PCA vs LDA

In context of Face recognition

1. Comparison between PCA and LDA

2. PCA applied to data identifies the directions in the feature space (principal components) that account for the most variance in the data. Linear Discriminant Analysis (LDA) tries to identify characteristics that account for the most variance between classes. Eigenfaces (PCA) project faces onto a lower dimensional sub-space no distinction between inter- and intra-class variabilities . optimal for representation but not for discrimination. Fisherfaces (LDA) find a sub-space which maximizes the ratio of inter-class and intra-class variability. same intra-class variability for all classes

3. There has been a tendency in the computer vision community to prefer LDA over PCA . This is mainly because LDA deals directly with discrimination between classes while PCA does not pay attention to the underlying class structure. LDA has lower error rates LDA works well even if different illumination LDA works well even if different facial express .

4. 4 Is LDA always better than PCA? This paper shows that when the training set is small, PCA can outperform LDA. A. Martinez, A. Kak , "PCA versus LDA", IEEE Transactions on Pattern Analysis and Machine Intelligence , vol. 23, no. 2, pp. 228-233, 2001 Our project also show the same result. When the number of samples is large and representative for each class, LDA outperforms PCA .

5. Implementation Training Database There are five classes (person) Each class has Eight elements (face images) 1 to 8 in class 1, 9 to 16 in class 2,and so on… Test faces 10 test images Result : PCA and show different face images even using the same training database

6. Efficiency=(Number of correct recognition)/(Total number of test faces)