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Additional info for Adaptive, Learning and Pattern Recognition Systems: Theory and Applications
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).
Most of these approaches can be viewed in a statistical setting in which the n-component feature vector x is assumed to be a random vector. , m. , m. If all errors are equally costly, minimizing the risk is equivalent to minimizing the probability of error. 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.
A general block diagram for a sequential recognition system is shown in Fig. 3. Likelihood Computers Decision FIGURE 3. ’s are chosen to be very small. In practical %? situations, it may become virtually necessary to interrupt the standard procedure and resolve among various courses of action. T h e application arises when the feature extractor of a recognition system has only a finite number of suitable feature measurements available to the classifier or when the cost of taking more feature measurements is found to be too high as the number of measurements exceeds a certain limit.
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