Page 48 - Introduction to Statistical Pattern Recognition

Introduction to Statistical Pattern Recognition

il

= XI
Fig. 2-2 Whitening process.

Sample generation: In pattern recognition experiments, it is often neces-
sary to generate samples which are to be normally distributed according to a given
expected vector M and covariance matrix X. In general, the variables are corre-
lated and this makes the generation of samples complex. However, the generation
of normal samples with the expected vector 0 and covariance matrix I is easy.
Therefore, samples may be generated as follows:
(1) From the given E, find the whitening transformation of Y =h-”2@TX.
In the transformed space, Cy =I.
(2) Generate N independent, normally distributed numbers for each
yi (i=l, . . . , n) with zero expected value and unit variance. Then, form N vectors
Y, . . . ,YN.
,
(3) Transform back the generated samples to the X-space by
Xk =Oh”2Yk (k=l, . . . , N).
(4) Add M to the samples in the X-space as Xk + M (k = 1, . . . , N).