Efficient exemplars for classifier design

Let X1, …, Xm denote subsets of a vector space. A function ϕ is said to classify (distinguish, recognize, …) the sets Xj if the set images ϕ(Xj), j = 1, …, m are distinctive. Although a broad variety of classifier designs (statistical, separating hyperplane, neural, etc.) are available, a common problem plagues these designs whenever sets Xj are of high cardinality. Namely, the identification of exemplars which (i) are representative of the several classes, (ii) emphasize the importance of critical boundaries, and (iii) in total are of small cardinality. Such exemplar sets lead to robust designs, reduce computational costs, enhance algorithm convergence and often reduce the hardware attendant to design implementation. present study we address the problem of choosing training sets for classifier designs. One result is an algorithm for selecting exemplars on the boundary of a set. Classifiers based on the boundary exemplars are effective for the binary problem: x ∈; X or x ∉ X. Using this algorithm we then present a procedure for obtaining boundary sets for the multiple classification case. These sets X′j ⊂ Xj have the following properties: (i) the cardinality of X′j is small, (ii) the critical boundaries between the Xj are delineated, and (iii) the sets Xj are synchronized in the sense that the boundary points are selected in pairs. These three properties suggest that the X′j will facilitate a computational speed up in several classifier design methodologies, in particular nearest neighbor, separating hyperplane and neural network classifiers. We also present some preliminary tests which confirm this hypothesis.