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Mathematical Preliminaries belong to class Sk be p(XISk). In some rare cases, the mathematical form of P(XISk) can be assumed. More often, however, it must be estimated on the basis of exemplary samples selected in preliminary studies. The theories of decision processes are centrally based on the concept of a loss function or cost function, the value of which depends on factors set up heuristically, or after extensive experience, for instance, on the importance of detection of a particular occurrence, or on a miss to detect it.

This solution, which is little known, can cope efficiently with the hardware methods, and being readily accessible to a common user of computers, ought to draw considerable attention. 17]. g, from the keyword by which the associated text is encoded. The original record or document may reside in a separate memory area, named the dictionary, and addressed by pointers stored in the hash index table. Unlike in the basic hash coding method, several hash addresses are now derived from the same keyword, whereas all of the corresponding home 24 1.

For each class Bi one can define the so-called discriminant function 8i (x), which is a continuous, scalar-valued function of the pattern vector x. If x E Bi , then for all j =f. i there shall hold 8i (x) ~ 8j (x). The tie situation, with a continuous probability density function of x, is assumed to have the zero probability. There are infinitely many possible choices for the discriminant function: linear, quadratic, etc. In the following we shall define them by statistical arguments. The class border, or the separating surface between two classes i and j is defined in terms of the 8i (x) as 8i (x) - 8j (x) = O.