Collaborative Clustering: New Perspective to Rank Factor Granules

  • Shihu Liu
  • Xiaozhou Chen
  • Patrick S. P. Wang
Part of the Studies in Computational Intelligence book series (SCI, volume 756)


The purpose of ranking, for decision makers, is to discover a mechanism that can produce a possible linear sequence of the data to be ranked. But this is not an easy thing, especially for the highly structured data. This paper will make a discussion on the ranking problem for factor granules in viewpoint of fuzzy collaborative clustering. Hereinto, each factor granule is composed by three parts: the patterns, the factors and the factor-induced information (i.e., the patterns attributes and the relationship between any two patterns). The overall ranking process is based on the ideology of fuzzy collaborative clustering by considering a referential factor granule, where the collaborative information, i.e., the partition matrices of factor granules, are used to collaborate the clustering for the referential factor granule. By comparing the difference of the referential factor granule before and after collaboration in aspects of clustering results, we can sort these factor granules: the little the difference, the closer to the top of the sequence.



This work has been supported by the National Natural Science Foundation of China(No. 31460297), Natural Science Foundation of Shandong Province(ZR2016AP12), Yunnan Applied Basic Research Youth Projects(No. 2015FD032), the Scientific Research Funds of Yunnan Provincial Department of Education(No. 2015Y224) and the Talent Introduction Research Project of Yunnan Minzu University.


  1. 1.
    Adler, N., Friedman, L., Sinuany-Stern, Z.: Review of ranking methods in the data envelopment analysis context. Eur. J. Oper. Res. 140(2), 249–265 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Agarwal, S.: Ranking on graph data. In: The 23rd ACM International Conference on Machine learning, Pittsburgh, Pennsylvania, USA, pp. 25-32 (2006)Google Scholar
  3. 3.
    Agarwal, S.: Learning to rank on graphs. Mach. Learn. 81(3), 333–357 (2010)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Agarwal, S., Dugar, D., Sengupta, S.: Ranking chemical structures for drug discovery: a new machine learning approach. J. Chem. Inf. Model. 50(5), 716–731 (2010)CrossRefGoogle Scholar
  5. 5.
    Bekkerman, R., Bilenko, M., Langford, J.: Scaling Up Machine Learning: Parallel and Distributed Approaches, Cambridge University Press (2012)Google Scholar
  6. 6.
    Bilsel, R.U., Büyüközkan, G., Ruan, D.: A fuzzy preference-ranking model for a quality evaluation of hospital web sites. Int. J. Intell. Syst. 21(11), 1181–1197 (2006)CrossRefzbMATHGoogle Scholar
  7. 7.
    Chechik, G., Sharma, V., Shalit, U., et al.: Large scale online learning of image similarity through ranking. J. Mach. Learn. Res. 11, 1109–1135 (2009)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Chen, H., Peng, J.T., Zhou, Y.C., et al.: Extreme learning machine for ranking: generalization analysis and applications. Neural Netw. 53, 119–126 (2014)CrossRefzbMATHGoogle Scholar
  9. 9.
    Choudhary, L., Burdak, B.S.: Role of ranking algorithms for information retrieval. Int. J. Artif. Intell. Appl. 3(4), 203–220 (2012)Google Scholar
  10. 10.
    Chun, Y.H., Sumichrast, R.T.: A rank-based approach to the sequential selection and assignment problem. Eur. J. Oper. Res. 174(2), 1338–1344 (2006)CrossRefzbMATHGoogle Scholar
  11. 11.
    Coletta, L.F.S., Vendramin, L., Hruschka, E.R., et al.: Collaborative fuzzy clustering algorithms: some refinements and design guidelines. IEEE Trans. Fuzzy Syst. 20(3), 444–462 (2012)CrossRefGoogle Scholar
  12. 12.
    Dubois, D., Prade, H.: Operations on fuzzy numbers. Int. J. Syst. Sci. 9(6), 613–626 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Džeroski, S.: Relational Data Mining, Springer (2010)Google Scholar
  14. 14.
    Figueira, J., Greco, S., Ehrgott, M.: Multiple Criteria Decision Analysis: State of the Art Surveys, Springer (2005)Google Scholar
  15. 15.
    Hsu, W.C., Liu, C.C., Chang, F., et al.: Selecting genes for cancer classification using SVM: an adaptive multiple features scheme. Int. J. Intell. Syst. 18(12), 1196–1213 (2013)CrossRefGoogle Scholar
  16. 16.
    Hwang, C.L., Yoon, K.: Multiple Attribute Decision Making: Methods and Applications. Springer, New York (1981)CrossRefzbMATHGoogle Scholar
  17. 17.
    Jiang, Y., Chung, F., Wang, S., et al.: Collaborative fuzzy clustering from multiple weighted views. IEEE Trans. Syst. Man Cybern. 45(4), 688–701 (2015)CrossRefGoogle Scholar
  18. 18.
    Lee, S., Song, S., Kahng, M. et al.: Random walk based entity ranking on graph for multidimensional recommendation. In: The 5th ACM International Conference on Recommender System, pp. 93–100 (2011)Google Scholar
  19. 19.
    Li, G., Wang, L.Y., Ou, W.H.: Robust personalized ranking from implicit feedback. Int. J. Pattern Recognit. Artif. Intell. 30(01) (2016)Google Scholar
  20. 20.
    Liu, S.H.: Clustering analysis for data with relational information. Ph.D. Thesis, Beijing Normal University (2014)Google Scholar
  21. 21.
    Liu, T.Y.: Learning to rank for information retrieval. Found. Trends Inf. Retr. 3(3), 225–331 (2009)CrossRefGoogle Scholar
  22. 22.
    Mansoori, E.G.: Using statistical measures for feature ranking. Int. J. Pattern Recognit. Artif. Intell. 27(01), 14 (2013)Google Scholar
  23. 23.
    Mihalcea, R.: Graph-based ranking algorithms for sentence extraction, applied to text summarization. In: The 2004 ACL on Interactive Poster and Demonstration Sessions, p. 4 (2004)Google Scholar
  24. 24.
    Omladic, M., Semrl, P.: On the distance between normal matrices. Proc. Am. Math. Soc. 110(3), 591–596 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Pathak, A., Pal, N.R.: Clustering of mixed data by integrating fuzzy probabilistic, and collaborative clustering framework. Int. J. Fuzzy Syst. 18(3), 339–348 (2016)CrossRefGoogle Scholar
  26. 26.
    Pawlak, Z.: Rough sets. J. Comput. Inf. Sci. 11(5), 341–356 (1982)CrossRefzbMATHGoogle Scholar
  27. 27.
    Pedersen, C.R., Nielsen, l.R., Andersen, K.A., et al.: An algorithm for ranking assignments using reoptimization. Comput. Oper. Res. 35(11), 3714–3726 (2008)Google Scholar
  28. 28.
    Pedrycz, W.: Collaborative fuzzy clustering. Pattern Recognit. Lett. 23(14), 1675–1686 (2002)CrossRefzbMATHGoogle Scholar
  29. 29.
    Przybylski, A., Gandibleux, X., Ehrgott, M.: A two phase method for multi-objective integer programming and its application to the assignment problem with three objectives. Discret. Optim. 7(3), 149–165 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Qian, Y.H., Liang, J.Y., Dang, C.Y.: Interval ordered information systems. Comput. Math. Appl. 56(8), 1994–2009 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Qian, Y.H., Liang, J.Y., Song, P., et al.: On dominance relations in disjunctive setvalued ordered information systems. Int. J. Inf. Technol. Decis. Mak. 9(1), 9–33 (2010)CrossRefzbMATHGoogle Scholar
  32. 32.
    Qin, T., Zhang, X.D., Tsai, M.F., et al.: Query-level loss functions for information retrieval. Inf. Process. Manage. 44(2), 838–855 (2008)CrossRefGoogle Scholar
  33. 33.
    Song, F.X., You, J., Zhang, D., et al.: Impact of full rank principal component analysis on classification algorithms for face recognition. Int. J. Pattern Recognit. Artif. Intell. 26(03), 1256005(23 pages) (2012)Google Scholar
  34. 34.
    Tiskin, A.: Fast distance multiplication of unit-monge matrices. Algorithmica 71(4), 859–888 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Wang, P.Z.: Factorial analysis and data science. J. Liaoning Tech. Univ. 34(2), 273–280 (2015)Google Scholar
  36. 36.
    Wang, H.D., Wang, P.Z., Shi, Y., et al.: Improved factorial analysis algorithm in factorspaces. In: Proceedings of 2014 International Conference on Informatics, Networking and Intelligent Computing, Shengzhen (2014)Google Scholar
  37. 37.
    Wang, P.Z., Li, H.X.: A Mathematical Theory on Knowledge Representation. Tianjin Scientific and Technical Press, Tianjing (1994)Google Scholar
  38. 38.
    Wang, P.Z., Liu, Z.L., Shi, Y., et al.: Factor space, the theoretical base of data science. Ann. Data Sci. 1(2), 233–251 (2014)CrossRefGoogle Scholar
  39. 39.
    Wang, P.Z., Sugeno, M.: The factors field and background structure for fuzzy subsets. Fuzzy Math. 2(2), 45–54 (1982)MathSciNetGoogle Scholar
  40. 40.
    Webber, W., Moffat, A., Zobel, J.: A similarity measure for indefinite rankings. ACM Trans. Inf. Syst. 28(4), 20 (2010)Google Scholar
  41. 41.
    Yu, F.S., Luo, C.Z.: Granule factors space and intelligent diagnostic expert systems. In: Proceedings of the 7th National Conference on Electric Mathematics, Advances of Electric Mathematics, China Science & Technology Press, Beijing (1999)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Shihu Liu
    • 1
  • Xiaozhou Chen
    • 2
  • Patrick S. P. Wang
    • 3
  1. 1.School of Mathematics and Computer SciencesYunnan Minzu UniversityKunmingPeople’s Republic of China
  2. 2.Key Laboratory of IOT Application Technology of Universities in Yunnan ProvinceYunnan Minzu UniversityKunmingPeople’s Republic of China
  3. 3.College of Computer and Information ScienceNortheastern UniversityBostonUSA

Personalised recommendations