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Extra resources for Adaptive, Learning and Pattern Recognition Systems: Theory and Applications
35 36 K . S . , fN , to be extracted for classification. , xN , where xJ = fj noise. Each set of N feature measurements can be represented as an N-dimensional vector x or as a point in the N-dimensional feature space Qx . , m. , 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 .
Thompson, Washington, D. , 1968. Greanias, E. C. , The recognition of handwritten numerals by contour analysis. I B M 1. 7, No. 1, pp. 14-22 (1963). Ide, E. R. and Tunis, C. , An experimental investigation of a nonsupervised adaptive algorithm. IEEC Trans. Electron. Comp. 16, No. 6, pp. 860-864 (1967). Kadota, T. T. and L. A. Shepp, On the best finite set of linear observables for discriminating two Gaussian signals. IEEE Trans. Info. Theory 13, No. 2, pp. 278-284 (1967). , The divergence and Bhattacharyya distance measures in signal selection.
T h e problem of estimating the probabilities P(B) and P(8) is exactly the same as before, and we shall again assume that they are equal. However, the problem of estimating p(x I B) and p(x I 8) is more difficult now, because we have functions of two variables, x1 and x 2 , that must be approximated. T h e graphical technique we used with one variable would be quite cumbersome to use with two, and would be hopeless for more than two. T h e difficulty of estimating the conditional densities depends in part upon the kinds of assumptions one can make.
Adaptive, Learning and Pattern Recognition Systems: Theory and Applications by Mendel