Page 167 - Introduction to Statistical Pattern Recognition

4 Parametric Classifiers 149

1
= -(uW - r)T(uTw r) , (4.78)
-
N
where

(4.79)
u = [Z, ' . -ZNI(,,+l)xN 9

The U and r are called the sample matrix and the desired output vector,
respectively. Taking the derivative of (4.78) with respect to W,

(4.8 1)

By analogy to (4.8 l), the following correction terms have been suggested
for the criteria [5]:
(1) W(&+ l)=W(u,)--U[UTW(t)- lu'W(t)lI], (4.82)
2P
N

(3) W(Z + 1) = ~(t) -u[uTw(t) - I-([)] , (4.84)
-
2P
N

where
(a) I U'W I is a vector whose components are the absolute values of the
corresponding components of UTW
(b) sign(UTW) is a vector whose components are +I or -1 depending
on the signs of the corresponding components of U'W;
(c) r, = [I 1 . . . 11';