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 April 7, 2019 Computer Vision

Comparison of PCA and FDA April 7, 2019 Computer Vision

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

LDA DLDA PCA DPCA PS: The decision thresholds, marked DPCA and DLDA, is yielded by the nearest-neighbor approach April 7, 2019 Computer Vision

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 April 7, 2019 Computer Vision

Localization and Morphing of face image 60 85 April 7, 2019 Computer Vision

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 } ) April 7, 2019 Computer Vision

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. April 7, 2019 Computer Vision

One Subject April 7, 2019 Computer Vision

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 April 7, 2019 Computer Vision

Small Training Data Sets April 7, 2019 Computer Vision

Small Training Data Sets April 7, 2019 Computer Vision

Small Training Data Sets April 7, 2019 Computer Vision

Small Training Data Sets April 7, 2019 Computer Vision

Small Training Data Sets April 7, 2019 Computer Vision

Small Training Data Sets April 7, 2019 Computer Vision

Small Training Data Sets April 7, 2019 Computer Vision

Using a Larger Training Set April 7, 2019 Computer Vision

Using a Larger Training Set April 7, 2019 Computer Vision

Experimental Results (cont.) For large training sample: 13 images of first session for training 13 images of second session for testing April 7, 2019 Computer Vision

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