Theory and practice of vector quantizers trained on small training sets

Examines how the performance of a memoryless vector quantizer changes as a function of its training set size. Specifically, the authors study how well the training set distortion predicts test distortion when the training set is a randomly drawn subset of blocks from the test or training image(s). Using the Vapnik-Chervonenkis (VC) dimension, the authors derive formal bounds for the difference of test and training distortion of vector quantizer codebooks. The authors then describe extensive empirical simulations that test these bounds for a variety of codebook sizes and vector dimensions, and give practical suggestions for determining the training set size necessary to achieve good generalization from a codebook. The authors conclude that, by using training sets comprising only a small fraction of the available data, one can produce results that are close to the results obtainable when all available data are used