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 Feature extraction Classification PCA, SFA, Short time PCA 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 w1w1 x

6. w1w1 w2w2 x d basic vectors reduce dimension

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

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

9. 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

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

15. Extract basic vectors by SFA W SFA x W PCA x

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 Classification

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

19. 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

20. 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

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

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