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On the Degree of Independence of a Contingency Matrix

  • Shoji Hirano
  • Shusaku Tsumoto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3066)

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 × n table compares two attributes with the same granularity, while a m × n (mn) 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Shoji Hirano
    • 1
  • Shusaku Tsumoto
    • 1
  1. 1.Department of Medical InformaticsShimane University, School of MedicineEnya-cho Izumo CityJapan

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