Flexible Indiscernibility Relations for Missing Attribute Values

• Autorzy: Latkowski R.
• Języki publikacji: EN

Abstrakty

EN

The indiscernibility relation is a fundamental concept of the rough set theory. The original definition of the indiscernibility relation does not capture the situation where some of the attribute values are missing. This paper tries to enhance former works by proposing an individual treatment of missing values at the attribute or value level. The main assumption of the theses presented in this paper considers that not all missing values are semantically equal. We propose two different approaches to create an individual indiscernibility relation for a particular information system. The first relation assumes variable, but fixed semantics of missing attribute values in different columns. The second relation assumes different semantics of missing attribute values, although this variability is limited with expressive power of formulas utilizing descriptors. We provide also a comparison of flexible indiscernibility relations and missing value imputation methods. Finally we present a simple algorithm for inducing sub-optimal relations from data.

Słowa kluczowe

EN

rough sets; missing attribute values; incomplete information systems

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2005
• Tom: Vol. 67, nr 1-3
• Strony: 131--147
• Opis fizyczny: Bibliogr. 35 poz.

Twórcy

autor

Latkowski R.

• Institute of Computer Science, Warsaw University ul. Banacha 2 02-097 Warsaw, Poland,

Bibliografia

• [1] Alpigini, J. J., Peters, J. F., Skowron, A., Zhong, N., Eds.: Rough Sets and Current Trends in Computing, Third International Conference, RSCTC 2002, LNCS 2475, Springer, 2002.
• [2] Bazan, J. G., Szczuka, M., Wojna, A., Wojnarski, M.: On the Evolution of Rough Set Exploration System., Rough Sets and Current Trends in Computing, RSCTC 2004 (S. Tsumoto, R. Słowiński, H. J. Komorowski, J. W. Grzymała-Busse, Eds.), LNCS 3066, Springer, 2004.
• [3] Candan, K. S., Grant, J., Subrahmanian, V. S.: A Unified Treatment of Null Values using Constraints, Information Sciences, 98(1-4), 1997, 99–156.
• [4] Codd, E. F.: Understanding Relations (Installment #7), FDT - Bulletin of ACM SIGMOD, 7(3/4), 1975, 23–28.
• [5] Fujikawa, Y., Ho, T. B.: Scalable Algorithms for Dealing with Missing Values, 2001.
• [6] Gediga, G., Düntsch, I.: Maximum Consistency of Incomplete Data via Non-Invasive Imputation, Artificial Intelligence Review, 19, 2003, 93–107.
• [7] Greco, S., Matarazzo, B., Słowiński, R.: Fuzzy Similarity Relation as a Basis for Rough Approximations, Rough Sets and Current Trends in Computing, RSCTC’98 (L. Polkowski, A. Skowron, Eds.), LNCS 1424, Springer, 1998.
• [8] Grzymała-Busse, J. W.: Rough set strategies to data with missing attribute values, Proc. of the Workshop on Foundations and New Directions in Data Mining, associated with ICDM-2003, 2003.
• [9] Grzymała-Busse, J. W.: Data with missing attribute values: Generalization of idiscernibility relation and rule induction, Transactions on Rough Sets 1, LNCS 3100, Springer, 2004.
• [10] Grzymała-Busse, J. W., Hu, M.: A Comparison of Several Approaches to Missing Attribute Values in Data Mining, in: Ziarko and Yao [34], 378–385.
• [11] Komorowski, J., Pawlak, Z., Polkowski, L., Skowron, A.: Rough Sets: A Tutorial, Rough Fuzzy Hybridization. A New Trend in Decision Making (S. K. Pal, A. Skowron, Eds.), Springer, Singapore, 1999.
• [12] Komorowski, J., Polkowski, L., Skowron, A.: Learning Tolerance Relations by Boolean Descriptors: Automatic Feature Extraction from Data Tables, RSFD’96 (S. Tsumoto, et al., Eds.), 1996.
• [13] Kryszkiewicz, M.: Properties of Incomplete Information Systems in the Framework of Rough Sets, in: Polkowski and Skowron [23], 422–450.
• [14] Latkowski, R.: Incomplete Data Decomposition for Classification, in: Alpigini et al. [1], 413–420.
• [15] Latkowski, R.: Optimal indiscernibility relation for missing attribute values using CAKE (in Polish), 2002.
• [16] Latkowski, R.: On Indiscernibility Relations for Missing Attribute Values, CS&P’2004, Volume 2. Informatik-Bericht Nr. 170 (e. a. G. Lindemann, Ed.), Humboldt University, 2004.
• [17] Lim, T.: Missing covariate values and classification trees, http://www.recursive-partitioning.com/mv.shtml, Recursive-Partitioning.com, 2000.
• [18] Lipski,W. J.: On Semantic Issues Connected with Incomplete Information Databases, ACM Transactions on Database Systems, 4(3), 1979, 262–296.
• [19] Little, R. J. A., Rubin, D. B.: Statistical Analysis with Missing Data, JohnWiley and Sons, 1987.
• [20] Nguyen, H. S.: Discretization of real value attributes. Boolean reasoning approach, Ph.D. Thesis, Warsaw University, Faculty of Mathematics, Computer Science and Mechanics, 1997.
• [21] Nguyen, S. H.: Regularity Analysis and its Application in Data Mining, Ph.D. Thesis, Warsaw University, Faculty of Mathematics, Computer Science and Mechanics, 1999.
• [22] Pawlak, Z.: Rough sets: Theoretical aspects of reasoning about data, Kluwer, Dordrecht, 1991.
• [23] Polkowski, L., Skowron, A., Eds.: Rough Sets in Knowledge Discovery 1: Methodology and Applications, Physica-Verlag, 1998.
• [24] Polkowski, L., Skowron, A., ˙Zytkow, J. M.: Tolerance Based Rough Sets, Soft Computing (T. Y. Lin, A. M. Wildberger, Eds.), San Diego Simulation Councils Inc., 1995.
• [25] Pomykała, J. A.: About Tolerance and Similarity Relations in Information Systems, in: Alpigini et al. [1], 175–182.
• [26] Skowron, A., Nguyen, H. S.: Boolean Reasoning Scheme with Some Applications in Data Mining, in: Żytkow and Rauch [35], 107–115.
• [27] Ślęzak, D.,Wróblewski, J.: Classification Algorithms Based on Linear Combinations of Features, in: Żytkow and Rauch [35], 548–553.
• [28] Ślęzak, D., Wróblewski, J.: Application of Normalized Decision Measures to the New Case Classification, in: Ziarko and Yao [34], 553–560.
• [29] Słowiński, R., Stefanowski, J.: Rough classification in incomplete information systems, Math. Computing Modelling, 12, 1989, 1347–1357.
• [30] Stefanowski, J.: On rough set based approaches to induction of decision rules, in: Polkowski and Skowron [23], 500–529.
• [31] Stefanowski, J., Tsoukiàs, A.: On the Extension of Rough Sets under Incomplete Information, New Directions in Rough Sets, Data Mining, and Granular-Soft Computing, RSFDGrC ’99 (N. Zhong, A. Skowron, S. Ohsuga, Eds.), LNCS 1711, Springer, 1999.
• [32] Stefanowski, J., Tsoukiàs, A.: Incomplete Information Tables and Rough Classification, International Journal of Computational Intelligence, 17(3), August 2001, 545–566.
• [33] Wróblewski, J.: Adaptative Methods for Object Classification (in Polish), Ph.D. Thesis, Warsaw University, Faculty of Mathematics, Computer Science and Mechanics, 2001.
• [34] Ziarko, W., Yao, Y. Y., Eds.: Rough Sets and Current Trends in Computing, RSCTC 2000, LNCS 2005, Springer, 2001.
• [35] ˙Zytkow, J. M., Rauch, J., Eds.: Principles of Data Mining and Knowledge Discovery, PKDD ’99, LNCS 1704, Springer, 1999.