Chapter 15: Classification of Time- Embedded EEG Using Short-Time Principal Component Analysis by Nguyen Duc Thang 5/2009

Outline Part one  Introduction  Principal Component Analysis (PCA)  Signal Fraction Analysis (SFA)  EEG signal representation  Short time PCA Part two  Classifier  Experimental setups, results, and analysis

Introduction Feature extraction Classification PCA, SFA, Short time PCA LDA, SVM

Outline Part one  Introduction  Principal Component Analysis (PCA)  Signal Fraction Analysis (SFA)  EEG signal representation  Short time PCA Part two  Classifier  Experimental setups, results, and analysis

Projection w1w1 x

w1w1 w2w2 x d basic vectors reduce dimension

Principal Component Analysis (PCA) Motivation: Reduce dimension + minimum information loss. W = ? w w w O

Principal Component Analysis w hihi hihi constant O Minimize projection errors Maximize variations

Principal Component Analysis - w i is the eigenvector of the covariance matrix C x - Among D eigenvectors of C x, choose d<D eigenvectors - W=[w 1,w 2,…,w d ] T is projection matrix, reduce dimension D → d w1w1 w2w2

Outline Part one  Introduction  Principal Component Analysis (PCA)  Signal Fraction Analysis (SFA)  EEG signal representation  Short time PCA Part two  Classifier  Experimental setups, results, and analysis

Signal Fraction Analysis (SFA)

Signal Fraction Analysis Assumption: The source signals are uncorrelated Algorithm

Results

Comparison between SFA and ICA Correlation between estimated sources and ground truths - SFA: suitable for small sample size, fast computation - ICA: suitable for large sample size

Extract basic vectors by SFA W SFA x W PCA x

Outline Part one  Introduction  Principal Component Analysis (PCA)  Signal Fraction Analysis (SFA)  EEG signal representation  Short time PCA Part two  Classifier  Experimental setups, results, and analysis

Feature extraction Classification

EEG signal representation (Feature extraction) Raw feature Time-embedded feature r EEG channels l+1 More temporal information

Extract PCA features Training data (embedded space) D=r(l+1) N samples PCA d basic vectors form projection matrix W PCA D W PCA X = d PCA features (d X D) Time-embedded features

Extract SFA features Training data (embedded space) D=r(l+1) N samples SFA d basic vectors form projection matrix W SFA D W SFA X = d SFA features (d X D) Time-embedded features

Outline Part one  Introduction  Principal Component Analysis (PCA)  Signal Fraction Analysis (SFA)  EEG signal representation  Short time PCA Part two  Classifier  Experimental setups, results, and analysis

The shortcomings of conventional PCA projection line Not good for large number of samples

Short time PCA approach Apply PCA on short durations

Extract short time PCA features D Time-embedded features h D h window PCA n basic vectors D n stack Short time PCA features D X n

Next Part one  Introduction  Principal Component Analysis (PCA)  Signal Fraction Analysis (SFA)  EEG signal representation  Short time PCA Part two  Classifier  Experimental setups, results, and analysis