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 (m ≥ n) 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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Hirano, S., Tsumoto, S. (2004). On the Degree of Independence of a Contingency Matrix. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds) Rough Sets and Current Trends in Computing. RSCTC 2004. Lecture Notes in Computer Science(), vol 3066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25929-9_26
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DOI: https://doi.org/10.1007/978-3-540-25929-9_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22117-3
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