Statistical Independence as Linear Independence

Abstract

A contingency table summarizes the conditional frequencies of two attributes and shows how these two attributes are dependent on each other. Thus, this table is a fundamental tool for pattern discovery with conditional probabilities, such as rule discovery. In this paper, a contingency table is interpreted from the viewpoint of granular computing. The first important observation is that a contingency table compares two attributes with respect to the number of equivalence classes. The second important observation is that matrix algebra is a key point of analysis of this table. Especially, the degree of independence, rank plays a very important role in extracting a probabilistic model from a given contingency table.