12 April 2004 Rank and independence in contingency table
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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.
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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

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