Abstract
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.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Butz, C.J.: Exploiting contextual independencies in web search and user profiling. In: Proceedings of World Congress on Computational Intelligence (WCCI 2002), CD-ROM (2002)
Coxeter, H.S.M.: Projective Geometry, 2nd edn. Springer, New York (1987)
Polkowski, L., Skowron, A. (eds.): Rough Sets and Knowledge Discovery 1. Physica Verlag, Heidelberg (1998)
Polkowski, L., Skowron, A. (eds.): Rough Sets and Knowledge Discovery 2. Physica Verlag, Heidelberg (1998)
Pawlak, Z.: Rough Sets. Kluwer Academic Publishers, Dordrecht (1991)
Rao, C.R.: Linear Statistical Inference and Its Applications, 2nd edn. John Wiley & Sons, New York (1973)
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)
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, pp. 63–69. AAAI Press, Palo Alto (1996)
Tsumoto, S.: Knowledge discovery in clinical databases and evaluation of discovered knowledge in outpatient clinic. Information Sciences 124, 125–137 (2000)
Yao, Y.Y., Wong, S.K.M.: A decision theoretic framework for approximating concepts. International Journal of Man-machine Studies 37, 793–809 (1992)
Yao, Y.Y., Zhong, N.: An analysis of quantitative measures associated with rules. In: Zhong, N., Zhou, L. (eds.) PAKDD 1999. LNCS (LNAI), vol. 1574, pp. 479–488. Springer, Heidelberg (1999)
Ziarko, W.: Variable Precision Rough Set Model. Journal of Computer and System Sciences 46, 39–59 (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tsumoto, S. (2005). Statistical Independence from the Viewpoint of Linear Algebra. In: Hacid, MS., Murray, N.V., Raś, Z.W., Tsumoto, S. (eds) Foundations of Intelligent Systems. ISMIS 2005. Lecture Notes in Computer Science(), vol 3488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11425274_6
Download citation
DOI: https://doi.org/10.1007/11425274_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25878-0
Online ISBN: 978-3-540-31949-8
eBook Packages: Computer ScienceComputer Science (R0)