A new approach to clustering

A general formulation of data reduction and clustering processes is proposed. These procedures are regarded as mappings or transformations of the original space onto a “representation” or “code” space subjected to some constraints. Current clustering methods, as well as three other data reduction techniques, are specified within the framework of this formulation. A new method of representation of the reduced data, based on the idea of “fuzzy sets,” is proposed to avoid some of the problems of current clustering procedures and to provide better insight into the structure of the original data.