October 2008
Intermediate to advanced
984 pages
30h 43m
English
Content preview from Pattern Recognition, 4th Edition
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2.4.2. The Bayesian Classifier for Normally Distributed Classes
Our goal in this section is to study the optimal Bayesian classifier when the involved pdfs, p(x|ωi), i = 1, 2,…, M (likelihood functions of ωi with respect to x), describing the data distribution in each one of the classes, are multivariate normal distributions, that is, N(μi, Σi), i = 1, 2,…, M. Because of the exponential form of the involved densities, it is preferable to work with the following discriminant functions,
which involve the (monotonic) logarithmic function ln(·):(2.33)
or(2.34)where ci is a constant equal to –(l/2) ln 2π – (1/2) ln|Σi|. Expanding, we obtain(2.35)
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