Page 190 - Introduction to Statistical Pattern Recognition
P. 190
172 Introduction to Statistical Pattern Recognition
complicated to be practical. Therefore, we will limit our discussion to convex
regions here.
The probability of error for each class, E;, can be expressed in terms of
the (L - 1)-dimensional distribution function as
>
E; = 1 - Pr(h;,(X) 0,. . .,hiL(X) > OIX E 0;)
= I - [- . .[-p (h; 1, . . . ,h;L I 0;)dh; . . . dh, (4.156)
.
I
[hii(X) is excluded] .
The total error is
L
E = ZP;E; . (4.157)
i=l
Knowing the structure of piecewise linear classifiers, our problem is how
to design the V’s and YO’S for a given set of L distributions. Because of the
complexity involved, solutions for this problem are not as clear-cut as in a
linear classifier.
Three approaches are mentioned briefly:
