Optimal pruning with applications to tree-structured source coding and modeling

An algorithm recently introduced by Breiman, Friedman, Olshen, and Stone in the context of classification and regression trees is reinterpreted and extended to cover a variety of applications in source coding and modeling in which trees are involved. These include variable-rate and minimum-entropy tree-structured vector quantization, minimum expected cost decision trees, variable-order Markov modeling, optimum bit allocation, and computer graphics and image processing using quadtrees. A concentration on the first of these and a detailed analysis of variable-rate tree-structured vector quantization are provided. We find that variable-rate tree-structured vector quantization outperforms not only the fixed-rate variety but also full-search vector quantization as well. Furthermore, the “successive approximation” character of variable-rate tree-structured vector quantization permits it to degrade gracefully if the rate is reduced at the encoder. This has applications to the problem of buffer overflow.