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Additional resources for Adaptive, Learning and Pattern Recognition Systems: Theory and Applications
I t is an objective of this chapter to cover some recent developments in the application of stastical techniques to feature selection, feature ordering, mode estimation, and pattern classification. 11, Sequential Decision Model for Pattern Classification Application of sequential decision procedures to pattern classification was proposed by Fu (1962). If there are two pattern classes to be recognized, Wald's sequential probability ratio test (SPRT) can be applied (Wald, 1947). , x,)' for pattern class mi.
T h e two stopping + 40 K. S. 21) - - where e . probability of deciding x w i when actually x w j is . a? true, z , j = 1, 2. Following Wald’s sequential analysis, it has been shown that a classifier, using the SPRT, has an optimal property for the case of two pattern classes; that is, for given eI2 and eZ1, there is no other procedure with at least as low error-probabilities or expected risk and with shorter length of average number of feature measurements than the sequential classification procedure.
27) for every i and select the category for which P(wiI x) is maximum. 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.
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