Theory of classification and its application to the interdependence analysis

This paper recapitulates Satosi Watanabe´s (1961) information-theoretical approach to pattern recognition, and sheds a new light upon his method of interdependence analysis (IDA) for object-predicate relationship. Assuming that each object is characterized by a set of predicates as a binary vector, whose components are 1 or 0 depending on if the object affirms a predicate or not, we first formulate a formal theory of classification of objects by predicates, and show some essential features of classification procedure. Then, from a point of view of the object-predicate reciprocity, we introduce the notion of weak indiscernibility between two objects, and extend it to the indiscernibility between two sets of objects. Based on this notion of generalized indiscernibility we propose an algorithm of clustering, and discuss its merit over the IDA by examples