Mathematical Classification and Clustering

The goal of this text is threefold; first, to serve as a reference for the enormous amount of existing clustering concepts and methods; second, to be used as a textbook; and, third, to present the author's and his Russian colleagues' results in the perspective of current developments. It contains a current review of clustering including the most recent theories about discrete clustering structures (subsets, partitions, hierarchies etc.) in their relation to data. An approximation framework is developed as a major construct substantiating and extending such existing approaches as agglomerative clustering and K-means method, and leading to new methods such as box and ideal type clustering, uniform partitioning, aggregation of flow tables, and principal cluster analysis. The opening chapter is devoted to a review of classification and clustering goals and forms prior to defining the scope and goals of clustering. Real-world illustrative examples are interwoven throughout the exposition. The text should be of use to both specialists and students in the field of data analysis and clustering as well as in biology, psychology, economics, marketing research, artificial intelligence, and other scientific disciplines.