This document compares PCA and LDA techniques. PCA finds directions of maximum variance in data but does not distinguish between inter-class and intra-class variability. LDA finds a subspace that maximizes inter-class variability while minimizing intra-class variability. When training sets are small, PCA can outperform LDA, but LDA generally has lower error rates and works better when there are differences in illumination or expression between faces.

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)