# -*- 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