Abstract
This paper presents results of experiments on 24 data sets with three different interpretations of missing attribute values: lost values, attribute-concept values, and “do not care” conditions. Lost values were erased or forgotten to be inserted. Attribute-concept values are any values from the attribute domain restricted to the respective concept. “Do not care” conditions are any values from the attribute domain without any restriction. For our experiments we used concept probabilistic approximations, a generalization of standard approximations. Our main objective was to determine the best interpretation of missing attribute values, in terms of the error rate. Results of experiments indicate that the lost value interpretation of missing attribute values is the best. Our secondary objective was to test how useful proper concept probabilistic approximations (i.e., different from standard concept lower and upper approximations) are for mining data with missing attribute values. Proper concept probabilistic approximations were better than standard concept approximations for 12 data sets and worse for five data sets (out of 24).
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References
Grzymała-Busse, J.W.: Generalized parameterized approximations. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 136–145. Springer, Heidelberg (2011)
Wong, S.K.M., Ziarko, W.: INFER—an adaptive decision support system based on the probabilistic approximate classification. In: Proceedings of the 6th International Workshop on Expert Systems and their Applications, pp. 713–726 (1986)
Grzymala-Busse, J.W., Ziarko, W.: Data mining based on rough sets. In: Wang, J. (ed.) Data Mining: Opportunities and Challenges, pp. 142–173. Idea Group Publ., Hershey (2003)
Pawlak, Z., Skowron, A.: Rough sets: Some extensions. Information Sciences 177, 28–40 (2007)
Pawlak, Z., Wong, S.K.M., Ziarko, W.: Rough sets: probabilistic versus deterministic approach. International Journal of Man-Machine Studies 29, 81–95 (1988)
Ślęzak, D., Ziarko, W.: The investigation of the bayesian rough set model. International Journal of Approximate Reasoning 40, 81–91 (2005)
Yao, Y.Y.: Probabilistic rough set approximations. International Journal of Approximate Reasoning 49, 255–271 (2008)
Yao, Y.Y., Wong, S.K.M.: A decision theoretic framework for approximate concepts. International Journal of Man-Machine Studies 37, 793–809 (1992)
Ziarko, W.: Variable precision rough set model. Journal of Computer and System Sciences 46(1), 39–59 (1993)
Ziarko, W.: Probabilistic approach to rough sets. International Journal of Approximate Reasoning 49, 272–284 (2008)
Clark, P.G., Grzymala-Busse, J.W.: Experiments on probabilistic approximations. In: Proceedings of the 2011 IEEE International Conference on Granular Computing, pp. 144–149 (2011)
Clark, P.G., Grzymala-Busse, J.W.: Rule induction using probabilistic approximations and data with missing attribute values. In: Proceedings of the 15th IASTED International Conference on Artificial Intelligence and Soft Computing, ASC 2012, pp. 235–242 (2012)
Grzymala-Busse, J.W., Wang, A.Y.: Modified algorithms LEM1 and LEM2 for rule induction from data with missing attribute values. In: Proceedings of the Fifth International Workshop on Rough Sets and Soft Computing, RSSC 1997, at the Third Joint Conference on Information Sciences, JCIS 1997, pp. 69–72 (1997)
Stefanowski, J., Tsoukias, A.: Incomplete information tables and rough classification. Computational Intelligence 17(3), 545–566 (2001)
Grzymala-Busse, J.W.: On the unknown attribute values in learning from examples. In: Proceedings of the ISMIS 1991, 6th International Symposium on Methodologies for Intelligent Systems, pp. 368–377 (1991)
Kryszkiewicz, M.: Rules in incomplete information systems. Information Sciences 113(3-4), 271–292 (1999)
Grzymala-Busse, J.W.: LERS—a system for learning from examples based on rough sets. In: Slowinski, R. (ed.) Intelligent Decision Support. Handbook of Applications and Advances of the Rough Set Theory, pp. 3–18. Kluwer Academic Publishers, Dordrecht (1992)
Grzymala-Busse, J.W.: Three approaches to missing attribute values—a rough set perspective. In: Proceedings of the Workshop on Foundation of Data Mining, in conjunction with the Fourth IEEE International Conference on Data Mining, pp. 55–62 (2004)
Grzymala-Busse, J.W., Rzasa, W.: A local version of the MLEM2 algorithm for rule induction. Fundamenta Informaticae 100, 99–116 (2010)
Grzymala-Busse, J.W.: MLEM2: A new algorithm for rule induction from imperfect data. In: Proceedings of the 9th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, pp. 243–250 (2002)
Grzymala-Busse, J.W.: Knowledge acquisition under uncertainty—A rough set approach. Journal of Intelligent & Robotic Systems 1, 3–16 (1988)
Grzymala-Busse, J.W.: Generalized probabilistic approximations. Transactions on Rough Sets 16, 1–16 (2013)
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Clark, P.G., Grzymała-Busse, J.W. (2013). An Experimental Comparison of Three Interpretations of Missing Attribute Values Using Probabilistic Approximations. In: Ciucci, D., Inuiguchi, M., Yao, Y., Ślęzak, D., Wang, G. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. RSFDGrC 2013. Lecture Notes in Computer Science(), vol 8170. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41218-9_9
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