Combinatorics of Information Granule in Contingency Table. Issue 9 (8th July 2013)

• Record Type: Journal Article
• Authors: Tsumoto, Shusaku; Hirano, Shoji; Lin, Tsau Young; Kudo, Yasuo; Miyamoto, Sadaaki
• Is Part Of: International journal of intelligent systems. Volume 28:Issue 9(2013:Sep.)
• Page Start: 892
• Page End: 906
• Publication Date: 2013-07-08
• Subjects: Artificial intelligence -- Periodicals; Expert systems (Computer science) -- Periodicals; Intelligence artificielle -- Périodiques; Systèmes experts (Informatique) -- Périodiques; 006.3
• DOI: 10.1002/int.21610
• Languages: English
• ISSNs: 0884-8173

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>This paper focuses on the degree of freedom and number of subdeterminants in a Pearson residual in a multiway contingency table. The results show that multidimensional residuals are represented as linear sum of determinants of 2 × 2 submatrices, which can be viewed as information granules measuring the degree of statistical dependence. Geometrical interpretation of Pearson residual is investigated. Furthermore, the number of subdeterminants in a residual is equal to the degree of freedom in χ²‐test statistic. Since the way of calculation of the number of subdeterminants corresponds to the construction of a statistical model for a contingency table, it has been found that the combinatorics of the number subdeterminants is closely related with permutation of attributes in a given table, where symmetric group may play an important role.</p> </abstract>