A linear classifier design approach

摘要

In this paper we discuss a linear classifier design approach based on an exhaustive search procedure. The pattern classes are projected onto subspaces of the pattern space and bounded by hyperplanes with fixed orientation. A set of such linear discriminators is then submitted to an optimization procedure which displaces the discriminators systematically. The optimization procedure is characterized as a linear exhaustive search which performs an ordering of the set of all possible positions of the discriminators. From this ordered sequence of solutions any particular solution can be chosen. A cost minimization procedure, in terms of classifier complexity, is introduced. The result of the minimization is the necessary and sufficient set of discriminators having the same discriminatory performance as the optimized solution. For multimodal pattern sets, we give a brief discussion of a simple set partition approach. In two examples we show the results of this design approach on synthetic data.