Upload New File

Perform_pca.py

+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Sun Sep  1 15:27:56 2024
+
+@author: Maya Coulson Theodorsen (mcoth@dtu.dk)
+
+
+This script performs Principal Component Analysis (PCA) on standardized data.
+
+It includes:
+- Bartlett's test for sphericity to check PCA suitability.
+- Kaiser-Meyer-Olkin (KMO) measure for sampling adequacy.
+- PCA scree plot visualization and explained variance analysis.
+- Calculation of PCA loadings and transformed data.
+
+Functions:
+- perform_pca: Performs PCA and diagnostic tests.
+
+Returns:
+- pca (PCA fitted model)
+- loadings (PCA loadings for each feature and component)
+- principleComponents 
+
+"""
+import pandas as pd
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn.decomposition import PCA
+from factor_analyzer.factor_analyzer import calculate_bartlett_sphericity, calculate_kmo
+
+def perform_pca(std_data, PCAcolumns, columnNames):
+
+    # Bartlett sphericity to check if suitable for PCA    
+    chi_square_value, p_value = calculate_bartlett_sphericity(std_data)
+    print("Bartlett's sphericity chi-square:", chi_square_value)
+    print(f"p_value: {p_value:.30f}")
+
+
+    # Kaiser-Meyer-Olkin(KMO) Test for sampling accuracy (0.8-1.0 is excellent)
+    # Test if data is appropriate for FA/PCA
+    kmo_all, kmo_model = calculate_kmo(std_data)
+    print("KMO model:", kmo_model)
+
+
+    # PCA (note: variance in eigenvalues, not percentage)
+    pca = PCA()
+    principleComponents = pd.DataFrame(pca.fit_transform(std_data))
+    
+    # Bar plot of the variances of PCA features
+    features = range(pca.n_components_)
+    plt.subplots(figsize=(20,15)) 
+    plt.bar(features, pca.explained_variance_)
+    plt.xticks(features)
+    plt.ylabel('Eigenvalue', fontsize=16)
+    plt.xlabel('PCA feature', fontsize=16)
+    plt.axhline(y=1, linewidth=2, color='r')
+    plt.title('Scree plot', fontsize=30)
+    plt.show()
+
+    # Display the actual amount of explained variance per component 
+    print('PCA explained variance:')
+    print(pca.explained_variance_)
+    
+    # Print the ratios of percentage explained by each feature
+    print('PCA explained variance ratio:')
+    print(pca.explained_variance_ratio_)
+
+    # Cumulative summation of the ratio explained variance of each feature
+    print('PCA explained variance ratio cumulative summation:')
+    print(pca.explained_variance_ratio_.cumsum())
+    
+    # Loadings for each PC
+    loadings = pd.DataFrame(pca.components_.T * np.sqrt(pca.explained_variance_))
+    loadings.columns = PCAcolumns
+    loadings.index = [columnNames]
+    
+    return pca, loadings, principleComponents
\ No newline at end of file