Algorithms for Fast Vector Quantizaton

Nearest neighbor searching is an important geometric subproblem in vector quanti-zation. Existing studies have shown that the diiculty of solving this problem eeciently grows rapidly with dimension. Indeed, existing approaches on unstructured codebooks in dimension 16 are little better than brute-force search. We show that if one is willing to relax the requirement of nding the true nearest neighbor then dramatic improvements in running time are possible, with negligible degradation in the quality of the result. We present an empirical study of three nearest neighbor algorithms on a number of data distributions, and in dimensions varying from 8 to 16. The rst algorithm is the standard k-d tree algorithm which has been enhanced to use incremental distance calculation, the second is a further improvement that orders search by the proximity of the k-d cell to the query point, and the third is based on a simple greedy search in a structure called a neighborhood graph.