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Equivalent alternatives are to compute the discriminant functions or and select the category corresponding to the largest discriminant function. Which form is chosen depends upon the simplicity of the resulting discriminant functions, the last form being particularly convenient when the conditional densities belong to the exponential family. T o implement the formal solution requires knowledge of both the a priori probabilities and the conditional densities, and in most pattem recognition problems neither of these is known exactly.

For example, the estimation of p ( x ) by differentiating a least-squares fit to an empirical cumulative distribution function is a distribution-free procedure. Another example is the nearest-neighbor rule of Cover and Hart (1967). Such general statistical procedures are treated in detail in Chapters 2 and 3, and we shall not investigate them further at this time. Suffice it to say that very general procedures exchange the need for precise assumptions about functional forms of the densities for the need for a large number of sample patterns to estimate the densities well.

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. Info. Theory 11, No. 4, pp. 544-549 (1965). , Learning without a teacher. IEEE Trans. Info. Theory 12, No. 2, pp. 223-230 (1966).

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