Vector quantization and fuzzy ranks for image reconstruction

The problem of clustering is often addressed with techniques based on a Voronoi partition of the data space. Vector quantization is based on a similar principle, but it is a different technical problem. We analyze some approaches to the synthesis of a vector quantization codebook, and their similarities with corresponding clustering algorithms. We outline the role of fuzzy concepts in these algorithms, both in data representation and in training. Then we propose an alternative way to use fuzzy concepts as a modeling tool for physical vector quantization systems, Neural Gas with a fuzzy rank function. We apply this method to the problem of quality enhancement in lossy compression and reconstruction of images with vector quantization.