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12 April 2004 Rank and independence in contingency table
Shusaku Tsumoto
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Proceedings Volume 5433, Data Mining and Knowledge Discovery: Theory, Tools, and Technology VI; (2004) https://doi.org/10.1117/12.542924
Event: Defense and Security, 2004, Orlando, Florida, United States
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 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 "Rank and independence in contingency table", Proc. SPIE 5433, Data Mining and Knowledge Discovery: Theory, Tools, and Technology VI, (12 April 2004); https://doi.org/10.1117/12.542924
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