Page 224 - Introduction to Statistical Pattern Recognition

206 Introduction to Statistical Pattern Recognition

Quadratic classifier: Although we do not need to know the value of v
to conduct Experiment 3 to estimate E, v can be computed by obtaining the
partial derivatives of h and carrying through the integration of (5.69) for a
specific classifier. When the quadratic classifier of (5.54) with the parameters
of (5.8) and (5.9) is adopted, the partial derivatives of h are, from (A.29)-
(A.32) and (A.36)-(A.38),

-- (5.72)
" - (-l)rA;'(X-A4r),
aM,.

(5.73)

(5.74)

Substituting (5.72)-(5.75) into (5.70), and noting that 1:" = 1, hj2' = h- I+
mil) = 0 and mj2' = m,, v of (5.71) becomes
1
2x
vy = -Jkq(X, o)ej""'X'p(x)dodX , (5.76)
where
If { }
1
fJX, 0) = - (n+l)C .,f -
2
I=I

The integration of (5.76) can be carried out by using the procedure discussed in