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
statistical independence and granular computing. The first important observation is that a contingency table compares two attributes with respect to the number of equivalence classes. For example, a n x n table compares two attributes with the same granularity, while a m x n(m ≥ n) table compares two attributes with different granularities. 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 evaluating the degree of statistical independence. Relations between rank and the degree of dependence are also investigated.
Shusaku Tsumoto, Shusaku Tsumoto,
"Rank and independence in contingency table", Proc. SPIE 5433, Data Mining and Knowledge Discovery: Theory, Tools, and Technology VI, (12 April 2004); doi: 10.1117/12.542924; https://doi.org/10.1117/12.542924