Primary Component Analysis

Initialize NeuroAnalyzer 
using NeuroAnalyzer
eeg = load("files/eeg.hdf")

Primary Component Analysis PCA is a statistical method that transforms a set of correlated variables (e.g., EEG channels) into a smaller set of uncorrelated variables called principal components (PCs).

PCA identifies patterns in data based on variance, helping to reduce dimensionality while preserving important information.

Key Steps in PCA for EEG

  1. Data Standardization:
  • EEG data is standardized (mean-centered and scaled) to ensure each channel contributes equally.
  1. Covariance Matrix Calculation:
  • Compute the covariance matrix to understand how EEG channels vary together.
  1. Eigenvalue Decomposition:
  • Decompose the covariance matrix to obtain eigenvalues (variance explained by each PC) and eigenvectors (directions of maximum variance).
  1. Component Selection:
  • Select the top PCs that capture the most variance (e.g., first 3–5 components).
  1. Projection:
  • Project the original EEG data onto the selected PCs to reduce dimensionality.

Why Use PCA for EEG?

  • Dimensionality Reduction: Reduces the number of features (channels) while retaining most of the signal’s variance.
  • Noise Reduction: Helps filter out noise by focusing on components with high variance.
  • Feature Extraction: Identifies dominant patterns in EEG data, useful for classification or visualization.
  • Computational Efficiency: Speeds up further analysis by working with fewer components.

PCA vs. ICA in EEG

Feature PCA ICA
Goal Maximize variance Maximize statistical independence
Components Uncorrelated (orthogonal) Independent (non-Gaussian)
Use Case Dimensionality reduction Artifact removal, source separation

Applications in EEG

  • Preprocessing: Reduce EEG data dimensionality before machine learning.
  • Visualization: Plot EEG data in lower-dimensional space (e.g., 2D/3D).
  • Artifact Mitigation: Combine with ICA for better artifact removal.

Generating PCA:

pc, pc_var, pc_m, pc_model = pca_decompose(eeg;
                                           ch = "eeg",
                                           n = 10)

Viewing components variance:

plot_bar(vec(pc_var);
         glabels = string.(1:10),
         xlabel = "Component",
         ylabel = "% of total variance")