Least-Squares Structuring, Clustering and Data Processing Issues

Approximation structuring clustering is an extension of what is usually called \square-error clustering" onto various cluster structures and data formats. It appears to be not only a mathematical device to support, specify and extend many clustering techniques, but also a framework for mathematical analysis of interrelations among the techniques and their relations to other concepts and problems in data analysis, statistics, machine learning, data compression and decompression, and design and use of multiresolution hierarchies. Based on the results found, a number of methods for solving data processing problems are described.