A Modification of the Silhouette Index for the Improvement of Cluster Validity Assessment
详细信息    查看全文
  • 关键词:Clustering ; Cluster validity ; Silhouette index
  • 刊名:Lecture Notes in Computer Science
  • 出版年:2016
  • 出版时间:2016
  • 年:2016
  • 卷:9693
  • 期:1
  • 页码:114-124
  • 全文大小:504 KB
  • 参考文献:1.Baskir, M.B., Türksen, I.B.: Enhanced fuzzy clustering algorithm and cluster validity index for human perception. Expert Syst. Appl. 40, 929–937 (2013)CrossRef
    2.Bas, E.: The training of multiplicative neuron model based artificial neural networks with differential evolution algorithm for forecasting. J. Artif. Intell. Soft Comput. Res. 6(1), 5–11 (2016)CrossRef
    3.Bertini, J.R., Nicoletti, M.C.: Enhancing constructive neural network performance using functionally expanded input data. J. Artif. Intell. Soft Comput. Res. 6(2), 119–131 (2016)
    4.Bilski, J., Smolag, J.: Parallel architectures for learning the RTRN and Elman dynamic neural networks. IEEE Trans. Parallel Distrib. Syst. 26(9), 2561–2570 (2015)CrossRef
    5.Bilski, J., Smoląg, J., Galushkin, A.I.: The parallel approach to the conjugate gradient learning algorithm for the feedforward neural networks. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2014, Part I. LNCS, vol. 8467, pp. 12–21. Springer, Heidelberg (2014)CrossRef
    6.Bilski, J., Smoląg, J.: Parallel approach to learning of the recurrent jordan neural network. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013, Part I. LNCS, vol. 7894, pp. 32–40. Springer, Heidelberg (2013)CrossRef
    7.Bilski, J., Smolag, J.: Parallel Realisation of the Recurrent Multi Layer Perceptron Learning. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2012, Part I. LNCS, vol. 7267, pp. 12–20. Springer, Heidelberg (2012)CrossRef
    8.Cpalka, K., Rutkowski, L.: Flexible Takagi-Sugeno fuzzy systems. In: Proceedings of the International Joint Conference on Neural Networks (IJCNN), vols 1-5 Book Series: IEEE International Joint Conference on Neural Networks, pp. 1764–1769 (2005)
    9.Cpaka, 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)CrossRef MATH
    10.Duch, W., Korbicz, J., Rutkowski, L., Tadeusiewicz, R. (eds.): Biocybernetics and biomedical engineering 2000. Neural Networks, vol. 6, Akademicka Oficyna Wydawnicza, EXIT, (2000)
    11.Fränti, P., Rezaei, M., Zhao, Q.: Centroid index: cluster level similarity measure. Pattern Recognit. 47(9), 3034–3045 (2014)CrossRef
    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)CrossRef
    13.Jain, A., Dubes, R.: Algorithms for Clustering Data. Prentice-Hall, Englewood Cliffs (1988)MATH
    14.Kim, M., Ramakrishna, R.S.: New indices for cluster validity assessment. Pattern Recogn. Lett. 26(15), 2353–2363 (2005)CrossRef
    15.Korytkowski, M., Rutkowski, L., Scherer, R.: Fast image classification by boosting fuzzy classifiers. Inf. Sci. 327, 175–182 (2016)MathSciNet CrossRef
    16.Korytkowski, M., Rutkowski, L., Scherer, R.: From ensemble of fuzzy classifiers to single fuzzy rule base classifier. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2008. LNCS (LNAI), vol. 5097, pp. 265–272. Springer, Heidelberg (2008)CrossRef
    17.Koshiyama, A.S., Vellasco, M., Tanscheit, R.: GPFIS-Control: a genetic fuzzy system for control tasks. J. Artif. Intell. Soft Comput. Res. 4(3), 167–179 (2014)CrossRef
    18.Laskowski, L., Jelonkiewicz, J.: Self-correcting neural network for stereo-matching problem solving. Fundamenta Informaticae 138(4), 457–482 (2015)MathSciNet CrossRef MATH
    19.Li, X., Er, M.J., Lim, B.S., et al.: Fuzzy regression modeling for tool performance prediction and degradation detection. Int. J. Neural Syst. 20(5), 405–419 (2010)CrossRef
    20.Lichman, M.: UCI Machine Learning Repository. University of California, School of Information and Computer Science, Irvine (2013). http://​archive.​ics.​uci.​edu/​ml
    21.Miyajima, H., Shigei, N., Miyajima, H.: Performance comparison of hybrid electromagnetism-like mechanism algorithms with descent method. J. Artif. Intell. Soft Comput. Res. 5(4), 271–282 (2015)CrossRef MATH
    22.Ozkan, I., Türksen, I.B.: MiniMax \(\varepsilon \) -stable cluster validity index for Type-2 fuzziness. Inf. Sci. 184(1), 64–74 (2012)CrossRef
    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.Patgiri, C., Sarma, M., Sarma, K.K.: A class of neuro-computational methods for assamese fricative classification. J. Artif. Intell. Soft Comput. Res. 5(1), 59–70 (2015)CrossRef
    25.Rigatos, G., Siano, P.: Flatness-based adaptive fuzzy control of spark-ignited engines. J. Artif. Intell. Soft Comput. Res. 4(4), 231–242 (2014)CrossRef
    26.Rutkowski, L., Cpalka, K.: Flexible neuro-fuzzy systems. IEEE Trans. Neural Networks 14(3), 554–574 (2003)CrossRef
    27.Rutkowski, L., Przybyl, A., Cpalka, K.: Novel online speed profile generation for industrial machine tool based on flexible neuro-fuzzy approximation. IEEE Trans. Industr. Electron. 59(2), 1238–1247 (2012)CrossRef
    28.Rutkowski, L., Cpalka, K.: Designing and learning of adjustable quasi-triangular norms with applications to neuro-fuzzy systems. IEEE Trans. Fuzzy Syst. 13(1), 140–151 (2005)CrossRef
    29.Rutkowski, L., Cpalka, K.: A general approach to neuro-fuzzy systems. In: 10th IEEE International Conference on Fuzzy Systems, vols. 1–3: Meeting the Grand Challenge: Machines that Serve People, pp. 1428–1431 (2001)
    30.Rutkowski, L., Cpalka, K.: A neuro-fuzzy controller with a compromise fuzzy reasoning. Control Cybern. 31(2), 297–308 (2002)MATH
    31.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, Part II. LNCS, vol. 6114, pp. 645–650. Springer, Heidelberg (2010)CrossRef
    32.Rutkowski, L., Cpalka, K.: Compromise approach to neuro-fuzzy systems. Technol. Book Ser. Frontiers Artif. Intell. Appl. 76, 85–90 (2002)MATH
    33.Rutkowski, L., Pietruczuk, L., Duda, P., Jaworski, M.: Decision trees for mining data streams based on the McDiarmids bound. IEEE Trans. Knowl. Data Eng. 25(6), 1272–1279 (2013)CrossRef
    34.Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: Decision trees for mining data streams based on the Gaussian approximation. IEEE Trans. Knowl. Data Eng. 26(1), 108–119 (2014)CrossRef
    35.Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: A new method for data stream mining based on the misclassification error. IEEE Trans. Neural Networks Learn. Syst. 26(5), 1048–1059 (2015)MathSciNet CrossRef
    36.Rutkowski, L., Jaworski, M., Pietruczuk, L., Duda, P.: The CART decision tree for mining data streams. Inf. Sci. 266, 1–15 (2014)CrossRef
    37.Saitoh, D., Hara, K.: Mutual learning using nonlinear perceptron. J. Artif. Intell. Soft Comput. Res. 5(1), 71–77 (2015)CrossRef
    38.Sameh, A.S., Asoke, K.N.: Development of assessment criteria for clustering algorithms. Pattern Anal. Appl. 12(1), 79–98 (2009)MathSciNet CrossRef
    39.Shieh, H.-L.: Robust validity index for a modified subtractive clustering algorithm. Appl. Soft Comput. 22, 47–59 (2014)CrossRef
    40.Starczewski, A.: A new validity index for crisp clusters. Pattern Anal. Appl. (2015). doi:10.​1007/​s10044-015-0525-8
    41.Starczewski, J., Rutkowski, L.: Interval type 2 neuro-fuzzy systems based on interval consequents. In: Rutkowski, L., Kacprzyk, J. (eds.) Neural Networks and Soft Computing. Advances in Soft Computing, pp. 570–577. Springer-Verlag, Physica-Verlag HD, Heidelberg (2003)CrossRef
    42.Starczewski, J.T., Rutkowski, L.: Connectionist structures of type 2 fuzzy inference systems. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds.) PPAM 2001. LNCS, vol. 2328, p. 634. Springer, Heidelberg (2002)CrossRef
    43.Weka 3: Data mining software in Java. University of Waikato, New Zealand. http://​www.​cs.​waikato.​ac.​nz/​ml/​weka
    44.Wozniak, M., Polap, D., Nowicki, R., Napoli, C., Pappalardo, G., Tramontana, E.: Novel approach toward medical signals classifier. In: 2015 International Joint Conference on Neural Networks (IJCNN), Killarney, Irlandia (2015). doi:10.​1109/​IJCNN.​2015.​7280556
    45.Wu, K.L., Yang, M.S., Hsieh, J.N.: Robust cluster validity indexes. Pattern Recogn. 42, 2541–2550 (2009)CrossRef MATH
    46.Zalik, K.R.: Cluster validity index for estimation of fuzzy clusters of different sizes and densities. Pattern Recogn. 43, 3374–3390 (2010)CrossRef MATH
    47.Zhang, D., Ji, M., Yang, J., Zhang, Y., Xie, F.: A novel cluster validity index for fuzzy clustering based on bipartite modularity. Fuzzy Sets Syst. 253, 122–137 (2014)MathSciNet CrossRef
  • 作者单位:Artur Starczewski (19)
    Adam Krzyżak (20) (21)

    19. Institute of Computational Intelligence, Częstochowa University of Technology, Al. Armii Krajowej 36, 42-200, Częstochowa, Poland
    20. Department of Computer Science and Software Engineering, Concordia University, Montreal, Canada
    21. Department of Electrical Engineering, Westpomeranian University of Technology, 70-313, Szczecin, Poland
  • 丛书名:Artificial Intelligence and Soft Computing
  • ISBN:978-3-319-39384-1
  • 刊物类别:Computer Science
  • 刊物主题:Artificial Intelligence and Robotics
    Computer Communication Networks
    Software Engineering
    Data Encryption
    Database Management
    Computation by Abstract Devices
    Algorithm Analysis and Problem Complexity
  • 出版者:Springer Berlin / Heidelberg
  • ISSN:1611-3349
  • 卷排序:9693
文摘
In this paper a modification of the well-known Silhouette validity index is proposed. This index, which can be considered a measure of the data set partitioning accuracy, enjoys significant popularity and is often used by researchers. The proposed modification involves using an additional component in the original index. This approach improves performance of the index and provides better results during a clustering process, especially when changes of cluster separability are big. The new version of the index is called the SILA index and its maximum value identifies the best clustering scheme. The performance of the new index is demonstrated for several data sets, where the popular algorithm has been applied as underlying clustering techniques, namely the Complete–linkage algorithm. The results prove superiority of the new approach as compared to the original Silhouette validity index.

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700