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A Framework of Three-Way Cluster Analysis

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Rough Sets (IJCRS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10314))

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Abstract

A new framework of clustering is proposed inspired by the theory of three-way decisions, which is an alternative formulation different from the ones used in the existing studies. The novel three-way representation intuitively shows which objects are fringe to the cluster and it is proposed for dealing with uncertainty clustering. Instead of using two regions to represent a cluster by a single set, a cluster is represented using three regions through a pair of sets, and there are three regions such as the core region, fringe region and trivial region. A cluster is therefore more realistically characterized by a set of core objects and a set of boundary objects. In this paper, we also illustrate an algorithm for incomplete data by using the proposed evaluation-based three-way cluster model. The preliminary experimental results show that the proposed method is effective for clustering incomplete data which is one kind of uncertainty data. Furthermore, this paper reviews some three-way clustering approaches and discusses some future perspectives and potential research topics based on the three-way cluster analysis.

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References

  1. Azam, N., Yao, J.T.: Analyzing uncertainties of probabilistic rough set regions with game-theoretic rough sets. Int. J. Approx. Reason. 55(1), 142–155 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chen, H.M., Li, T.R., Luo, C., Horng, S., Wang, G.Y.: A decision-theoretic rough set approach for dynamic data mining. IEEE Trans. Fuzzy Syst. 99(1) (2015). doi:10.1109/TFUZZ.2014.2387877

  3. Chen, M., Miao, D.Q.: Interval set clustering. Expert Syst. Appl. 38(4), 2923–2932 (2011)

    Article  Google Scholar 

  4. Estivill-Castro, V.: Why so many clustering algorithms: a position paper. ACM SIGKDD Explor. Newsl. 4(1), 65–75 (2002)

    Article  MathSciNet  Google Scholar 

  5. Hathaway, R.J., Bezdek, J.C.: Fuzzy C-means clustering of incomplete data. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 31(5), 735–744 (2001)

    Article  Google Scholar 

  6. Höppner, F., Klawonn, F., Kruse, R., Runkler, T.: Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition. Wiley, Chichester (1999)

    MATH  Google Scholar 

  7. Li, H.X., Zhou, X.Z.: Risk decision making based on decision-theoretic rough set: a three-way view decision model. Int. J. Comput. Intell. Syst. 4(1), 1–11 (2011)

    Article  MathSciNet  Google Scholar 

  8. Li, Y., Zhang, Z., Chen, W.B., Min, F.: TDUP: an approach to incremental mining of frequent itemsets with three-way-decision pattern updating. Int. J. Mach. Learn. Cybern. 8(1), 441–453 (2015)

    Google Scholar 

  9. Liang, D.C., Xu, Z.S., Liu, D.: Three-way decisions with intuitionistic fuzzy decision-theoretic rough sets based on point operators. Inf. Sci. 375, 183–201 (2017)

    Article  Google Scholar 

  10. Liang, D.C., Liu, D.: A novel risk decision-making based on decision-theoretic rough sets under hesitant fuzzy information. J. IEEE Trans. Fuzzy Syst. 23(2), 237–247 (2015)

    Article  Google Scholar 

  11. Liu, D., Liang, D.C., Wang, C.C.: A novel three-way decision model based on incomplete information system. Knowl. Based Syst. 91, 32–45 (2016)

    Article  Google Scholar 

  12. Lingras, P., Yan, R.: Interval clustering using fuzzy and rough set theory. In: Proceedings of the 2004 IEEE Annual Meeting of the Fuzzy Information, Banff, Alberta, pp. 780–784 (2004)

    Google Scholar 

  13. Lingras, P., West, C.: Interval set clustering of web users with rough K-means. J. Intell. Inf. Syst. 23(1), 5–16 (2004)

    Article  MATH  Google Scholar 

  14. Lu, C., Song, S., Wu, C.: K-nearest neighbor intervals based AP clustering algorithm for large incomplete data. Math. Probl. Eng. 2015 (2015). http://dx.doi.org/10.1155/2015/535932

  15. Rodriguez, A., Laio, A.: Clustering by fast search and find of density peaks. Science 344(6191), 1492–1496 (2014)

    Article  Google Scholar 

  16. Xu, R., Wunsch, D.: Survey of clustering algorithms. IEEE Trans. Neural Netw. 16(3), 645–678 (2005)

    Article  Google Scholar 

  17. Yao, Y.: An outline of a theory of three-way decisions. In: Yao, J.T., Yang, Y., Słowiński, R., Greco, S., Li, H., Mitra, S., Polkowski, L. (eds.) RSCTC 2012. LNCS, vol. 7413, pp. 1–17. Springer, Heidelberg (2012). doi:10.1007/978-3-642-32115-3_1

    Chapter  Google Scholar 

  18. Yao, Y.: Three-way decisions and cognitive computing. Cogn. Comput. (2016). doi:10.1007/s12559-016-9397-5

  19. Yao, Y.: Interval sets and three-way concept analysis in incomplete contexts. Int. J. Mach. Learn. Cybern. 8(1), 3–20 (2017)

    Article  MathSciNet  Google Scholar 

  20. Yao, Y.Y., Lingras, P., Wang, R.Z., Miao, D.Q.: Interval set cluster analysis: a re-formulation. Rough Sets. Fuzzy Sets, Data Mining and Granular Computing, pp. 398–405. Springer, Berlin Heidelberg (2009). doi:10.1007/978-3-642-10646-0_48

    Google Scholar 

  21. Yu, H., Jiao, P., Yao, Y.Y., Wang, G.Y.: Detecting and refining overlapping regions in complex networks with three-way decisions. Inf. Sci. 373, 21–41 (2016)

    Article  Google Scholar 

  22. Yu, H., Liu, Z.G., Wang, G.Y.: An automatic method to determine the number of clusters using decision-theoretic rough set. Int. J. Approx. Reason. 55, 101–115 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  23. Yu, H., Su, T., Zeng, X.: A three-way decisions clustering algorithm for incomplete data. In: Miao, D., Pedrycz, W., Ślȩzak, D., Peters, G., Hu, Q., Wang, R. (eds.) RSKT 2014. LNCS, vol. 8818, pp. 765–776. Springer, Cham (2014). doi:10.1007/978-3-319-11740-9_70

    Google Scholar 

  24. Yu, H., Wang, Y.: Three-way decisions method for overlapping clustering. In: Yao, J.T., Yang, Y., Słowiński, R., Greco, S., Li, H., Mitra, S., Polkowski, L. (eds.) RSCTC 2012. LNCS, vol. 7413, pp. 277–286. Springer, Heidelberg (2012). doi:10.1007/978-3-642-32115-3_33

    Chapter  Google Scholar 

  25. Yu, H., Zhang, C., Wang, G.Y.: A tree-based incremental overlapping clustering method using the three-way decision theory. Knowl.-Based Syst. 91, 189–203 (2016)

    Article  Google Scholar 

  26. Yu, H., Wang, G.Y., Li, T.R., Liang, J.Y., Miao, D.Q., Yao, Y.Y.: Three-way Decisions: Methods and Practices for Complex Problem Solving. Science Press, Beijing (2015). (in Chinese)

    Google Scholar 

  27. Zhang, H.R., Min, F., Shi, B.: Regression-based three-way recommendation. Inf. Sci. 378, 444–461 (2017)

    Article  Google Scholar 

  28. Zhang, Y., Zou, H., Chen, X., Wang, X., Tang, X., Zhao, S.: Cost-sensitive three-way decisions model based on CCA. In: Cornelis, C., Kryszkiewicz, M., Ślȩzak, D., Ruiz, E.M., Bello, R., Shang, L. (eds.) RSCTC 2014. LNCS, vol. 8536, pp. 172–180. Springer, Cham (2014). doi:10.1007/978-3-319-08644-6_18

    Google Scholar 

  29. Zhang, L., Li, B., Zhang, L., Li, D.: Fuzzy clustering of incomplete data based on missing attribute interval size. In: 2015 IEEE 9th International Conference on Anticounterfeiting, Security, and Identification (ASID), pp. 101–104. IEEE (2015)

    Google Scholar 

  30. Zhang, Y., Yao, J.T.: Gini objective functions for three-way classifications. Int. J. Approx. Reason. 81, 103–114 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  31. Zhou, B., Yao, Y., Luo, J.G.: Cost-sensitive three-way email spam filtering. J. Intell. Inf. Syst. 42, 19–45 (2013)

    Article  Google Scholar 

  32. UCI Machine Learning Repository. http://archive.ics.uci.edu/ml

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Acknowledgments

I am grateful to Professor Yiyu Yao for his suggestions, and I would like to thank Ms. Ting Su for her help to complete the experimental work. In addition, this work was supported in part by the National Natural Science Foundation of China under grant No. 61379114 and No. 61533020.

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Authors and Affiliations

  1. Chongqing Key Laboratory of Computational Intelligence, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Hong Yu

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  1. Hong Yu
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Correspondence to Hong Yu .

Editor information

Editors and Affiliations

  1. Polish-Japanese Academy of Information Technology, Warsaw, Poland

    Lech Polkowski

  2. University of Regina, Regina, Saskatchewan, Canada

    Yiyu Yao

  3. University of Warmia and Mazury, Olsztyn, Poland

    Piotr Artiemjew

  4. University of Milano-Bicocca, Milano, Italy

    Davide Ciucci

  5. Southwest Jiaotong University, Chengdu, China

    Dun Liu

  6. Warsaw University, Warszawa, Poland

    Dominik Ślęzak

  7. Silesian University, Sosnowiec, Poland

    Beata Zielosko

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Yu, H. (2017). A Framework of Three-Way Cluster Analysis. In: Polkowski, L., et al. Rough Sets. IJCRS 2017. Lecture Notes in Computer Science(), vol 10314. Springer, Cham. https://doi.org/10.1007/978-3-319-60840-2_22

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  • DOI: https://doi.org/10.1007/978-3-319-60840-2_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60839-6

  • Online ISBN: 978-3-319-60840-2

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