On degree of dependence based on contingency matrix

Authors:
Shusaku Tsumoto;Shoji Hirano
Affiliations:
Department of Medical Informatics, Shimane University, School of Medicine, Enya-cho Izumo City, Shimane, Japan;Department of Medical Informatics, Shimane University, School of Medicine, Enya-cho Izumo City, Shimane, Japan
Venue:
RSFDGrC'05 Proceedings of the 10th international conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing - Volume Part I
Year:
2005

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Abstract

This paper discusses the degree of granularity and dependence of contingency tables from the viewpoint of linear algebra. From the results of determinantal divisors, it seems that the devisors provide information on the degree of dependencies between the matrix of the whole elements and its submatrices and the increase of the degree of granularity may lead to that of dependence. However, this paper shows that a constraint on the sample size of a contingency table is very strong, which leads to the evaluation formula where the increase of degree of granularity gives the decrease of dependency.