By William S. Meisel
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Additional resources for Computer-Oriented Approaches to Pattern Recognition
We thus define a decision rule c(x) which tells us the classification of a point x : c(x) = 1 2 if g(x) 2 0, if g(x) < 0, where the 1 and 2 refer to classes S , and S2, respectively. Using the example of Eq. 7), y = ( I , 1, 1, 1) gives g(y) = 1 > 0, and y is classified a member of class SIby the decision rule of (1 3). Suppose, however, that we have more than two classes of samples. The boundary might be as in Fig. 8, a three-class problem. We may consider *2 FIG. 8 Three-class boundaries: class 2; A class 3.
9) are given by In particular, in the two-class problem, we may work efficiently with Eq. 8) or use two discriminant functions, in which case the two approaches are related by A third alternative is to convert an N-class problem into a series of twoclass problems by successive dichotomy, by successively splitting the classes remaining into two groups. If we began with eight classes, we could solve the following three problems in the order given: (1) Find a decision boundary separating classes 1 through 4 from classes 5 through 8.
Electron. Comput. 6 , 247-254 (1957). 6. Cooper, D. , and Cooper, P. , Nonsupervised Adaptive Signal Detection and Pattcrn Recognition, Information and Control 7 , 416-444 (1964). 7. Cooper, P. , The Hypersphere in Pattern Recognition, Information and Control 5, 324346 (1962). 8. Cooper, P. , A Note on an Adaptive Hypersphere Decision Boundary, IEEE Trans. Electron. Comput. 15,948-949 (1966). 9. Day, N. , Lincar and Quadratic Discrimination in Pattern Recognition, IEEE Trans. Information Theory 14,419420 (1969).