Voronoi Projection-Based Fast Nearest-Neighbor Search Algorithms: Box-Search and Mapping Table-Based Search Techniques

Abstract

In this paper we consider fast nearest-neighbor search techniques based on the projections of Voronoi regions. The Voronoi diagram of a given set of points provides an implicit geometric interpretation of nearest-neighbor search and serves as an important basis for several proximity search algorithms in computational geometry and in developing structure-based fast vector quantization techniques. The Voronoi projections provide an approximate characterization of the Voronoi regions with respect to their locus property of localizing the search to a small subset of codevectors. This can be viewed as a simplified and practically viable equivalent of point location using the Voronoi diagram while circumventing the complexity of the full Voronoi diagram. In this paper, we provide a comprehensive study of two fast search techniques using the Voronoi projections, namely, the box-search and mapping table-based search in the context of vector quantization encoding. We also propose and study the effect and advantage of using the principal component axes for data with high degree of correlation across their components, in reducing the complexity of the search based on Voronoi projections.