Abstract

A fundamental activity common to many image processing, pattern classification, and clustering algorithms involves searching a set of n, k-dimensional data for the one which is nearest to a given target item with respect to a distance function. Our goal is to find fast search algorithms which are full-search equivalent---that is, the resulting match is as good as what we could obtain if we were to search the set exhaustively. We propose a framework made up of three components, namely (i) a technique for obtaining a good initial match, (ii) an inexpensive method for determining whether the current match is a full-search equivalent match, and (iii) an effective technique for improving the current match. Our approach is to consider good solutions for each component in order to find an algorithm which balances the overall complexity of the search. We also propose a technique for hierarchical ordering and cluster elimination using a minimal cost spanning tree. Our experiments on vector quantisation coding of images show that the framework and techniques we proposed can be used to construct suitable algorithms for most of our data sets which require full-search equivalent matches at an average arithmetic cost of less than O(k log n) while using only O(n) space.

Citations