By P.W. Becker
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Extra info for An Introduction to the Design of Pattern Recognition Devices
A first group could be the first 3 attributes and a second group the remaining (p-3 attributes. In such a case p~ (3) can be written in the follow ing simpler form. (11) _) P~ C...... M........ ...... '''''3 .. . p) t .... 4,· .. , ..... A numerical example will illustrate the advan tage of the decomposition. Assume that (i) all attributes are three valued, (ii) p =6 , (iii) Nc == 2 , and (iv) the number of = design data patterns from Clas s I and 2 is M1D Mz0 ,",3 6=729 . If so, the designer can estimate ClIP1 , IlP1 , CIIP2 and ~P2 ; each of the four densities will consist of 3~'"'27 discrete probabilities which maybe estimated reasonably well given 729 pattern points.
4 One Attribute. The attribute is called 8 1 , as in Fig. 1. In this subsection it is discussed how the designer may estimate the effectiveness of probability density functions of Bi" It is assumed that the the 5 1 -values for members of Class 1, members of Class 2, etc. have been obtained; in practice normalized histograms areoften used as approximations to the Nt probability density functions. 1, 11, ' .. _,p, in a sense may be considered as one attribute with a One Attribute 43 number of discrete values equal to the product: E.
The remai~ ing micro-regions are then all classified as C 2 -regions. sified the least number of C 2 -patterns are misclassified. When the Neyman-Pearson method is used and R N-P is specified, the percentage of correctly classified C2 - patterns would constitute a reasonable index of performance. 6 Three Practical Difficulties. What has been obtained this far in this section is development of some techniques by which all unlabelled pat terns, which are represented by points in the micro-region W'k , maybe classified as being members of one and only one of the N c possible pattern classes.
An Introduction to the Design of Pattern Recognition Devices by P.W. Becker