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Inspection of Fig. 9. T h u s it happens that we have come full circle and have returned to our original, intuitively suggested decision rule. Now, however, we have a theoretical justification for this rule, and we have a much more general approach for deriving decision rules, the method of statistical decision theory. D. Improving the Feature Extractor Unfortunately, the major practical result of our attempt to improve the classifier was a demonstration that it was doing about as well as can be expected.

X, 1 Ftn) = the cost of continuing the sequential recognition process at the nth stage, when Fin is selected. , x, when Ftn is selected. , x, on the sequence of features Ftn . , x,; di 1 Ftn) If the classifier decides to take an additional measurement, then the measurement must be optimally selected from the remaining features F, in order to minimize the risk. 40) Again, Eq. 40) can be recursively solved by setting the terminal condition to be and computing backwards for risk functions R , , n < N.

Finally, the classifier maps each x into a discrete-valued scalar d in decision space, where d = di if the classifier assigns x to the ith category. These mappings are almost always many-to-one, with some information usually being lost at each step. With the transducer, the loss of information may be unintentional, while with the feature extractor and the classifier, the loss of information is quite intentional. T h e feature extractor is expected to preserve only the information needed for classification, and the classifier preserves only the classification itself.

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