Introduction to Pattern Recognition: A Matlab Approach

3.4 Fisher’s Linear Discriminant Analysis 87

the performance of the two methods lies in the fact that in PCA we perform eigendecomposition on

the l ×l covariance matrix while in SVD we perform eigendecomposition on the N ×NX

T

X and then,

with a simple transformat i on, compute the eigenvectors of XX

T

(which may be viewed as a scaled

approximation of the autocorrelation matrix). Moreover , it has to be emphasized that, in general for

such cases where N < l, the obtained esti mate of t he autocorrelati on matrix is not a good one. Such

cases, where N < l, arise i n image-processing applications, in Web mining, in microarray analysis, and

the like.

3.4