+GC_data_df.to_pickle(os.path.join(Feature_savepath,"GC_data_source_drop_interpol_df.pkl"))
+
+# Testing if df was formatted correctly
+expected_GC_values = n_subjects*n_eye_status*n_ch_combinations*n_freq_bands*2 # 2 because it is bidirectional
+assert GC_data_df.shape[0] == expected_GC_values
+# Testing a random GC value
+random_connection = np.random.randint(0,GC_data_df.shape[0])
+test_connection = GC_data_df.iloc[random_connection,:]
+i = np.where(Subject_id==test_connection["Subject_ID"])[0]
+e = np.where(np.array(eye_status)==test_connection["Eye_status"])[0]
+chx = np.where(np.array(ch_names)==test_connection["chx"])[0]
+chy = np.where(np.array(ch_names)==test_connection["chy"])[0]
+f = np.where(np.array(freq_bands_name)==test_connection["Freq_band"])[0]
+value = test_connection["Value"]
+if chx < chy: # the GC array is only lower diagonal to save memory
+    assert GC_data[0,i,e,chy,chx,f] == value
+if chx > chy:
+    assert GC_data[1,i,e,chx,chy,f] == value

LICENSE

+Copyright 2022 Qianliang Li
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.

Preamble.py

+# -*- coding: utf-8 -*-
+"""
+Updated Oct 18 2022
+
+@author: Qianliang Li (glia@dtu.dk)
+
+This preamble contains the code to load all the relevant libraries
+Refer to the requirements.txt for the specific versions used
+"""
+
+# Libraries
+import os
+import sys
+import re
+import warnings
+import time
+import pickle
+import concurrent.futures # for multiprocessing
+
+import numpy as np # Arrays and mathematical computations
+import matplotlib.pyplot as plt # Plotting
+import mne # EEG library
+import scipy # Signal processing
+import sklearn # Machine learning
+import nitime # Time series analysis
+import nolds # DFA exponent
+import statsmodels # multipletest
+import pysparcl # Sparse Kmeans
+import fooof # Peak Alpha Freq and 1/f exponents
+import pandas as pd # Dataframes
+import seaborn as sns # Plotting library
+import autoreject # Automatic EEG artifact detection
+import mlxtend # Sequential Forward Selection
+
+from mne.time_frequency import psd_multitaper
+from mne.preprocessing import (ICA, create_eog_epochs, create_ecg_epochs, corrmap)
+from mne.stats import spatio_temporal_cluster_test, permutation_cluster_test
+from mne.channels import find_ch_adjacency
+from mne.connectivity import spectral_connectivity
+
+import nitime.analysis as nta
+import nitime.timeseries as nts
+import nitime.utils as ntsu
+from nitime.viz import drawmatrix_channels, drawmatrix_channels_modified
+
+from sklearn import preprocessing
+from sklearn import manifold
+from sklearn.svm import LinearSVC, SVC
+from sklearn.decomposition import PCA
+from sklearn.ensemble import RandomForestClassifier
+from sklearn.tree import plot_tree
+from sklearn.neighbors import KNeighborsClassifier
+from sklearn.linear_model import LogisticRegression, Ridge, LassoCV, RidgeCV, LogisticRegressionCV
+from sklearn.model_selection import StratifiedKFold, GridSearchCV, StratifiedGroupKFold
+from sklearn.pipeline import Pipeline
+from sklearn.feature_selection import RFECV
+from sklearn.metrics import accuracy_score, confusion_matrix, classification_report, make_scorer
+
+import matplotlib.gridspec as gridspec
+from matplotlib import cm
+
+from statsmodels.tsa.stattools import adfuller
+from statsmodels.formula.api import mixedlm
+
+from autoreject import AutoReject
+
+from mlxtend.evaluate import permutation_test
+from mlxtend.feature_selection import SequentialFeatureSelector as SFS
+from mlxtend.plotting import plot_sequential_feature_selection as plot_sfs
+
+from tqdm import tqdm # progress bars
+from mayavi import mlab # Plotting with MNE
+from mpl_toolkits.mplot3d import Axes3D # registers 3D projections
+
+# Non-library scripts
+# EEG microstate package by von Wegner & Lauf, 2018
+from eeg_microstates import * # downloaded from https://github.com/Frederic-vW/eeg_microstates
+# minimum Redundancy Maximum Relevance script by Kiran Karra
+from feature_select import * # downloaded from https://github.com/stochasticresearch/featureselect/blob/master/python/feature_select.py
+
+plt.style.use('ggplot') # plotting style
+
+### Some of the functions in the libraries were modified by defining
+# modified functions in the respective .py files in the different libraries
+
+# Modified Kmeans in eeg_microstates
+# Modified T_empirical in eeg_microstates
+# Modified sparcl cluster_permute
+
+# # For eeg_microstates.py
+# def kmeans_return_all(data, n_maps, n_runs=10, maxerr=1e-6, maxiter=500):
+#     """Modified K-means clustering as detailed in:
+#     [1] Pascual-Marqui et al., IEEE TBME (1995) 42(7):658--665
+#     [2] Murray et al., Brain Topography(2008) 20:249--264.
+#     Variables named as in [1], step numbering as in Table I.
+
+#     Args:
+#         data: numpy.array, size = number of EEG channels
+#         n_maps: number of microstate maps
+#         n_runs: number of K-means runs (optional)
+#         maxerr: maximum error for convergence (optional)
+#         maxiter: maximum number of iterations (optional)
+#         doplot: plot the results, default=False (optional)
+#     Returns:
+#         maps: microstate maps (number of maps x number of channels)
+#         L: sequence of microstate labels
+#         gfp_peaks: indices of local GFP maxima
+#         gev: global explained variance (0..1)
+#         cv: value of the cross-validation criterion
+#     """
+#     n_t = data.shape[0]
+#     n_ch = data.shape[1]
+#     data = data - data.mean(axis=1, keepdims=True)
+
+#     # GFP peaks
+#     gfp = np.std(data, axis=1)
+#     gfp_peaks = locmax(gfp)
+#     gfp_values = gfp[gfp_peaks]
+#     gfp2 = np.sum(gfp_values**2) # normalizing constant in GEV
+#     n_gfp = gfp_peaks.shape[0]
+
+#     # clustering of GFP peak maps only
+#     V = data[gfp_peaks, :]
+#     sumV2 = np.sum(V**2)
+
+#     # store results for each k-means run
+#     cv_list =   []  # cross-validation criterion for each k-means run
+#     gev_list =  []  # GEV of each map for each k-means run
+#     gevT_list = []  # total GEV values for each k-means run
+#     maps_list = []  # microstate maps for each k-means run
+#     L_list =    []  # microstate label sequence for each k-means run
+#     for run in range(n_runs):
+#         # initialize random cluster centroids (indices w.r.t. n_gfp)
+#         rndi = np.random.permutation(n_gfp)[:n_maps]
+#         maps = V[rndi, :]
+#         # normalize row-wise (across EEG channels)
+#         maps /= np.sqrt(np.sum(maps**2, axis=1, keepdims=True))
+#         # initialize
+#         n_iter = 0
+#         var0 = 1.0
+#         var1 = 0.0
+#         # convergence criterion: variance estimate (step 6)
+#         while ( (np.abs((var0-var1)/var0) > maxerr) & (n_iter < maxiter) ):
+#             # (step 3) microstate sequence (= current cluster assignment)
+#             C = np.dot(V, maps.T)
+#             C /= (n_ch*np.outer(gfp[gfp_peaks], np.std(maps, axis=1)))
+#             L = np.argmax(C**2, axis=1)
+#             # (step 4)
+#             for k in range(n_maps):
+#                 Vt = V[L==k, :]
+#                 # (step 4a)
+#                 Sk = np.dot(Vt.T, Vt)
+#                 # (step 4b)
+#                 evals, evecs = np.linalg.eig(Sk)
+#                 v = evecs[:, np.argmax(np.abs(evals))]
+#                 maps[k, :] = v/np.sqrt(np.sum(v**2))
+#             # (step 5)
+#             var1 = var0
+#             var0 = sumV2 - np.sum(np.sum(maps[L, :]*V, axis=1)**2)
+#             var0 /= (n_gfp*(n_ch-1))
+#             n_iter += 1
+#         if (n_iter < maxiter):
+#             print("\t\tK-means run {:d}/{:d} converged after {:d} iterations.".format(run+1, n_runs, n_iter))
+#         else:
+#             print("\t\tK-means run {:d}/{:d} did NOT converge after {:d} iterations.".format(run+1, n_runs, maxiter))
+
+#         # CROSS-VALIDATION criterion for this run (step 8)
+#         C_ = np.dot(data, maps.T)
+#         C_ /= (n_ch*np.outer(gfp, np.std(maps, axis=1)))
+#         L_ = np.argmax(C_**2, axis=1)
+#         var = np.sum(data**2) - np.sum(np.sum(maps[L_, :]*data, axis=1)**2)
+#         var /= (n_t*(n_ch-1))
+#         cv = var * (n_ch-1)**2/(n_ch-n_maps-1.)**2
+
+#         # GEV (global explained variance) of cluster k
+#         gev = np.zeros(n_maps)
+#         for k in range(n_maps):
+#             r = L==k
+#             gev[k] = np.sum(gfp_values[r]**2 * C[r,k]**2)/gfp2
+#         gev_total = np.sum(gev)
+
+#         # store
+#         cv_list.append(cv)
+#         gev_list.append(gev)
+#         gevT_list.append(gev_total)
+#         maps_list.append(maps)
+#         L_list.append(L_)
+
+#     # select best run
+#     k_opt = np.argmin(cv_list)
+#     #k_opt = np.argmax(gevT_list)
+#     maps = maps_list[k_opt]
+#     # ms_gfp = ms_list[k_opt] # microstate sequence at GFP peaks
+#     gev = gev_list[k_opt]
+#     L_ = L_list[k_opt]
+#     # lowest cv criterion
+#     cv_min = np.min(cv_list)
+
+#     return maps, L_, gfp_peaks, gev, cv_min
+
+# # For eeg_microstates.py
+# def T_empirical(data, n_clusters, gap_idx = []):
+#     """Modified empirical transition matrix to take gap_idx argument
+
+#     Args:
+#         data: numpy.array, size = length of microstate sequence
+#         n_clusters: number of microstate clusters
+#         gap_idx: index for gaps in data which should be excluded in T
+#     Returns:
+#         T: empirical transition matrix
+#     """
+#     T = np.zeros((n_clusters, n_clusters))
+#     n = len(data)
+#     for i in range(n-1):
+#         # Do not count transitions between gaps in data
+#         if i in gap_idx:
+#             continue
+#         else:
+#             T[data[i], data[i+1]] += 1.0
+#     p_row = np.sum(T, axis=1)
+#     for i in range(n_clusters):
+#         if ( p_row[i] != 0.0 ):
+#             for j in range(n_clusters):
+#                 T[i,j] /= p_row[i]  # normalize row sums to 1.0
+#     return T    
+
+# # From sparcl.cluster.permute
+# def permute_modified(x, k=None, nperms=25, wbounds=None, nvals=10, centers=None,
+#             verbose=False):
+#     # I added sdgaps output
+#     n, p = x.shape
+#     if k is None and centers is None:
+#         raise ValueError('k and centers are None.')
+#     if k is not None and centers is not None:
+#         if centers.shape[0] != k or centers.shape[1] != p:
+#             raise ValueError('Invalid shape of centers.')
+#     if wbounds is None:
+#         wbounds = np.exp(
+#             np.linspace(np.log(1.2), np.log(np.sqrt(p) * 0.9), nvals))
+#     if wbounds.min() <= 1 or len(wbounds) < 2:
+#         raise ValueError('len(wbounds) and each wbound must be > 1.')
+
+#     permx = np.zeros((nperms, n, p))
+#     nnonzerows = None
+#     for i in range(nperms):
+#         for j in range(p):
+#             permx[i, :, j] = np.random.permutation(x[:, j])
+#     tots = None
+#     out = kmeans(x, k, wbounds, centers=centers, verbose=verbose)
+
+#     for i in range(len(out)):
+#         nnonzerows = utils._cbind(nnonzerows, np.sum(out[i]['ws'] != 0))
+#         bcss = subfunc._get_wcss(x, out[i]['cs'])[1]
+#         tots = utils._cbind(tots, np.sum(out[i]['ws'] * bcss))
+#     permtots = np.zeros((len(wbounds), nperms))
+#     for i in range(nperms):
+#         perm_out = kmeans(
+#             permx[i], k, wbounds, centers=centers, verbose=verbose)
+#         for j in range(len(perm_out)):
+#             perm_bcss = subfunc._get_wcss(permx[i], perm_out[j]['cs'])[1]
+#             permtots[j, i] = np.sum(perm_out[j]['ws'] * perm_bcss)
+    
+#     sdgaps = np.std(np.log(permtots),axis=1)
+#     gaps = np.log(tots) - np.log(permtots).mean(axis=1)
+#     bestw = wbounds[gaps.argmax()]
+#     out = {'bestw': bestw, 'gaps': gaps, 'sdgaps': sdgaps, 'wbounds': wbounds,
+#            'nnonzerows': nnonzerows}
+#     return out
\ No newline at end of file

Preprocessing.py

+# -*- coding: utf-8 -*-
+"""
+Updated Oct 18 2022
+
+@author: Qianliang Li (glia@dtu.dk)
+
+The following preprocessing steps were employed:
+    1. Load the data
+    2. 1-100Hz Bandpass filtering
+    3. 50Hz Notch filtering
+    4. Retrieving event information about eyes open/closed states
+    5. Epoching to 4s non-overlapping segments
+    6. Visual inspection of the data
+        Bad channels and non-ocular artifacts are removed
+    7. Robust re-reference to common average (without bad channels)
+    8. Interpolation of bad channels
+    9. ICA artifact removal of ocular and ECG artifacts
+    10. AutoReject guided final visual inspection
+
+Due to privacy issues of clinical data, our data is not publically available.
+For demonstration purposes, I am using a publically available EEG dataset
+and treating it as resting-state eyes open/closed
+Link to the demonstration data: www.bci2000.org
+"""
+
+# Set working directory
+import os
+wkdir = "/home/glia/EEG"
+os.chdir(wkdir)
+
+# Load all libraries from the Preamble
+from Preamble import *
+
+# To demonstrate the script, a publically available EEG dataset are used
+# EEG recordings from 2 subjects are used as an example
+# The EEGBCI200 is task based, but we will treat it as "resting-state"
+# And the 2 runs as Eyes Closed and Eyes Open
+n_subjects = 2
+Subject_id = [1,2]
+# Download and get filenames
+from mne.datasets import eegbci
+files = []
+for i in range(n_subjects):
+    raw_fnames = eegbci.load_data(Subject_id[i], [1,2]) # The first 2 runs
+    files.append(raw_fnames)
+
+# # Original code to get filenames in a folder
+# data_path = "EEG_folder"
+# # Get filenames
+# files = []
+# for r, d, f in os.walk(data_path):
+#     for file in f:
+#         if ".bdf" in file:
+#             files.append(os.path.join(r, file))
+
+# Eye status
+anno_to_event = {'Eyes Closed': 1, 'Eyes Open': 2} # manually defined event id
+eye_status = list(anno_to_event.keys())
+n_eye_status = len(eye_status)
+
+# Epoch settings
+epoch_len = 4 # length of epochs in seconds
+n_epochs_trial = int(60/epoch_len) # number of epochs in a trial
+n_trials = 2 # 1 eyes closed followed by 1 eyes open
+
+# Montage settings
+montage = mne.channels.make_standard_montage('standard_1005')
+#montage = mne.channels.read_custom_montage(filename) # custom montage file
+
+# %% Load, filter and epoch (Steps 1 to 5)
+# Pre-allocate memory
+epochs = [0]*n_subjects
+for i in range(n_subjects):
+    # MNE python supports many EEG formats. Make sure to use the proper one
+    raw = mne.io.concatenate_raws([mne.io.read_raw_edf(f, preload=True) for f in files[i]])
+    # Fix EEGBCI channel names
+    eegbci.standardize(raw)
+    # Set montage
+    raw.set_montage(montage)
+    # Only use the EEG channels
+    raw.pick_types(meg=False, eeg=True, stim=False)
+    # Bandpass filter (will also detrend, median = 0)
+    raw.filter(1, 70, fir_design="firwin", verbose=0) # Due to sfreq = 160 I cannot lowpass at 100Hz
+    # raw.filter(1, 100, fir_design="firwin", verbose=0) # original line
+    # Notch filter to remove power-line noise (50Hz is common in Europe)
+    raw.notch_filter(50, fir_design="firwin", verbose=0)
+    # Epoch to 4 sec
+    # The first 60s are treated as Eyes Closed and following 60s as Eyes Open
+    event = np.zeros((int(2*n_epochs_trial),3), dtype=int) # manually make event array (n_events,3)
+    event[:,0] = np.array(np.linspace(0,2*60-epoch_len,int(2*n_epochs_trial))*int(raw.info["sfreq"]), dtype=int) # first column, the time for events
+    # Hardcoded based on data format
+    event[:n_epochs_trial,2] = 1 # Eyes closed
+    event[n_epochs_trial:,2] = 2 # Eyes open
+    # Make the epochs. (The -1/int(raw[n].info["sfreq"]) is needed because python start with 0, so 30000 points is 0 to 29999
+    epochs[i] = mne.Epochs(raw, event, event_id=anno_to_event,
+                 tmin=0, tmax=epoch_len-1/int(raw.info["sfreq"]),baseline=None, verbose=0).load_data()
+    
+    print("Subject:{} finished epoching ({}/{})".format(Subject_id[i],i+1,n_subjects))
+
+# Compute the number of epochs in each trial
+n_epochs = pd.DataFrame(np.zeros((n_subjects,n_trials)))
+for i in range(n_subjects):
+    for t in range(n_trials):
+        try:
+            n_epochs_ec = len(epochs[i][t:int((t+1)*n_epochs_trial)][eye_status[0]])
+        except:
+            n_epochs_ec = 0
+        try: 
+            n_epochs_eo = len(epochs[i][t:int((t+1)*n_epochs_trial)][eye_status[1]])
+        except:
+            n_epochs_eo = 0
+        n_epochs.iloc[i,t] = np.max([n_epochs_ec,n_epochs_eo])
+# Calculate cumulative sum which is used for later indexing
+cumsum_n_epochs = np.cumsum(n_epochs, axis=1)
+# Insert 0 as first column
+cumsum_n_epochs.insert(0,"Start",0)
+
+# %% First visual inspection, re-referencing and ch interpolation (Steps 6 to 8)
+# When in doubt, I did not exclude the data
+# Ocular artifacts are not removed, as we will use ICA to correct for those
+# Bad epochs are dropped
+# Bad channels are removed and interpolated on a trial basis
+# i.e. for each 1min eyes open or eyes closed trial
+
+# Visualize each
+epochs[0].plot(scalings=200e-6, n_epochs=15, n_channels=24)
+epochs[1].plot(scalings=200e-6, n_epochs=15, n_channels=24)
+
+# Pre-allocate memory
+bad_channels = [0]*len(epochs)
+bad_epochs = [0]*len(epochs)
+
+# Manually found bad data segments
+#bad_channels[0] = [0] # If all trials are fine I do not make a line with bad channels
+bad_epochs[0] = [6] # Epoch 6
+bad_channels[1] = ["T7",0] # T7 is bad in first eyes closed trial
+bad_epochs[1] = [12,13] # 2 bad epochs
+
+# Cautionary note: bad_epochs are using index. Not the epoch number in MNE-viewer
+# They are often the same, but not always, like in this demonstration
+# where there are no Epoch 15 because it was not full length data due to
+# the way I defined the event times, so when you drop Epoch idx 15, it is the
+# epoch that MNE labeled as 16 in this example!
+
+# Pre-allocate memory
+cleaned_epochs = epochs.copy()
+
+# Interpolate bad channels and re-reference to robust common average
+bad_ch_counter = 0 # count how many bad channels for summary
+bad_ch_idx = np.array(bad_channels,dtype=object).nonzero()[0]
+for i in range(len(bad_ch_idx)):
+    n = bad_ch_idx[i]
+    n_epochs_trial = int(60/epoch_len)
+    # Get epoch number for each subject
+    epoch_number = np.arange(0,len(epochs[n]))
+    # Pre-allocate memory
+    temp_epochs = [0]*n_trials
+    for trial in range(n_trials):
+        # Retrieve trial
+        trial_idx = (epoch_number >= cumsum_n_epochs.iloc[n,trial]) & (epoch_number < cumsum_n_epochs.iloc[n,trial+1])
+        temp_epochs[trial] = epochs[n].copy().drop(np.invert(trial_idx))
+        # Set bad channel
+        trial_bad_ch = bad_channels[bad_ch_idx[i]][trial]
+        if trial_bad_ch == 0:
+            # Do not perform interpolation, only re-referencing to average
+            temp_epochs[trial].set_eeg_reference(ref_channels="average", verbose=0)
+        else:
+            if type(trial_bad_ch) == str: # fix if only one ch is provided
+                trial_bad_ch = [trial_bad_ch] # make it to list
+            temp_epochs[trial].info["bads"] = trial_bad_ch
+            # Re-reference to Cz
+            temp_epochs[trial].set_eeg_reference(ref_channels="average", verbose=0)
+            # Interpolate the bad channels
+            temp_epochs[trial].interpolate_bads(reset_bads=True)
+            # Increase counter
+            bad_ch_counter += len(trial_bad_ch)
+    # Concatenate temporary epoch and save
+    cleaned_epochs[n] = mne.concatenate_epochs(temp_epochs, add_offset=False)
+    # Notice that an offset is still added when using to_data_frame!
+
+# Re-reference all other data (that did not have bad channels) to common avg
+good_ch_idx = np.where(np.array(bad_channels,dtype=object) == 0)[0]
+for i in range(len(good_ch_idx)):
+    n = good_ch_idx[i]
+    cleaned_epochs[n].set_eeg_reference(ref_channels="average", verbose=0)
+
+# Drop bad epochs
+bad_epoch_counter = 0
+bad_epochs_idx = np.array(bad_epochs,dtype=object).nonzero()[0]
+for i in range(len(bad_epochs_idx)):
+    n = bad_epochs_idx[i]
+    subject_bad_epochs = bad_epochs[n]
+    cleaned_epochs[n].drop(subject_bad_epochs)
+    bad_epoch_counter += len(subject_bad_epochs)
+
+# Summarize how many bad channels and epochs there were manually defined
+(bad_ch_counter/(n_trials*epochs[0].info["nchan"]*n_subjects))*100 # 0.4% bad channels
+(bad_epoch_counter/(141+150*(n_subjects-1)))*100 # 1% bad epochs rejected
+
+
+# %% ICA is performed to remove eye blinks, ECG and EOG artifacts
+# Make list to contain all ICAs
+ica = [0]*len(cleaned_epochs)
+# Make ICA objects
+for n in range(len(cleaned_epochs)):
+    # Matrix rank is -1 because I used common average reference
+    # If any channels were interpolated the rank is further reduced
+    if any([i in [n] for i in bad_ch_idx]):
+        inter_pol_ch = [i for i in bad_channels[n] if i != 0] # remove all 0
+        # Make a flat list to use np.unique
+        flat_list = []
+        for sublist in inter_pol_ch:
+            if type(sublist) == str: # fix if only one ch is provided
+                sublist = [sublist]
+            for item in sublist:
+                flat_list.append(item)
+        n_inter_pol_ch = len(np.unique(flat_list))
+        matrix_rank = cleaned_epochs[n].info["nchan"]-1-n_inter_pol_ch
+    else:
+        matrix_rank = cleaned_epochs[n].info["nchan"]-1
+
+    ica[n] = mne.preprocessing.ICA(method="fastica", random_state=42, verbose=0,
+                                       max_iter=500, n_components=matrix_rank)
+    ica[n].fit(cleaned_epochs[n])
+    print("{} out of {} ICAs processed".format(n+1,len(cleaned_epochs)))
+
+# Plot the components for visual inspection
+def ica_analysis(n):
+    plt.close("all")
+    # Plot original
+    cleaned_epochs[n].plot(scalings=200e-6, n_epochs = 10)
+    # Plot ICA - compontents
+    ica[n].plot_sources(cleaned_epochs[n], start = 0, stop = 10)
+    ica[n].plot_sources(cleaned_epochs[n], start = 5, stop = 8) # zoomed in helps for ECG artifact recognition
+    ica[n].plot_components(picks=np.arange(0,20))
+
+# Manual ICA decomposition visualization
+n = 1; ica_analysis(n) # manually change n
+
+# # Plot specific component for further inspection of the marked artifacts
+# ica[n].plot_properties(cleaned_epochs[n], picks = artifacts[n])
+
+# Pre-allocate memeory
+artifacts = [0]*len(cleaned_epochs)
+# Manually determine artifacts
+artifacts[0] = [0, 5, 12] # eye blinks, eye blinks, eye movement
+artifacts[1] = [0, 2] # eye blinks, eye movement
+
+# Remove the artifact components from the signal
+corrected_epochs = cleaned_epochs.copy()
+
+for n in range(len(cleaned_epochs)):
+    # Define the components with artifacts    
+    ica[n].exclude = artifacts[n]
+    # Remove on corrected data
+    ica[n].apply(corrected_epochs[n].load_data())
+
+# Inspect how the ICA worked
+n=0; corrected_epochs[n].plot(scalings=200e-6, n_epochs = 10)
+
+# %% Detect bad epochs automatically using AutoReject
+"""
+AutoReject will use cross-validation to determine optimal Peak-to-Peak threshold
+This threshold will be determined for each channel for each subject
+The threshold is used to mark whether each ch and epoch are bad
+Interpolation is performed on bad epoch/ch segments
+If many neighboring ch are bad, then the algorithm will score the worst ch
+(based on peak-to-peak amplitude) and only interpolate the worst
+If too many ch in one epoch are bad, the epoch will be rejected
+
+I am not using Autoreject directly to interpolate, but as a guide.
+The marked bad ch and epochs are then manually inspected and determined
+whether they should be dropped or not.
+The algorithm is run for each eye status separately
+"""
+
+# Suppress plots
+# import matplotlib
+# matplotlib.use("Agg")
+
+save_path = "./Autoreject_overview" # for autoreject overview
+# Pre-allocate memory
+reject_log = [0]*len(corrected_epochs)
+dropped_epochs = [0]*len(corrected_epochs)
+ar = [0]*len(corrected_epochs)
+mean_threshold = [0]*len(corrected_epochs)
+for i in range(len(corrected_epochs)):
+    reject_log0 = [0]*n_eye_status
+    ar0 = [0]*n_eye_status
+    mean_threshold0 = [0]*n_eye_status
+    drop_epochs0 = [0]*n_eye_status
+    for e in range(n_eye_status):
+        ee = eye_status[e]
+        # Initialize class
+        ar0[e] = AutoReject(consensus=np.linspace(0,1,11), cv=10, n_jobs=8,
+                            verbose=False, random_state=42)
+        # Fit to data - but do not transform
+        ar0[e].fit(corrected_epochs[i][ee])
+        # Get rejection log
+        reject_log0[e] = ar0[e].get_reject_log(corrected_epochs[i][ee])
+        # Plot and save Autorejected epochs
+        fig = reject_log0[e].plot(orientation="horizontal", show=False)
+        fig.savefig(os.path.join(save_path,"AR_" + str(Subject_id[i]) + "_" + str(ee) + ".png"))
+        # Close figure window
+        plt.close(fig)
+        # Save mean peak-to-peak voltage threshold used
+        mean_threshold0[e] = np.mean(list(ar0[e].threshes_.values()))
+        # Save suggested dropped epochs
+        drop_epochs0[e] = reject_log0[e].bad_epochs
+    # Concatenate dropped epochs
+    drop_epochs1 = np.concatenate(drop_epochs0)
+    # Save
+    dropped_epochs[i] = drop_epochs1.nonzero()[0]
+    reject_log[i] = reject_log0
+    ar[i] = ar0
+    mean_threshold[i] = mean_threshold0
+    print("{} out of {} subjects finished autorejecting".format(i+1,len(corrected_epochs)))
+
+# Overview of dropped epochs
+Drop_epochs_df = pd.DataFrame.from_records(dropped_epochs) # convert to dataframe
+Drop_epochs_df.insert(0, "Subject_id", Subject_id)
+
+# Re-enable plots
+# import matplotlib.pyplot as plt
+# %matplotlib qt
+
+print(Drop_epochs_df) # no further bad epochs after ICA
+# But for demonstration purposes we will add one more bad epochs in subject 2
+
+### Dropped epochs are used as guide to manually inspect potential thresholded bad epochs
+# Visualize
+n=1 ; corrected_epochs[n].plot(scalings=100e-6, n_channels=31, n_epochs=15)
+
+bad_epochs_ar = dropped_epochs # make copy before modifying
+# Manually modify when appropriate
+# n = 0 - agreed to all
+bad_epochs_ar[1] = np.array([8], dtype="int64") # added 1 more than suggested
+# n = 1: T7 is an outlier and bad
+
+# Combine dropped epochs from first visual inspection and Autoreject
+bad_epochs_comb = [0]*len(corrected_epochs)
+for i in range(len(corrected_epochs)):
+    # Retrieve bad epochs from first manual inspection
+    bad1 = np.array(bad_epochs[i])
+    # If there are no dropped epochs from first inspection, just use second
+    if type(bad_epochs[i]) == int:
+        bad_epochs_comb[i] = bad_epochs_ar[i]
+        continue
+    else:
+        # Retrieve bad epochs from manual of AR
+        bad2 = bad_epochs_ar[i].copy()
+        # Fix index due to iterative dropped epoch
+        # E.g. if 45 is dropped, then all epochs above 45 will have 1 index lower and should be fixed
+        for drops in range(len(bad1)):
+            bad2[bad2 >= bad1[drops]] += 1
+        # Concatenate from both
+        bad_epochs_comb[i] = np.sort(np.concatenate([bad1,bad2]))
+
+# Convert to dataframe
+bad_epochs_comb_df = pd.DataFrame.from_records(bad_epochs_comb)
+bad_epochs_comb_df.insert(0, "Subject_ID", Subject_id)
+# Save
+bad_epochs_comb_df.to_pickle("./Preprocessing/dropped_epochs.pkl")
+
+# Drop bad epochs
+final_epochs = corrected_epochs.copy()
+bad_epochs_df = pd.DataFrame.from_records(bad_epochs_ar)
+bad_epoch_counter2 = 0
+bad_epochs_idx2 = np.where(bad_epochs_df.iloc[:,0].notnull())[0]
+for i in range(len(bad_epochs_idx2)):
+    n = bad_epochs_idx2[i]
+    subject_bad_epochs = bad_epochs_ar[n]
+    final_epochs[n].drop(subject_bad_epochs)
+    bad_epoch_counter2 += len(subject_bad_epochs)
+
+# Summarize how many bad channels and epochs there were manually defined
+(bad_epoch_counter2+bad_epoch_counter)/(141+150*(n_subjects-1))*100 # in total 1.37% epochs rejected
+
+# Re-reference and interpolate
+def re_reference_interpolate(input_epochs, n, bads):
+    # Re-reference to Cz from average
+    input_epochs[n].set_eeg_reference(ref_channels=["Cz"], verbose=0)
+    # Set bads
+    input_epochs[n].info["bads"] = bads
+    # Re-reference to average without bads
+    input_epochs[n].set_eeg_reference(ref_channels="average", verbose=0)
+    # Interpolate
+    input_epochs[n].interpolate_bads(reset_bads=True)
+
+re_reference_interpolate(final_epochs, 1, ["T7"]) # n = 1
+
+# Save all bad channels from first visual inspection and autorejection guided
+bad_channels[1] = ["T7"]*n_trials
+# To keep track of which channels were interpolated
+with open("./Preprocessing/bad_ch.pkl", "wb") as filehandle:
+    pickle.dump(bad_channels, filehandle)
+
+
+# %% Save the preprocessed epochs
+save_path = "./PreprocessedData"
+for n in range(len(corrected_epochs)):
+    final_epochs[n].save(fname = os.path.join(save_path,str("{}_preprocessed".format(Subject_id[n]) + "-epo.fif")),
+                    overwrite=True, verbose=0)
+
+# %% Evaluate dropped epochs to determine threshold for exclusion
+dropped_epochs_df = np.load("./Preprocessing/dropped_epochs.pkl", allow_pickle=True)
+
+# Convert the df to number of dropped epochs
+# In the original data I had multiple datasets and combined the dropped df here
+All_drop_epoch_df = dropped_epochs_df # originally using pd.concat
+
+def drop_epoch_counter(row,df_row):
+    res = np.sum(df_row.iloc[row,1:].notnull())
+    return res
+
+Number_dropped_epochs = [0]*All_drop_epoch_df.shape[0]
+for i in range(All_drop_epoch_df.shape[0]):
+    Number_dropped_epochs[i] = drop_epoch_counter(i,All_drop_epoch_df)
+
+All_drop_epoch_df2 = pd.DataFrame({"Subject_ID":All_drop_epoch_df["Subject_ID"],
+                                   "Number_drop_epoch":Number_dropped_epochs})
+
+# Plot histogram
+bin_seq = range(0,np.max(All_drop_epoch_df2["Number_drop_epoch"])+1)
+All_drop_epoch_df2.hist(column="Number_drop_epoch",figsize=(12,8),bins=bin_seq)
+
+# View all subjects with more than 15 dropped epochs
+All_drop_epoch_df2.loc[All_drop_epoch_df2["Number_drop_epoch"]>=15,:]
+# Number of dropped subjects using above 30 as cutoff
+len(list(All_drop_epoch_df2.loc[All_drop_epoch_df2["Number_drop_epoch"]>30,"Subject_ID"]))
+# Using cutoff for exclusion: 20% or more dropped epochs

README.md

-# Sample GitLab Project
+# Resting-state EEG analysis
 
+This repository contains the code used to analyze the data that supports the findings from the following publication:
+
+Qianliang Li, Maya Coulson Theodorsen, Ivana Konvalinka, Kasper Eskelund, Karen-Inge Karstoft, Søren Bo Andersen and Tobias S Andersen. Resting-state EEG functional connectivity predicts post-traumatic stress disorder subtypes in veterans. Journal of Neural Engineering, 2022 (https://doi.org/10.1088/1741-2552/ac9aaf).
+
+The code consist of 4 python script files, which covers different steps fo the analysis framework:
+1. Preamble
+2. Preprocessing
+3. Feature Estimation
+4. Machine Learning
+
+A requirement.txt file with the library versions employed for the analysis in the study.
+
+And the parcellation file used for source localization.
+
+The data is not publicly available due to privacy issues of clinical data, so the preprocessing script was modified for demonstration on a publically available EEG dataset, however the feature estimation and machine learning scripts were kept original. Hence the scripts might not run perfectly with the demonstration EEG files, and are provided as is for reference.

requirements.txt

+numpy==1.18.1
+matplotlib==3.1.3
+mne==0.22.0
+scipy==1.4.1
+nitime==0.8.1
+nolds==0.5.2
+statsmodels==0.11.1
+spm1d==0.4.2
+pysparcl==1.4.1
+fooof==1.0.0
+pandas==1.0.3
+seaborn==0.10.1
+pingouin==0.3.11
+sklearn==0.24.2
+autoreject==0.2.1
+mlxtend==0.17.0
+mayavi==4.7.1
\ No newline at end of file