1. Outline
A. M. Martinez and A. C. Kak, “PCA versus LDA,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 23, no. 2, pp , 2001.

2. The Goal
The main goal of the paper is to examine where LDA is always superior to PCA
This is a natural tendency as LDA is designed for discrimination while PCA is not
April 7, 2019
Computer Vision

3. Comparison of PCA and FDA
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Computer Vision

4. Illustration LDA vs. PCA LDA PCA DLDA DPCA April 7, 2019
Computer Vision

5. LDA
DLDA
PCA
DPCA
PS: The decision thresholds, marked DPCA and DLDA, is yielded by the nearest-neighbor approach
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Computer Vision

6. Localization and Morphing of face image
The paper compares PCA and LDA with regard to only the identification of faces.
Localization step:
A face was first manually localized by marking the left, the right, the top, and the bottom limits of the face, as well as the left and the right eyes and the nose
Morphing step:
After localization, faces are morphed so as to fit a grid of size 85 by 60
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Computer Vision

7. Localization and Morphing of face image60 85
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Computer Vision

8. Segmentation
Each image is segmented by means of an oval-shaped mask centered at the middle of the morphed image rectangle
There are t pixels in the oval-shaped segment  t-dimensional vector xi
( N sample images X = { x1 , , xN } )
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Computer Vision

9. Experimental Results AR-face database
This database consist of 126 classes (people), and there are 26 different images per class.
For each class, these images were recorded in two different sessions separated by two weeks, each session consists of 13 images.
50 different classes (25 males, 25 females) were randomly select from database.
As state earlier, images were morphed to the final 85x60 pixel array, segmented using an oval-shaped mask.
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Computer Vision

10. One Subject
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Computer Vision

11. Small Training Data Sets
For each classes, we use only 7 image (a ~ g)
2 images for training and 5 images for testing
There are in total 21 different ways of separating the data for each class
They are labeled as Test#1 , Test#2 , , Test#21
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Computer Vision

12. Small Training Data Sets
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13. Small Training Data Sets
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Computer Vision

14. Small Training Data Sets
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15. Small Training Data Sets
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16. Small Training Data Sets
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Computer Vision

17. Small Training Data Sets
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Computer Vision

18. Small Training Data Sets
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19. Using a Larger Training Set
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Computer Vision

20. Using a Larger Training Set
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Computer Vision

21. Experimental Results (cont.)
For large training sample:
13 images of first session for training
13 images of second session for testing
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Computer Vision

22. Conclusion
PCA and LDA have been demonstrated to be useful for many application such as face recognition.
One might think that LDA should always outperform PCA (since it deals directly with class discrimination)
The experiments we report here suggest otherwise.
When PCA outperforms LDA, the number of training samples per class is small
April 7, 2019
Computer Vision