Definition of the Subject
The degree of granularity of a contingency table is closely related with that of dependence of contingency tables. We investigate these relations from the viewpoints of determinantal devisors and determinants. From the results of determinantal divisors , it seems that the devisors provide information on the degree of dependencies between the matrix of all elements and its submatrices and that an increase in degree of granularity may lead to an increase in dependency. However, another approach shows that a constraint on the sample size of a contingency table is very strong, which leads to an evaluation formula in which an increase of degree of granularity gives a decrease of dependency.
Introduction
Independence (dependence) is a very important concept in data mining, especially for feature selection. In rough sets [2], if two attribute‐value pairs, say \( { [c=0] } \) and \( { [d=0] } \) are independent, their supporting sets, denoted by C and Ddo not have...
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Notes
- 1.
The threshold δ is the degree of the closeness of overlapping sets, which will be given by domain experts. For more information, please refer to Sect. “ Rank of Contingency Table (\( { {2 \times 2} } \))”.
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Acknowledgment
This work was supported by the Grant-in-Aid for Scientific Research (13131208) on PriorityAreas (No.759) “Implementation of Active Mining in the Era of Information Flood” by the Ministry of Education, Science, Culture, Sports,Science and Technology of Japan.
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Tsumoto, S., Hirano, S. (2009). Dependency and Granularity in Data -Mining . In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_119
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DOI: https://doi.org/10.1007/978-0-387-30440-3_119
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