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Improvement of the Validity Index for Determination of an Appropriate Data Partitioning

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Artificial Intelligence and Soft Computing (ICAISC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10246))

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Abstract

In this paper a detail analysis of an improvement of the Silhouette validity index is presented. This proposed approach is based on using an additional component which improves clusters validity assessment and provides better results during a clustering process, especially when the naturally existing groups in a data set are located in very different distances. The performance of the modified index is demonstrated for several data sets, where the Complete–linkage method has been applied as the underlying clustering technique. The results prove superiority of the new approach as compared to other methods.

A. Krzyżak—Carried out this research at WUT during his sabbatical leave from Concordia University.

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References

  1. Arbelaitz, O., Gurrutxaga, I., Muguerza, J., Prez, J.M., Perona, I.: An extensive comparative study of cluster validity indices. Pattern Recogn. 46, 243–256 (2013)

    Article  Google Scholar 

  2. Bilski, J., Smoląg, J.: Parallel architectures for learning the RTRN and Elman dynamic neural networks. IEEE Trans. Parallel Distrib. Syst. 26(9), 2561–2570 (2015)

    Article  Google Scholar 

  3. Bilski, J., Wilamowski, B.M.: Parallel learning of feedforward neural networks without error backpropagation. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2016. LNCS, vol. 9692, pp. 57–69. Springer, Cham (2016). doi:10.1007/978-3-319-39378-0_6

    Google Scholar 

  4. Bilski, J., Kowalczyk, B., Żurada, J.M.: Application of the givens rotations in the neural network learning algorithm. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2016. LNCS, vol. 9692, pp. 46–56. Springer, Cham (2016). doi:10.1007/978-3-319-39378-0_5

    Google Scholar 

  5. Bradley, P., Fayyad, U.: Refining initial points for K-Means clustering. In: Proceedings of the Fifteenth International Conference on Knowledge Discovery and Data Mining, pp. 9–15. AAAI Press, New York (1998)

    Google Scholar 

  6. Cpałka, K., Rebrova, O., Nowicki, R., Rutkowski, L.: On design of flexible neuro-fuzzy systems for nonlinear modelling. Int. J. Gen. Syst. 42(6), 706–720 (2013)

    Article  MATH  Google Scholar 

  7. Cpałka, K., Rutkowski, L.: Flexible Takagi-Sugeno fuzzy systems. In: Proceedings of the 2005 IEEE International Joint Conference on Neural Networks IJCNN (2005)

    Google Scholar 

  8. Davies, D.L., Bouldin, D.W.: A cluster separation measure. IEEE Trans. Pattern Anal. Mach. Intell. 1(2), 224–227 (1979)

    Article  Google Scholar 

  9. Duch, W., Korbicz, J., Rutkowski, L., Tadeusiewicz, R. (eds.): Biocybernetics and Biomedical Engineering 2000. Neural Networks, vol. 6. Akademicka Oficyna Wydawnicza EXIT, Warsaw (2000)

    Google Scholar 

  10. Dunn, J.C.: Well separated clusters and optimal fuzzy partitions. J. Cybernetica 4, 95–104 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  11. Fränti, P., Rezaei, M., Zhao, Q.: Centroid index: cluster level similarity measure. Pattern Recogn. 47(9), 3034–3045 (2014)

    Article  Google Scholar 

  12. Fred, L.N., Leitao, M.N.: A new cluster isolation criterion based on dissimilarity increments. IEEE Trans. Pattern Anal. Mach. Intell. 25(8), 944–958 (2003)

    Article  Google Scholar 

  13. Gabryel, M.: A bag-of-features algorithm for applications using a NoSQL database. Inf. Softw. Technol. 639, 332–343 (2016)

    Article  Google Scholar 

  14. Gabryel, M., Grycuk, R., Korytkowski, M., Holotyak, T.: Image indexing and retrieval using GSOM algorithm. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2015. LNCS, vol. 9119, pp. 706–714. Springer, Cham (2015). doi:10.1007/978-3-319-19324-3_63

    Chapter  Google Scholar 

  15. Halkidi, M., Batistakis, Y., Vazirgiannis, M.: Clustering validity checking methods: part II. ACM SIGMOD Rec. 31(3), 19–27 (2002)

    Article  MATH  Google Scholar 

  16. Jain, A., Dubes, R.: Algorithms for Clustering Data. Prentice-Hall, Englewood Cliffs (1988)

    MATH  Google Scholar 

  17. Kim, M., Ramakrishna, R.S.: New indices for cluster validity assessment. Pattern Recogn. Lett. 26(15), 2353–2363 (2005)

    Article  Google Scholar 

  18. Lago-Fernández, L.F., Corbacho, F.: Normality-based validation for crisp clustering. Pattern Recogn. 43(3), 782–795 (2010)

    Article  MATH  Google Scholar 

  19. Meng, X., van Dyk, D.: The EM algorithm - an old folk-song sung to a fast new tune. J. R. Stat. Soc. Ser. B (Methodol.) 59(3), 511–567 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  20. Murtagh, F.: A survey of recent advances in hierarchical clustering algorithms. Comput. J. 26(4), 354–359 (1983)

    Article  MATH  Google Scholar 

  21. Pakhira, M.K., Bandyopadhyay, S., Maulik, U.: Validity index for crisp and fuzzy clusters. Pattern Recogn. 37(3), 487–501 (2004)

    Article  MATH  Google Scholar 

  22. Pal, N.R., Bezdek, J.C.: On cluster validity for the fuzzy c-means model. IEEE Trans. Fuzzy Syst. 3(3), 370–379 (1995)

    Article  Google Scholar 

  23. Pascual, D., Pla, F., Sánchez, J.S.: Cluster validation using information stability measures. Pattern Recogn. Lett. 31(6), 454–461 (2010)

    Article  Google Scholar 

  24. Pelleg, D., Moore, A.W.: X-means: extending k-means with efficient estimation of the number of clusters. In: Proceedings of the Seventeenth International Conference on Machine Learning, pp. 727–734 (2000)

    Google Scholar 

  25. Rohlf, F.: Single-link clustering algorithms. In: Krishnaiah, P.R., Kanal, L.N. (eds.) Handbook of Statistics, vol. 2, pp. 267–284. Amsterdam, North-Holland (1982)

    Google Scholar 

  26. Rousseeuw, P.J.: Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math. 20, 53–65 (1987)

    Article  MATH  Google Scholar 

  27. Rutkowski, L., Cpałka, K.: Compromise approach to neuro-fuzzy systems. In: Sincak, P., Vascak, J., Kvasnicka, V., Pospichal, J. (eds.) Intelligent Technologies - Theory and Applications. New Trends in Intelligent Technologies. Frontiers in Artificial Intelligence and Applications, pp. 85–90. IOS Press, Amsterdam (2002)

    Google Scholar 

  28. Rutkowski, L., Przybył, A., Cpałka, K., Er, M.J.: Online speed profile generation for industrial machine tool based on neuro-fuzzy approach. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010. LNCS, vol. 6114, pp. 645–650. Springer, Heidelberg (2010). doi:10.1007/978-3-642-13232-2_79

    Chapter  Google Scholar 

  29. Rutkowski, L., Cpałka, K.: A neuro-fuzzy controller with a compromise fuzzy reasoning. Control Cybern. 31(2), 297–308 (2002)

    MATH  Google Scholar 

  30. Saha, S., Bandyopadhyay, S.: Some connectivity based cluster validity indices. Appl. Soft Comput. 12(5), 1555–1565 (2012)

    Article  Google Scholar 

  31. Sameh, A.S., Asoke, K.N.: Development of assessment criteria for clustering algorithms. Pattern Anal. Appl. 12(1), 79–98 (2009)

    Article  MathSciNet  Google Scholar 

  32. Shieh, H.-L.: Robust validity index for a modified subtractive clustering algorithm. Appl. Soft Comput. 22, 47–59 (2014)

    Article  Google Scholar 

  33. Starczewski, A.: A new validity index for crisp clusters. Pattern Anal. Appl. 1–14 (2015). doi:10.1007/s10044-015-0525-8

  34. Starczewski, A., Krzyżak, A.: A modification of the silhouette index for the improvement of cluster validity assessment. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2016. LNCS, vol. 9693, pp. 114–124. Springer, Cham (2016). doi:10.1007/978-3-319-39384-1_10

    Google Scholar 

  35. Weka 3: Data Mining Software in Java. University of Waikato, New Zealand. http://www.cs.waikato.ac.nz/ml/weka/

  36. Wu, K.L., Yang, M.S., Hsieh, J.N.: Robust cluster validity indexes. Pattern Recogn. 42, 2541–2550 (2009)

    Article  MATH  Google Scholar 

  37. Zhao, Q., Fränti, P.: WB-index: a sum-of-squares based index for cluster validity. Data Knowl. Eng. 92, 77–89 (2014)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Computational Intelligence, Częstochowa University of Technology, Al. Armii Krajowej 36, 42-200, Częstochowa, Poland

    Artur Starczewski

  2. Department of Computer Science and Software Engineering, Concordia University, Montreal, Canada

    Adam Krzyżak

  3. Department of Electrical Engineering, Westpomeranian University of Technology, 70-313, Szczecin, Poland

    Adam Krzyżak

Authors
  1. Artur Starczewski
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  2. Adam Krzyżak
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Corresponding author

Correspondence to Artur Starczewski .

Editor information

Editors and Affiliations

  1. Częstochowa University of Technology, Częstochowa, Poland

    Leszek Rutkowski

  2. Częstochowa University of Technology, Częstochowa, Poland

    Marcin Korytkowski

  3. Częstochowa University of Technology, Częstochowa, Poland

    Rafał Scherer

  4. AGH University of Science and Technology, Kraków, Poland

    Ryszard Tadeusiewicz

  5. University of California, Berkeley, California, USA

    Lotfi A. Zadeh

  6. University of Louisville, Louisville, Kentucky, USA

    Jacek M. Zurada

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Starczewski, A., Krzyżak, A. (2017). Improvement of the Validity Index for Determination of an Appropriate Data Partitioning. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2017. Lecture Notes in Computer Science(), vol 10246. Springer, Cham. https://doi.org/10.1007/978-3-319-59060-8_16

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  • DOI: https://doi.org/10.1007/978-3-319-59060-8_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59059-2

  • Online ISBN: 978-3-319-59060-8

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