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Additional resources for Adaptive, Learning and Pattern Recognition Systems: Theory and Applications
The optimum classifier is still called a Bayes’ classifier, and the value of the minimum risk is called the Bayes’ risk. ELEMENTS OF PATTERN RECOGNITION 23 concentrate on feature extraction and classification, outlining some of the more important general methods of approach to these problems. B. Feature Extraction T h e performance of a pattern recognition system often depends crucially on the performance of the feature extractor. This was certainly the case in our B-8 example, where improved performance was only achieved after obtaining better features.
M, the function of a statistical classifier is to perform the classification task for minimizing probability of misrecognition. T h e problem of pattern classification can now be formulated as a statistical decision problem (testing of statistical hypotheses) by defining a decision function d(x), + Input Decision Pottern FIGURE I . A simple block diagram of a pattern recognition system where d(x) = di means that the hypothesis x w i (x is from the class wi)is accepted (Chow, 1957; Anderson, 1958; Blackwell and Girshick, 1954; Sebestyen, 1962).
2 Decision *N Likelihood Computers FIGURE 2. A simplified block diagram of a Bayes’ classifier 38 K. S. FU It is noted from Eq. , m(i # j ) [Nilsson, 19651. 16) Eq. 16) is, in general, a hyperquadric. If 2% = ZJ = Z, Eq. 17) which is a hyperplane. It is noted from Eq. 8) that the Bayes’ decision rule with (0, 1) loss function is also the unconditional maximum-likelihood decision rule. Furthermore, the (conditional) maximum-likelihood decision may be regarded as the Bayes’ decision rule, Eq. , m.
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