(PCA) principal component analysis Analysis

Information about principal component analysis

1. Principal Component Analysis Principal Component Analysis
(PCA)(PCA)

2. Principal Component Analysis Principal Component Analysis
(PCA)(PCA)

3. Principal Component Analysis Principal Component Analysis
(PCA)(PCA)

4. Principal Component Analysis Principal Component Analysis
(PCA)(PCA)

5. Principal Component Analysis Principal Component Analysis
(PCA)(PCA)

6. Principal Component Analysis Principal Component Analysis
(PCA)(PCA)

7. Principal Component Analysis Principal Component Analysis
(PCA)(PCA)

8. Principal Component Analysis Principal Component Analysis
(PCA)(PCA)

9. Principal Component Analysis Principal Component Analysis
(PCA)(PCA)

10. Principal Component Analysis Principal Component Analysis
(PCA)(PCA)

11. Alternative Derivation Alternative Derivation
(PCA)(PCA)

12. Alternative Derivation Alternative Derivation
(PCA)(PCA)

13. Alternative Derivation Alternative Derivation
(PCA)(PCA)

14. Alternative Derivation Alternative Derivation
(PCA)(PCA)

15. Singular Value DecompositionSingular Value Decomposition

16. Singular Value DecompositionSingular Value Decomposition

17. Singular Value DecompositionSingular Value Decomposition

18. Example 1Example 1
•Use the data set "noisy.mat" available on
your CD. The data set consists of 1965,
20-pixel-by-28-pixel grey-scale images
distorted by adding Gaussian noises to
each pixel with s=25.

19. Example 1Example 1
•Apply PCA to the noisy data. Suppose the
intrinsic dimensionality of the data is 10.
Compute reconstructed images using the
top d = 10 eigenvectors and plot original
and reconstructed images

20. Example 1Example 1
•If original images are stored in matrix X (it is 560
by 1965 matrix) and reconstructed images are in
matrix X_hat , you can type in
• colormap gray
and then
•imagesc(reshape(X(:, 10), 20 28)’)
•imagesc(reshape(X_hat(:, 10), 20 28)’)
to plot the 10th original image and its
reconstruction.

21. Example 2Example 2

22. Example 2Example 2
•Load the sample data, which includes digits 2 and 3 of
64 measurements on a sample of 400.

load 2_3.mat
•Extract appropriate features by PCA
[u s v]=svd(X','econ');
•Create data
Low_dimensional_data=u(:,1:2);
•Observe low dimensional data
Imagesc(Low_dimensional_data)