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 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, 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. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Tsumoto, S. (2005). Statistical independence from the viewpoint of linear algebra. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3488 LNAI, pp. 56–64). Springer Verlag. https://doi.org/10.1007/11425274_6
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