CLUSTERING AND QUANTIZATION BY MSP-PARTITIONS
Klaus Pötzelberger, Helmut Strasser · Statistics & Risk Modeling · 2001
: The paper deals with a class of quantization problems and algorithms based on partitions of R d which are defined by maximal support planes (MSP) of a convex function. This kind of problems generalizes the well-known minimum variance partition problem of statistical cluster analysis. The extension is a multivariate version of the topic considered by Bock, [4]. It is basically different from those kinds of quantization problems which have been considered by Pollard, [15], and Prna, [14], and which are called principal point problems by Flury, [7]. As a side result it is shown that some competitive learning problems considered by Kohonen, [10], belong to the class considered in this paper. The paper contains theoretical results like existence of optima, consistency of approximate optima and characterization of local optima as fixpoints of a fixpoint algorithm. A fix point algorithm is proposed and its termination after finite time is proved for empirical distributions. Modifying the ...