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Fuzzy K-Minpen Clustering and K-nearest-minpen Classification Procedures Incorporating Generic Distance-Based Penalty Minimizers

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Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 611))

Abstract

We discuss a generalization of the fuzzy (weighted) k-means clustering procedure and point out its relationships with data aggregation in spaces equipped with arbitrary dissimilarity measures. In the proposed setting, a data set partitioning is performed based on the notion of points’ proximity to generic distance-based penalty minimizers. Moreover, a new data classification algorithm, resembling the k-nearest neighbors scheme but less computationally and memory demanding, is introduced. Rich examples in complex data domains indicate the usability of the methods and aggregation theory in general.

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References

  1. Ban, A.I., Coroianu, L., Grzegorzewski, P.: Trapezoidal approximation and aggregation. Fuzzy Sets Syst. 177(1), 45–59 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  2. Beliakov, G., Bustince, H., Calvo, T.: A Practical Guide to Averaging Functions. Studies in Fuzziness and Soft Computing. Springer, Heidelberg (2016)

    Book  Google Scholar 

  3. Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Advanced Applications in Pattern Recognition. Springer, Heidelberg (1981)

    Book  MATH  Google Scholar 

  4. Bock, H.H.: Origins and extensions of the \(k\)-means algorithm in cluster analysis. Electron. J. Hist. Probab. Stat. 4(2), 1–18 (2008)

    MathSciNet  Google Scholar 

  5. Boytsov, L.: Indexing methods for approximate dictionary searching: comparative analyses. ACM J. Exp. Algorithmics 16, 1–86 (2011)

    MathSciNet  MATH  Google Scholar 

  6. Calvo, T., Beliakov, G.: Aggregation functions based on penalties. Fuzzy Sets Syst. 161, 1420–1436 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cena, A., Gagolewski, M.: Aggregation and soft clustering of informetric data. In: Baczynski, M., De Baets, B., Mesiar, R. (eds.) Proceeding 8th International Summer School on Aggregation Operators (AGOP 2015), pp. 79–84. University of Silesia, Katowice (2015)

    Google Scholar 

  8. Chavent, M., Saracco, J.: Central tendency and dispersion measures for intervals and hypercubes. Commun. Stat. Theor. Methods 37, 1471–1482 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Coppersmith, D., Fleischer, L., Rudra, A.: Ordering by weighted number of wins gives a good ranking for weighted tournaments. In: Proceeding 17th Annual ACM-SIAM Symposium Discrete Algorithms (SODA 2006), pp. 776–782. ACM (2006)

    Google Scholar 

  10. Dinu, L.P., Manea, F.: An efficient approach for the rank aggregation problem. Theor. Comput. Sci. 359(1–3), 455–461 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  11. Dwork, C., Kumar, R., Naor, M., Sivakumar, D.: Rank aggregation methods for the web. In: Proceedings of the 10th International Conference on World Wide Web, pp. 613–622. ACM (2001)

    Google Scholar 

  12. Gagolewski, M.: Data Fusion: Theory, Methods, and Applications. Institute of Computer Science, Polish Academy of Sciences, Warsaw (2015)

    Google Scholar 

  13. Golub, T., et al.: Molecular classification of cancer: class discovery and class prediction by gene expression monitoring. Science 286, 531–537 (1999)

    Article  Google Scholar 

  14. Grabisch, M., Marichal, J.L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press, Cambridge (2009)

    Book  MATH  Google Scholar 

  15. Grzegorzewski, P.: Metrics and orders in space of fuzzy numbers. Fuzzy Sets Syst. 97, 83–94 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  16. Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer Series in Statistics. Springer, NewYork (2013)

    MATH  Google Scholar 

  17. Klawonn, F., Höppner, F.: What is fuzzy about fuzzy clustering? Understanding and improving the concept of the fuzzifier. In: Berthold, M., Lenz, H.-J., Bradley, E., Kruse, R., Borgelt, C. (eds.) IDA 2003. LNCS, vol. 2810, pp. 254–264. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  18. Leisch, F.: A toolbox for K-centroids cluster analysis. Computat. Stat. Data Anal. 51(2), 526–544 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  19. MacQueen, J.B.: Some methods for classification and analysis of multivariate observations. In: Proceeding Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 281–297. University of California Press, Berkeley (1967)

    Google Scholar 

  20. Tibshirani, R., Hastie, T., Narasimhan, B., Chu, G.: Diagnosis of multiple cancer types by shrunken centroids of gene expression. Proc. Nat. Acad. Sci. 99(10), 6567–6572 (2002)

    Article  Google Scholar 

  21. Winkler, R., Klawonn, F., Kruse, R.: Fuzzy clustering with polynomial fuzzifier in connection with M-estimators. Appl. Comput. Math. 10, 146–163 (2011)

    MathSciNet  MATH  Google Scholar 

  22. Yu, J., Yang, M.S.: Optimality test for generalized FCM and its application to parameter selection. IEEE Trans. Fuzzy Syst. 13(1), 164–176 (2005)

    Article  Google Scholar 

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Acknowledgments

This study was supported by the National Science Center, Poland, research project 2014/13/D/HS4/01700.

Author information

Authors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Anna Cena & Marek Gagolewski

  2. Faculty of Mathematics and Information Science, Warsaw University of Technology, ul. Koszykowa 75, 00-662, Warsaw, Poland

    Marek Gagolewski

Authors
  1. Anna Cena
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  2. Marek Gagolewski
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Corresponding author

Correspondence to Marek Gagolewski .

Editor information

Editors and Affiliations

  1. INESC-ID,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Joao Paulo Carvalho

  2. LIP 6, Université Pierre et Marie Curie, Paris, France

    Marie-Jeanne Lesot

  3. School of Industrial Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Uzay Kaymak

  4. IDMEC,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Susana Vieira

  5. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  6. Iona College, Machine Intelligence Institute, New Rochelle, New York, USA

    Ronald R. Yager

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Cena, A., Gagolewski, M. (2016). Fuzzy K-Minpen Clustering and K-nearest-minpen Classification Procedures Incorporating Generic Distance-Based Penalty Minimizers. In: Carvalho, J., Lesot, MJ., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2016. Communications in Computer and Information Science, vol 611. Springer, Cham. https://doi.org/10.1007/978-3-319-40581-0_36

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  • DOI: https://doi.org/10.1007/978-3-319-40581-0_36

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40580-3

  • Online ISBN: 978-3-319-40581-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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