An Introduction to the Design of Pattern Recognition Devices by P.W. Becker

By P.W. Becker

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Extra resources for An Introduction to the Design of Pattern Recognition Devices (CISM International Centre for Mechanical Sciences)

Sample text

Ppr(N c) he cannot afford to guess; he will want to cla,! sify in such a manner that the largest possible average classiQ cation cost has been minimized. To do this the designer will make use of the minimaxing classification procedure, a proc~ dure that will now be described in principle. All patterns that are represented by points falling in Wk will be classified as belonging to CLk , ~k E {1 ,2'''JNc}'~kwill be defined shortly; ~k- should not be confused with the minimizing quantity i. (k) from Bayes' procedure.

Of a11 the possible subsets the subset with the largest IP-value is selected and this truly optimum sub set is used. For~c>2 and normal distributions with equal cova- riance matrices a procedure has been used (Chen 1965) where the set ofp attributes is so chosen that the minimum symmetric divergence among the (NC 1) Nc/2 pairs of classes is :maxi:mized; the purpose of this selection procedure is to obtain a safeguard against the choice of attribute sets that may result in large mi~ recognition percentages for certain pattern classes.

4 The Likelihood Method. 2 In many cases the values of the Nc possible classification costs, and the Nc a priori probabilities are unknown to the designer. In such situation only the Nc of P(m) k are available; P(m)k is the probability of a em -point falling in the micro-region Wk rather than in one of the (N M-1)other micr~ regions, P(m)k was defined by Equation 1. A more or less ob- 62 6. Decision Procedures and Indices of Performance vious basis for a decision rule is given by what is called the likelihood principle.

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