28 March 2005 On statistical independence of a contingency matrix
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Abstract
A contingency table summarizes the conditional frequencies of two attributes and shows how these two attributes are dependent on each other with the information on a partition of universe generated by these attributes. Thus, this table can be viewed as a relation between two attributes with respect to information granularity. This paper focuses on several characteristics of linear and statistical independence in a contingency table from the viewpoint of granular computing, which shows that statistical independence in a contingency table is a special form of linear dependence. The discussions also show that when a contingency table is viewed as a matrix, called a contingency matrix, its rank is equal to 1.0. Thus, the degree of independence, rank plays a very important role in extracting a probabilistic model from a given contingency table. Furthermore, it is found that in some cases, partial rows or columns will satisfy the condition of statistical independence, which can be viewed as a solving process of Diophatine equations.
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Shusaku Tsumoto, Shoji Hirano, "On statistical independence of a contingency matrix", Proc. SPIE 5812, Data Mining, Intrusion Detection, Information Assurance, and Data Networks Security 2005, (28 March 2005); doi: 10.1117/12.604975; https://doi.org/10.1117/12.604975
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