On the Degree of Independence of a Contingency Matrix
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.
Unable to display preview. Download preview PDF.
- 2.Tsumoto, S.: Knowledge discovery in clinical databases and evaluation of discovered knowledge in outpatient clinic. Information Sciences, 125–137 (2000)Google Scholar
- 3.Tsumoto, S., Tanaka, H.: Automated discovery of medical expert system rules from clinical databases based on rough sets. In: Proceedings of the Second International Conference on Knowledge Discovery and Data Mining 1996, Palo Alto, pp. 63–69. AAAI Press, Menlo Park (1996)Google Scholar
- 4.Tsumoto, S.: Statistical independence as linear independence. In: Skowron, A., Szczuka, M. (eds.) Electronic Notes in Theoretical Computer Science, vol. 82, Elsevier, Amsterdam (2003)Google Scholar
- 5.Skowron, A., Grzymala-Busse, J.: From rough set theory to evidence theory. In: Yager, R., Fedrizzi, M., Kacprzyk, J. (eds.) Advances in the Dempster-Shafer Theory of Evidence, pp. 193–236. John Wiley & Sons, New York (1994)Google Scholar
- 6.Butz, C.: Exploiting contextual independencies in web search and user profiling. In: Proceedings of World Congress on Computational Intelligence (WCCI 2002), CDROM (2002)Google Scholar