March 7, 2017

Adaptive, Learning and Pattern Recognition Systems: Theory by Mendel

By Mendel

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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.

111. Forward Sequential Classification Procedure with Time-Varying Stopping Boundaries As described in Section 11, the error probabilities eii can be prespecified in SPKT and GSPRT. However, in S P R T and GSPRT, the number of feature measurements required for a terminal decision is a random variable, which, in general, depends upon the specified eii and has a positive probability of being greater than any constant. Since it is impractical to allow an arbitrarily large number of feature measuremcnts to terminate the sequential process, one is frequently interested in setting an upper bound for the number of feature measurements within which the pattern classifier must make a terminal decision.

If this distance is less than r , x2 is also assigned to the first subset, and m, is updated so that it is the average of x1 and x2. I n general, if n subsets have been created and a new pattern x is introduced, all n distances 11 x - mi I] are computed. If the smallest is less than Y , x is assigned to that subset and the corresponding mean vector is updated. Otherwise a new subset is created with mean m,,, = x. There are many variations on this theme, the most prominent ones being described in a good survey article by Ball (1965).

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