Outline
• A. M. Martinez and A. C. Kak, “PCA versus
LDA,” IEEE Transactions on Pattern
Analysis and Machine Intelligence, vol. 23,
no. 2, pp. 228-233, 2001.
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
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Comparison of PCA and FDA
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Illustration
• LDA vs. PCA
LDA
PCA
DLDA
DPCA
PCA
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LDA
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LDA
PCA
DLDA
DPCA
PCA
LDA
PS: The decision thresholds, marked DPCA and DLDA, is
yielded by the nearest-neighbor approach
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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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Localization and Morphing of face image
Localization
Morphing
60
85
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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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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 ovalshaped mask.
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One Subject
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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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Small Training Data Sets
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Small Training Data Sets
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Small Training Data Sets
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Small Training Data Sets
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Small Training Data Sets
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Small Training Data Sets
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Small Training Data Sets
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Using a Larger Training Set
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Using a Larger Training Set
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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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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
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