A decision theoretic framework for approximating concepts
International Journal of Man-Machine Studies
Fuzzy Sets and Systems - Special issue: fuzzy sets: where do we stand? Where do we go?
Rough Sets in Knowledge Discovery 2: Applications, Case Studies, and Software Systems
Rough Sets in Knowledge Discovery 2: Applications, Case Studies, and Software Systems
Handbook of data mining and knowledge discovery
Foreword to the Special Section on Granular Computing
IEEE Transactions on Fuzzy Systems
Pearson residuals in multi-way contingency tables
SMC'09 Proceedings of the 2009 IEEE international conference on Systems, Man and Cybernetics
Distribution of derminants of contingency tables
SMC'09 Proceedings of the 2009 IEEE international conference on Systems, Man and Cybernetics
Residual analysis of statistical dependence in multiway contingency tables
RSKT'10 Proceedings of the 5th international conference on Rough set and knowledge technology
Analysis of Markov Boundary Induction in Bayesian Networks: A New View From Matroid Theory
Fundamenta Informaticae
Combinatorics in Pearson residuals
International Journal of Knowledge Engineering and Soft Data Paradigms
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This paper analyzes pearson residuals, which is an important element of chi-square test statistic, in a contingency table from the viewpoint of matrix theory as follows. First, a given contingency table is viewed as a matrix and the residual of each element in a matrix are obtained as the difference bewteen observed values and expected values calculated by marginal distributions. Then, each residual σ$_{ij}$ is decomposed into the linear sum of the 2 × 2 subderminants of a original matrix, except for i-th column and j-th row. Furthermore, the number of the determinants is equal to the degree of freedom for the chi-square test statistic for a given contingency table. Thus, 2 × 2 subdeterminants in a contingencymatrix determine the degree of statistical independence of two attributes as elementary granules.