Improving search for tree-structured vector quantization

The authors analyze the approximate performance of tree search and provide tight upper bounds on the amount of error resulting from tree search and for a single input vector. These bounds are not encouraging but fortunately, the performance of tree-structured VQ in practice does not seem to be as bad. From the analysis, they derive a simple heuristic to improve the approximation of tree search. The strategy is to identify for each code vector some of its closest neighboring code vectors determined by the partition. After a code vector is found for an input vector by tree search, the closest neighboring code vectors are then searched for the best match. Unfortunately, the average number of neighboring code vectors of a given code vector can be as many as the total number of code vectors. Thus, the performance improvement of the strategy depends on the number of code vectors that are searched. Experimental results show that a number logarithmic in the size of the codebook provides significant performance gain while preserving the asymptotic search time complexity.<<ETX>>