Face Recognition (2)--fisherface

Fisherface and Eigenface thinking about, are from the overall image information on the composition analysis.

The difference is that fisherface that the same person due to the light and angle of the differences tend to be greater than the differences between different people , and eigenface pure extraction of the main component may be a category of different lighting conditions.
Therefore, Fisherface attempts to maximize inter-class divergence while minimizing intra-class divergence. The implementation of the algorithm is the first PCA to do initial screening, and then the class divergence and intra-class divergence as the criteria to do LDA (Linear discriminant analysis, linear discriminant analyses). linear discriminant Analysis (LDA) derivation 1 (1) Two types of situations

In linear algebra, the left-multiply y=wtx y=w^tx of matrices can be interpreted as x x to represent Y y through W-w mapping to another space, so the key to classification is to find the appropriate mapping W W.

For Class I wi w_i, its center point is Μi=1ni∑x∈wix \mu_i=\frac{1}{n_i}\sum_{x\in w_i}x, where Ni N_i is the number of samples for that class.
Assuming that there is a mapping W, the center point is projected back to Μ˜i=1ni∑x∈wiwtx=1niwtμi \widetilde\mu_i=\frac{1}{n_i}\sum_{x\in w_i}w^tx=\frac{1}{n_i}w^t\mu_i

A desirable mapping w W will make the distance between the projection classes as large as possible, and the distance within the class as small as possible. For two types of cases, the larger the value of the B (w) in the lower the better, the smaller I (W) the Better:
B (w) =|Μ˜1−Μ˜2|=|WT (μ1