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Extra info for Adaptive, Learning and Pattern Recognition Systems: Theory and Applications
I t is one of a number of rules having the property that after a finite number of corrections it will yield a vector 8 that will classify all of the samples correctly, provided only that such a vector exists. T h e properties of this rule and related adaptive procedures will be considered in detail in Chapter 3. These procedures have the virtue that they can be applied to patterns from a wide variety of distributions, and that they control the complexity of the classifier by prior specification.
T h e various procedures available for this task differ in the assumptions they make, and we shall examine a few of the most important procedures. 2. Parametric learning. If the conditional densities p(x I mi) can be assumed to be known except for the values of some parameters, then 25 ELEMENTS OF PATTERN RECOGNITION the samples can be used to estimate these parameters, and the resulting estimated densities can be used in the formal solution as if they were the true parameters. 30) where the parameters are the mean vector pi and the covariance matrix Zi.
20) If B < A, < A, then an additional feature measurement will be taken and the process proceeds to the (n 1)th stage. 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.
Adaptive, Learning and Pattern Recognition Systems: Theory and Applications by Mendel