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By P.W. Becker

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E:. Let the probability with which a L~ -point falls in micro-region W be P(~)k' (1) Let Ppr(~) be the a priori probability of an unlabelled pattern belonging to pattern class C~. •• ,N H is unity. Let be the cost of classifying a member of C~ as being a member of C~ • The convention is used that for any given i, K ~~ is non- positive and the (N c-1) K~~ -values, where ~ oF ~ , all are nonnegative. To describe the cost of all possible correct and erroneous classifications, a matrix with Nc by Nc entries is neei ed.

Tern classes. (d) The realization in hardware of the receptor and the categorizer. Here the problem is raised of selecting forms of rec'eptors and categorizers which will perform reliably when implemented, and which will meet the PRD constraints on weight, vo.!. ume, etc. 5. The Selection of the Attributes The problem of how to select an effective set of attributes for a PRD is generally considered the single most difficult problem in the design. The problem is frequently discussed in the literature (Levine 1969; Nagy 1969; Nelson and Levy; Fu et ale 1970; Henderson and Lainiotis 1970) and is the topic of September 1971 issue of the IEEE Transactions on Com puters.

3 .. . p) t .... 4,· .. , ..... A numerical example will illustrate the advan tage of the decomposition. Assume that (i) all attributes are three valued, (ii) p =6 , (iii) Nc == 2 , and (iv) the number of = design data patterns from Clas s I and 2 is M1D Mz0 ,",3 6=729 . If so, the designer can estimate ClIP1 , IlP1 , CIIP2 and ~P2 ; each of the four densities will consist of 3~'"'27 discrete probabilities which maybe estimated reasonably well given 729 pattern points.

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