Data Compression by Unsupervised Classification

This paper deals with a general class of classification methods which are related both to vector quantization in the sense of Pollard, [12], as well as to competitive learning in the sense of Kohonen, [10]. The basic duality of minimum variance partitioning and vector quantization known from statistical cluster analysis is shown to be true for this whole class of classification problems. The paper contains theoretical results like existence of optima, consistency of approximate optima and characterization of local optima as fixpoints of a fix point algorithm. A fix point algorithm is proposed and its termination after finite time is proved for empirical distributions. The construction of a particular classification method is based on a statistical information measure specified by a convex function. Modifying this convex function gives room for suggesting a large variety of new classification procedures, e.g. of robust quantifiers. (author's abstract)