Linear independence in contingency table

Authors:
Shusaku Tsumoto
Affiliations:
Department of Medical Informatics, Shimane Medical University, School of Medicine, Enya-cho Izumo City, Shimane, Japan
Venue:
RSFDGrC'03 Proceedings of the 9th international conference on Rough sets, fuzzy sets, data mining, and granular computing
Year:
2003

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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 granular computing. The first important observation is that contingency tables compare two attributes with respect to granularity, which means that a n × n table compares two attributes with the same granularity, while a m × n(m ≥ n) table can be viewed as the projection from m-partitions to n partition. 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 extracting a probabilistic model from a given contingency table.