Page 215 - Introduction to Statistical Pattern Recognition
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5 Parameter Estimation 197
(5.34)
where h(X) is the discriminant function of an n-dimensional vector X. The
prohahiliries of error for this classifier from ol and o2 are from (3.105) and
(3.106)
(5.35)
(5.36)
where pi(X) represents the class i distribution to be tested. The roral prohahil-
iry oj'error is
(5.37)
where
(5.38)
Effect of Test Samples
Error expression: When a finite number of samples is available for test-
ing a given classifier, an error-counting procedure is the only feasible possibil-
ity in practice. That is, the samples are tested by the classifier, and the number
of misclassified samples is counted. The other alternative is to estimate the test
densities from the samples, and to integrate them in complicated regions. This
procedure is, as seen in Chapter 3, complex and difficult even for normal distri-
butions with known expected vectors and covariance matrices.
In the error-counting procedure, pi(X) of (5.38) may be replaced by
