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2015 | OriginalPaper | Buchkapitel

A Rough Set Approach to Incomplete Data

verfasst von : Jerzy W. Grzymala-Busse

Erschienen in: Rough Sets and Knowledge Technology

Verlag: Springer International Publishing

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Abstract

This paper presents main directions of research on a rough set approach to incomplete data. First, three different types of lower and upper approximations, based on the characteristic relation, are defined. Then an idea of the probabilistic approximation, an extension of lower and upper approximations, is presented. Local probabilistic approximations are also discussed. Finally, some special topics such as consistency of incomplete data and a problem of increasing data set incompleteness to improve rule set quality, in terms of an error rate, are discussed.

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Vorheriges Kapitel Correction to: Interactive Granular Computing
Nächstes Kapitel PICKT: A Solution for Big Data Analysis
Literatur
1.
Breiman, L., Friedman, J.H., Olshen, R.A., Stone, C.J.: Classification and Regression Trees. Wadsworth & Brooks, Monterey (1984)MATH
2.
Chan, C.C., Grzymala-Busse, J.W.: On the attribute redundancy and the learning programs ID3, PRISM, and LEM2. Technical report, Department of Computer Science, University of Kansas (1991)
3.
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)
4.
Clark, P.G., Grzymala-Busse, J.W.: Consistency of incomplete data. In: Proceedings of the Second International Conference on Data Technologies and Applications, pp. 80–87 (2013)
5.
Clark, P.G., Grzymala-Busse, J.W.: A comparison of two versions of the MLEM2 rule induction algorithm extended to probabilistic approximations. In: Cornelis, C., Kryszkiewicz, M., Ślȩzak, D., Ruiz, E.M., Bello, R., Shang, L. (eds.) RSCTC 2014. LNCS, vol. 8536, pp. 109–119. Springer, Heidelberg (2014)
6.
Clark, P.G., Grzymala-Busse, J.W., Hippe, Z.S.: An analysis of probabilistic approximations for rule induction from incomplete data sets. Fundam. Informaticae 55, 365–379 (2014)CrossRef
7.
Clark, P.G., Grzymala-Busse, J.W., Kuehnhausen, M.: Local probabilistic approximations for incomplete data. In: Chen, L., Felfernig, A., Liu, J., Raś, Z.W. (eds.) ISMIS 2012. LNCS, vol. 7661, pp. 93–98. Springer, Heidelberg (2012) CrossRef
8.
Clark, P.G., Grzymala-Busse, J.W., Kuehnhausen, M.: Mining incomplete data with many missing attribute values. A comparison of probabilistic and rough set approaches. In: Proceedings of the Second International Conference on Intelligent Systems and Applications, pp. 12–17 (2013)
9.
Clark, P.G., Grzymala-Busse, J.W., Rzasa, W.: Mining incomplete data with singleton, subset and concept approximations. Inf. Sci. 280, 368–384 (2014)MathSciNetCrossRef
10.
Cyran, K.A.: Modified indiscernibility relation in the theory of rough sets with real-valued attributes: application to recognition of fraunhofer diffraction patterns. Trans. Rough Sets 9, 14–34 (2008)
11.
12.
Dai, J., Xu, Q.: Approximations and uncertainty measures in incomplete information systems. Inf. Sci. 198, 62–80 (2012)MathSciNetCrossRef
13.
Dai, J., Xu, Q., Wang, W.: A comparative study on strategies of rule induction for incomplete data based on rough set approach. Int. J. Adv. Comput. Technol. 3, 176–183 (2011)
14.
Dardzinska, A., Ras, Z.W.: Chasing unknown values in incomplete information systems. In: Workshop Notes, Foundations and New Directions of Data Mining, in Conjunction with the 3-rd International Conference on Data Mining, pp. 24–30 (2003)
15.
Dardzinska, A., Ras, Z.W.: On rule discovery from incomplete information systems. In: Workshop Notes, Foundations and New Directions of Data Mining, in Conjunction with the 3-rd International Conference on Data Mining, pp. 24–30 (2003)
16.
Greco, S., Matarazzo, B., Slowinski, R.: Dealing with missing data in rough set analysis of multi-attribute and multi-criteria decision problems. In: Zanakis, H., Doukidis, G., Zopounidis, Z. (eds.) Decision Making: Recent developments and Worldwide Applications, pp. 295–316. Kluwer Academic Publishers, Dordrecht (2000)CrossRef
17.
Grzymala-Busse, J.W.: On the unknown attribute values in learning from examples. In: Raś, Z.W., Zemankova, M. (eds.) ISMIS 1991. LNCS, vol. 542, pp. 368–377. Springer, Heidelberg (1991) CrossRef
18.
Grzymala-Busse, J.W.: LERS–a system for learning from examples based on rough sets. In: Slowinski, R. (ed.) Intelligent Decision Support, pp. 3–18. Handbook of Applications and Advances of the Rough Set Theory. Kluwer Academic Publishers, Dordrecht (1992)CrossRef
19.
Grzymala-Busse, J.W.: A new version of the rule induction system LERS. Fundamenta Informaticae 31, 27–39 (1997)MATHCrossRef
20.
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)
21.
Grzymala-Busse, J.W.: Rough set strategies to data with missing attribute values. In: Notes of the Workshop on Foundations and New Directions of Data Mining, in Conjunction with the Third International Conference on Data Mining, pp. 56–63 (2003)
22.
Grzymała-Busse, J.W.: Characteristic relations for incomplete data: a generalization of the indiscernibility relation. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 244–253. Springer, Heidelberg (2004) CrossRef
23.
Grzymala-Busse, J.W.: Data with missing attribute values: generalization of indiscernibility relation and rule induction. Trans. Rough Sets 1, 78–95 (2004)
24.
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)
25.
Grzymała-Busse, J.W.: Incomplete data and generalization of indiscernibility relation, definability, and approximations. In: Slezak, D., Wang, G., Szczuka, M.S., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 244–253. Springer, Heidelberg (2005) CrossRef
26.
Grzymala-Busse, J.W.: A comparison of traditional and rough set approaches to missing attribute values in data mining. In: Proceedings of the 10-th International Conference on Data Mining, Detection, Protection and Security, Royal Mare Village, Crete, pp. 155–163 (2009)
27.
Grzymala-Busse, J.W.: Mining data with missing attribute values: A comparison of probabilistic and rough set approaches. In: Proceedings of the 4-th International Conference on Intelligent Systems and Knowledge Engineering, pp. 153–158 (2009)
28.
Grzymala-Busse, J.W.: Rough set and CART approaches to mining incomplete data. In: Proceedings of the International Conference on Soft Computing and Pattern Recognition, IEEE Computer Society, pp. 214–219 (2010)
29.
Grzymala-Busse, J.W.: A comparison of some rough set approaches to mining symbolic data with missing attribute values. In: Kryszkiewicz, M., Rybinski, H., Skowron, A., Raś, Z.W. (eds.) ISMIS 2011. LNCS, vol. 6804, pp. 52–61. Springer, Heidelberg (2011) CrossRef
30.
Grzymała-Busse, J.W.: Generalized parameterized approximations. In: Yao, J.T., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 136–145. Springer, Heidelberg (2011) CrossRef
31.
Grzymala-Busse, J.W., Clark, P.G., Kuehnhausen, M.: Generalized probabilistic approximations of incomplete data. Int. J. Approximate Reasoning 132, 180–196 (2014)MathSciNetCrossRef
32.
Grzymala-Busse, J.W., Grzymala-Busse, W.J.: Handling missing attribute values. In: Maimon, O., Rokach, L. (eds.) Data Mining and Knowledge Discovery Handbook, pp. 37–57. Springer, Heidelberg (2005)CrossRef
33.
Grzymala-Busse, J.W., Grzymala-Busse, W.J.: An experimental comparison of three rough set approaches to missing attribute values. Trans. Rough Sets 6, 31–50 (2007)MATH
34.
Grzymala-Busse, J.W., Grzymala-Busse, W.J.: Improving quality of rule sets by increasing incompleteness of data sets. In: Proceedings of the Third International Conference on Software and Data Technologies, pp. 241–248 (2008)
35.
Grzymala-Busse, J.W., Grzymala-Busse, W.J.: Inducing better rule sets by adding missing attribute values. In: Chan, C.-C., Grzymala-Busse, J.W., Ziarko, W.P. (eds.) RSCTC 2008. LNCS (LNAI), vol. 5306, pp. 160–169. Springer, Heidelberg (2008) CrossRef
36.
Grzymala-Busse, J.W., Grzymala-Busse, W.J.: Handling missing attribute values. In: Maimon, O., Rokach, L. (eds.) Data Mining and Knowledge Discovery Handbook, 2nd edn, pp. 33–51. Springer, Heidelberg (2010)MATH
37.
Grzymala-Busse, J.W., Grzymala-Busse, W.J., Goodwin, L.K.: A comparison of three closest fit approaches to missing attribute values in preterm birth data. Int. J. Intell. Syst. 17(2), 125–134 (2002)CrossRef
38.
Grzymala-Busse, J.W., Grzymala-Busse, W.J., Hippe, Z.S., Rzasa, W.: An improved comparison of three rough set approaches to missing attribute values. In: Proceedings of the 16-th International Conference on Intelligent Information Systems, pp. 141–150 (2008)
39.
Grzymala-Busse, J.W., Hippe, Z.S.: Mining data with numerical attributes and missing attribute values–a rough set approach. In: Proceedings of the IEEE International Conference on Granular Computing, pp. 144–149 (2011)
40.
Grzymała-Busse, J.W., Hu, M.: A comparison of several approaches to missing attribute values in data mining. In: Ziarko, W.P., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, p. 378. Springer, Heidelberg (2001) CrossRef
41.
Grzymala-Busse, J.W., Rzasa, W.: Local and global approximations for incomplete data. In: Greco, S., Hata, Y., Hirano, S., Inuiguchi, M., Miyamoto, S., Nguyen, H.S., Słowiński, R. (eds.) RSCTC 2006. LNCS (LNAI), vol. 4259, pp. 244–253. Springer, Heidelberg (2006) CrossRef
42.
Grzymala-Busse, J.W., Rzasa, W.: Local and global approximations for incomplete data. Trans. Rough Sets 8, 21–34 (2008)MathSciNetMATH
43.
Grzymala-Busse, J.W., Rzasa, W.: A local version of the MLEM2 algorithm for rule induction. Fundamenta Informaticae 100, 99–116 (2010)MathSciNetMATHCrossRef
44.
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 5-th International Workshop on Rough Sets and Soft Computing in conjunction with the Third Joint Conference on Information Sciences, pp. 69–72 (1997)
45.
Grzymala-Busse, J.W., Yao, Y.: Probabilistic rule induction with the LERS data mining system. Int. J. Intell. Syst. 26, 518–539 (2011)CrossRef
46.
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)CrossRef
47.
Guan, L., Wang, G.: Generalized approximations defined by non-equivalence relations. Inf. Sci. 193, 163–179 (2012)MathSciNetCrossRef
48.
Hong, T.P., Tseng, L.H., Chien, B.C.: Learning coverage rules from incomplete data based on rough sets. In: Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, pp. 3226–3231 (2004)
49.
Hong, T.P., Tseng, L.H., Wang, S.L.: Learning rules from incomplete training examples by rough sets. Expert Syst. Appl. 22, 285–293 (2002)CrossRef
50.
Kryszkiewicz, M.: Rough set approach to incomplete information systems. In: Proceedings of the Second Annual Joint Conference on Information Sciences, pp. 194–197 (1995)
51.
52.
Latkowski, R.: On decomposition for incomplete data. Fundamenta Informaticae 54, 1–16 (2003)MathSciNetMATH
53.
Latkowski, R., Mikołajczyk, M.: Data decomposition and decision rule joining for classification of data with missing values. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 254–263. Springer, Heidelberg (2004) CrossRef
54.
Leung, Y., Wu, W., Zhang, W.: Knowledge acquisition in incomplete information systems: a rough set approach. Eur. J. Ope. Res. 168, 164–180 (2006)MathSciNetCrossRef
55.
Li, D., Deogun, I., Spaulding, W., Shuart, B.: Dealing with missing data: algorithms based on fuzzy set and rough set theories. Trans. Rough Sets 4, 37–57 (2005)MATH
56.
Li, H., Yao, Y., Zhou, X., Huang, B.: Two-phase rule induction from incomplete data. In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds.) RSKT 2008. LNCS (LNAI), vol. 5009, pp. 47–54. Springer, Heidelberg (2008) CrossRef
57.
Li, T., Ruan, D., Geert, W., Song, J., Xu, Y.: A rough sets based characteristic relation approach for dynamic attribute generalization in data mining. Knowl. Based Syst. 20(5), 485–494 (2007)CrossRef
58.
Li, T., Ruan, D., Song, J.: Dynamic maintenance of decision rules with rough set under characteristic relation. In: Proceedings of the International Conference on Wireless Communications, Networking and Mobile Computing, pp. 3713–3716 (2007)
59.
Meng, Z., Shi, Z.: A fast approach to attribute reduction in incomplete decision systems with tolerance relation-based rough sets. Inf. Sci. 179, 2774–2793 (2009)MathSciNetCrossRef
60.
Meng, Z., Shi, Z.: Extended rough set-based attribute reduction in inconsistent incomplete decision systems. Inf. Sci. 204, 44–69 (2012)MathSciNetCrossRef
61.
Nakata, M., Sakai, H.: Rough sets handling missing values probabilistically interpreted. In: Slezak, D., Wang, G., Szczuka, M.S., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 325–334. Springer, Heidelberg (2005) CrossRef
62.
Nakata, M., Sakai, H.: Applying rough sets to information tables containing missing values. In: Proceedings of the 39-th International Symposium on Multiple-Valued Logic, pp. 286–291 (2009)
63.
Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341–356 (1982)CrossRef
64.
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991) CrossRef
65.
Pawlak, Z., Grzymala-Busse, J.W., Slowinski, R., Ziarko, W.: Rough sets. Commun. ACM 38, 89–95 (1995)CrossRef
66.
67.
Pawlak, Z., Wong, S.K.M., Ziarko, W.: Rough sets: probabilistic versus deterministic approach. Int. J. Man-Mach. Stud. 29, 81–95 (1988)CrossRef
68.
Peng, H., Zhu, S.: Handling of incomplete data sets using ICA and SOM in data mining. Neural Comput. Appl. 16, 167–172 (2007)CrossRef
69.
Qi, Y.S., Wei, L., Sun, H.J., Song, Y.Q., Sun, Q.S.: Characteristic relations in generalized incomplete information systems. In: International Workshop on Knowledge Discovery and Data Mining, pp. 519–523 (2008)
70.
Qi, Y.S., Sun, H., Yang, X.B., Song, Y., Sun, Q.: Approach to approximate distribution reduct in incomplete ordered decision system. J. Inf. Comput. Sci. 3, 189–198 (2008)
71.
Qian, Y., Dang, C., Liang, J., Zhang, H., Ma, J.: On the evaluation of the decision performance of an incomplete decision table. Data Knowl. Eng. 65, 373–400 (2008)CrossRef
72.
Qian, Y., Li, D., Wang, F., Ma, N.: Approximation reduction in inconsistent incomplete decision tables. Knowl. Based Syst. 23, 427–433 (2010)CrossRef
73.
Ślȩzak, D., Ziarko, W.: The investigation of the bayesian rough set model. Int. J. Approx. Reason. 40, 81–91 (2005)MathSciNetCrossRef
74.
Song, J., Li, T., Ruan, D.: A new decision tree construction using the cloud transform and rough sets. In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds.) RSKT 2008. LNCS (LNAI), vol. 5009, pp. 524–531. Springer, Heidelberg (2008) CrossRef
75.
Song, J., Li, T., Wang, Y., Qi, J.: Decision tree construction based on rough set theory under characteristic relation. In: Proceedings of the ISKE 2007, the 2-nd International Conference on Intelligent Systems and Knowledge Engineering Conference, pp. 788–792 (2007)
76.
Stefanowski, J., Tsoukiàs, A.: On the extension of rough sets under incomplete information. In: Zhong, N., Skowron, A., Ohsuga, S. (eds.) RSFDGrC 1999. LNCS (LNAI), vol. 1711, pp. 73–82. Springer, Heidelberg (1999) CrossRef
77.
Stefanowski, J., Tsoukias, A.: Incomplete information tables and rough classification. Computat. Intell. 17(3), 545–566 (2001)CrossRef
78.
Wang, G.: Extension of rough set under incomplete information systems. In: Proceedings of the IEEE International Conference on Fuzzy Systems, pp. 1098–1103 (2002)
79.
Wong, S.K.M., Ziarko, W.: INFER–an adaptive decision support system based on the probabilistic approximate classification. In: Proceedings of the 6-th International Workshop on Expert Systems and their Applications, pp. 713–726 (1986)
80.
Yang, X., Yang, J.: Incomplete Information System and Rough Set Theory: Model and Attribute Reduction. Springer, Heidelberg (2012) CrossRef
81.
Yang, X., Zhang, M., Dou, H., Yang, J.: Neighborhood systems-based rough sets in incomplete information systems. Knowl. Based Syst. 24, 858–867 (2011)CrossRef
82.
Yao, Y.Y.: Probabilistic rough set approximations. Int. J. Approx. Reason. 49, 255–271 (2008)CrossRef
83.
Yao, Y.Y., Wong, S.K.M.: A decision theoretic framework for approximate concepts. Int. J. Man Mach. Stud. 37, 793–809 (1992)CrossRef
84.
Yao, Y.Y., Wong, S.K.M., Lingras, P.: A decision-theoretic rough set model. In: Ras, Z.W., Zemankova, M., Emrich, M.L. (eds.) Methodologies for Intelligent Systems, North-Holland, pp. 388–395 (1990)
85.
86.
Metadaten
Titel
A Rough Set Approach to Incomplete Data
verfasst von
Jerzy W. Grzymala-Busse
Copyright-Jahr
2015
Buch
Rough Sets and Knowledge Technology

Print ISBN: 978-3-319-25753-2

Electronic ISBN: 978-3-319-25754-9

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-3-319-25754-9_1

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