Top

Published in:

2018 | OriginalPaper | Chapter

Improvement of the Simplified Silhouette Validity Index

Authors : Artur Starczewski, Krzysztof Przybyszewski

Published in: Artificial Intelligence and Soft Computing

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

The fundamental issue of data clustering is an evaluation of results of clustering algorithms. Lots of methods have been proposed for cluster validation. The most popular approach is based on internal cluster validity indices. Among this kind of indices, the Silhouette index and its computationally simpled version, i.e. the Simplified Silhouette, are frequently used. In this paper modification of the Simplified Silhouette index is proposed. The suggested approach is based on using an additional component, which improves clusters validity assessment. The performance of the new cluster validity indices has been demonstrated for artificial and real datasets, where the PAM clustering algorithm has been applied as the underlying clustering technique.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Automating Feature Extraction and Feature Selection in Big Data Security Analytics

next chapter Feature Extraction in Subject Classification of Text Documents in Polish

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)CrossRef

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)CrossRef

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 (LNAI), vol. 9692, pp. 57–69. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-39378-0_6CrossRef

Bologna, G., Hayashi, Y.: Characterization of symbolic rules embedded in deep DIMLP networks: a challenge to transparency of deep learning. J. Artif. Intell. Soft Comput. Res. 7(4), 265–286 (2017). https://doi.org/10.1515/jaiscr-2017-0019CrossRef

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)

Chang, O., Constante, P., Gordon, A., Singana, M.: A novel deep neural network that uses space-time features for tracking and recognizing a moving object. J. Artif. Intell. Soft Comput. Res. 7(2), 125–136 (2017). https://doi.org/10.1515/jaiscr-2017-0009CrossRef

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)MATHCrossRef

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

Devi, V.S., Meena, L.: Parallel MCNN (PMCNN) with application to prototype selection on large and streaming data. J. Artif. Intell. Soft Comput. Res. 7(3), 155–169 (2017). https://doi.org/10.1515/jaiscr-2017-0011CrossRef

10.

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

11.

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

12.

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 (LNAI), vol. 9119, pp. 706–714. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-19324-3_63CrossRef

13.

Gałkowski, T.: Kernel estimation of regression functions in the boundary regions. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013. LNCS (LNAI), vol. 7895, pp. 158–166. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38610-7_15CrossRef

14.

Galkowski, T., Pawlak, M.: Nonparametric estimation of edge values of regression functions. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2016. LNCS (LNAI), vol. 9693, pp. 49–59. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-39384-1_5CrossRef

15.

Hruschka, E.R., de Castro, L.N., Campello, R.J.: Evolutionary algorithms for clustering gene-expression data. In: Fourth IEEE International Conference on Data Mining, ICDM 2004, pp. 403–406. IEEE (2004)

16.

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

17.

Ke, Y., Hagiwara, M.: An English neural network that learns texts, finds hidden knowledge, and answers questions. J. Artif. Intell. Soft Comput. Res. 7(4), 229–242 (2017). https://doi.org/10.1515/jaiscr-2017-0016CrossRef

18.

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

19.

Lichman, M.: UCI Machine Learning Repository. University of California, School of Information and Computer Science, Irvine, CA (2013). http://archive.ics.uci.edu/ml

20.

Liu, H., Gegov, A., Cocea, M.: Rule based networks: an efficient and interpretable representation of computational models. J. Artif. Intell. Soft Comput. Res. 7(2), 111–123 (2017). https://doi.org/10.1515/jaiscr-2017-0008CrossRef

21.

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

22.

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

23.

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

24.

Park, H.S., Jun, C.H.: A simple and fast algorithm for K-medoids clustering. Expert Syst. Appl. 36(2), 3336–3341 (2009)CrossRef

25.

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

26.

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

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, vol. 76, pp. 85–90 (2002)

28.

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

29.

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

30.

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

31.

Serdah, A.M., Ashour, W.M.: Clustering large-scale data based on modified affinity propagation algorithm. J. Artif. Intell. Soft Comput. Res. 6(1), 23–33 (2016). https://doi.org/10.1515/jaiscr-2016-0003CrossRef

32.

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

33.

Starczewski, A.: A new validity index for crisp clusters. Pattern Anal. Appl. 20(3), 687–700 (2017)MathSciNetCrossRef

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 (LNAI), vol. 9693, pp. 114–124. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-39384-1_10CrossRef

35.

Starczewski, A., Krzyżak, A.: Improvement of the validity index for determination of an appropriate data partitioning. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2017. LNCS (LNAI), vol. 10246, pp. 159–170. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59060-8_16CrossRef

36.

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

37.

Vendramin, L., Campello, R.J., Hruschka, E.R.: Relative clustering validity criteria: a comparative overview. Stat. Anal. Data Min. 3(4), 209–235 (2010)MathSciNet

38.

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

Title: Improvement of the Simplified Silhouette Validity Index
Authors: Artur Starczewski
Krzysztof Przybyszewski
Publisher: Springer International Publishing
Book: Artificial Intelligence and Soft Computing
Print ISBN: 978-3-319-91261-5

Electronic ISBN: 978-3-319-91262-2

Copyright Year: 2018
DOI: https://doi.org/10.1007/978-3-319-91262-2_39

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partner