Adaptive, Learning and Pattern Recognition Systems: Theory by Mendel

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536-551 (1967). Roberts, L. , Machine perception of three-dimensional solids. In “Optical and ElectroOptical Information Processing” (J. T. ) pp. 159-197. , 1965. , The perceptron: a perceiving and recognizing automaton. Report No. 85-460-1. Cornell Aeronautical Laboratory, Buffalo, New York, 1957. Sebestyen, G. , Pattern recognition by an adaptive process of sample set construction. I R E Trans. Info. Theory 8, No. 5 , pp. S82-S91 (1962). , A note on the iterative application of Bayes’ rule. IEEE Trans.

A somewhat better assumption, one that at least takes account of the different scale factors for x1 and x 2 , is to assume that 20 R. 0. DUDA where u12 is the variance of x1 and uZ2is the variance of x 2 . 24) - and ~ If we once again assume that the a priori probabilities are equal, the condition p(x 1 B) > p(x 1 8) leads to the decision rule Decide B if (X - pB)’ E 1 ( x- PB) otherwise decide 8. < (X - p8)’ P 1 ( x - p8); There are two ways to interpret this result. One is to say that we again classify x as a B if it is closer to the average of the B’s than to the average of the 8’s, except that we are using a normalized distance [the so-called Mahalanobis distance (x - p)’ P 1 ( x - p)] to measure closeness.

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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