Entropy-constrained learning vector quantization algorithms and their application in image compression

This paper presents entropy-constrained learning vector quantization (ECLVQ) algorithms and their application in image compression. The development of these algorithms relies on reformulation, which is a powerful new methodology that essentially establishes a link between learning Vector quantization and clustering algorithms developed using alternating optimization. ECLVQ algorithms are developed in this paper by reformulating entropy-constrained fuzzy clustering (ECFC) algorithms, which were developed by minimizing an objective function incorporating the partition entropy and the average distortion between the feature vectors and their prototypes. The proposed algorithms allow the gradual transition from a maximally fuzzy partition to a nearly crisp partition of the feature vectors during the learning process. This paper presents two alternative implementations of the proposed algorithms, which differ in terms of the strategy employed for updating the prototypes during learning. The proposed algorithms are tested and evaluated on the design of codebooks used for image data compression. (C) 2000 SPIE and IS&T. {[}S1017-9909(00)00304-4].