Chapter 15: Classification of Time-Embedded EEG Using Short-Time Principal Component Analysis

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

2. 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

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

4. 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

5. Projection x w1

6. Projection x w1 w2 dbasic vectors reduce dimension

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

8. Principal Component Analysis w hi Minimize projection errors hi Maximize variations constant O

9. Principal Component Analysis • wi is the eigenvector of the covariance matrix Cx • Among D eigenvectors of Cx, choose d<D eigenvectors • W=[w1,w2,…,wd]T is projection matrix, reduce dimension D → d w1 w2

10. 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

11. Signal Fraction Analysis (SFA)

12. Signal Fraction Analysis • Assumption: The source signals are uncorrelated • Algorithm

13. Results

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

15. Extract basic vectors by SFA WPCAx WSFAx

16. 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

17. Feature extraction Feature extraction Classification

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

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

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

21. 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

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

23. Short time PCA approach Apply PCA on short durations

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

25. 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