Enhancing prototype reduction schemes with recursion: a method applicable for "large" data sets.

Abstract

Most of the prototype reduction schemes (PRS), which have been reported in the literature, process the data in its entirety to yield a subset of prototypes that are useful in nearest-neighbor-like classification. Foremost among these are the prototypes for nearest neighbor classifiers, the vector quantization technique, and the support vector machines. These methods suffer from a major disadvantage, namely, that of the excessive computational burden encountered by processing all the data. In this paper, we suggest a recursive and computationally superior mechanism referred to as adaptive recursive partitioning (ARP)_PRS. Rather than process all the data using a PRS, we propose that the data be recursively subdivided into smaller subsets. This recursive subdivision can be arbitrary, and need not utilize any underlying clustering philosophy. The advantage of ARP_PRS is that the PRS processes subsets of data points that effectively sample the entire space to yield smaller subsets of prototypes. These prototypes are then, in turn, gathered and processed by the PRS to yield more refined prototypes. In this manner, prototypes which are in the interior of the Voronoi spaces, and thus ineffective in the classification, are eliminated at the subsequent invocations of the PRS. We are unaware of any PRS that employs such a recursive philosophy. Although we marginally forfeit accuracy in return for computational efficiency, our experimental results demonstrate that the proposed recursive mechanism yields classification comparable to the best reported prototype condensation schemes reported to-date. Indeed, this is true for both artificial data sets and for samples involving real-life data sets. The results especially demonstrate that a fair computational advantage can be obtained by using such a recursive strategy for "large" data sets, such as those involved in data mining and text categorization applications.