Book Chapter10.1016/B978-012369531-4/50004-4
Chepter 4 – Nonlinear Classifiers
Sergios Theodoridis
- 01 Jan 2006
pp 121-211
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TL;DR: In this paper, the authors considered the problem of linear classifiers for nonlinearly separable classes and proposed a linear classifier for non-separable classes with linear discriminant functions (hyperplanes) g(x).
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Abstract: Publisher Summary
This chapter deals with the design of linear classifiers described by linear discriminant functions (hyperplanes) g(x). In the simple two-class case, it is seen that the perceptron algorithm computes the weights of the linear function g (x), provided that the classes are linearly separable. For nonlinearly separable classes linear classifiers were optimally designed, for example, by minimizing the squared error. The chapter discusses the problems that are not linearly separable and for which the design of a linear classifier, even in an optimal way, does not lead to satisfactory performance. The design of nonlinear classifiers emerges now as an unescapable necessity. To seek nonlinearly separable problems one does not need to go into complicated situations. The well-known Exclusive OR (XOR) Boolean function is a typical example of such a problem. Boolean functions are interpreted as classification tasks. The major concern of this chapter is to tackle the XOR problem and then to extend the procedure to more general cases of nonlinearly separable classes.
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