Page 250 - Introduction to Statistical Pattern Recognition

232 Introduction to Statistical Pattern Recognition

,.
design sample as well as a test sample, both contribute to the variation of h.
Thus, we can no longer use the same argument as in Section 5.2 to compute
Ed{ However, the relationship between iL and LR is given exactly by
(5.129) and (5.130) and approximately by (5.147). Therefore, using the
approximation of (5.147) for simplicity,
1
iR(X$I)) GL(X$')) - -[d:(X$')) + n] for 01 , (5.148)
2N I

+
Applying (5.148), (5.149) and another approximation, eJwoiN : jw/N
1
*
(valid for large N), the classification error by the R method, eR, may be calcu-
lated from (5.98) as

(5.150)

where

(5.151)

and cL is the classification error by the L method.

,.
A
Moments of the bias: By converting hR to hL, design and test samples
are now independent, and the discussion of Section 5.2 can be directly applied.