Page 260 - Introduction to Statistical Pattern Recognition
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242 Introduction to Statistical Pattern Recognition
(5.168)
where
(5.169)
,.*
Quadratic classifier: When a quadratic classifier is used, h (X) in
(5.169) becomes
,,* ,,* ** r*
h*(X) =f(X,M,,Z,) -f(X,M2A), (5.170)
,.* ,.=
wheref(.,.,.) is defined in (5.143). The bootstrap parameters, Mi, and Z, , are
(5.171)
(5.172)
,.* A’
Note that h, = (X~~iX~))/N, instead of M, is used to compute E,. In the con-
ventional sample covariance matrix, the sample mean is used, because the true
A
expected vector is not available. However, the true expected vector, M,, is
,.x
available in the bootstrap operation, and the use of M, instead of M, simplifies
the discussion significantly. Their expectations are
