Fuzzy Systems and its Applications

Fuzzy Systems and its Applications

Investigating the effect of using different loss functions on the performance of the fuzzy clustering model for fuzzy data in the presence of outlier data

Document Type : Original Article

Authors
Department of Mathematics, Institute for Advanced Studies in Basic Sciences, Zanjan, Iran
10.22034/jfsa.2024.420390.1187
Abstract
In this article, we propose the use of a new loss function in the fuzzy clustering model for fuzzy data and investigate the effect of using this loss function and Squared, Huber, Linear, Sigmoidal, and Logarithmic loss functions on the performance of the model in the presence of outlier data in the simulation. The used datasets have a suitable variety in terms of the number of features (2 and 3), the number of classes (3 and 4), and the distribution and number of outlier data (20, 138 and 4). The simulation results confirm that Haber loss function and the new loss function are robust to the presence of outlier data.
Keywords
Subjects

[1]    Bezdek, J. (1981) Pattern recognition with fuzzy objective function algorithms. Plenum Press, New York.
[2]    Butkiewicz, B. (2005) Robust fuzzy clustering with fuzzy data. Advances in Web Intelligence, Third International Atlantic Web Intelligence Conjerence, AWIC 2005, Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, 3528, 76-82.
[3]    Campello, R. (2007) A fuzzy extension of the Rand index and other related indexes for clustering and classification assessment. Pattern Recognition Letters, 28 (7), 833-841.
[4]    D'Urso, P. (2007) Fuzzy clustering of fuzzy data. Advances in Fuzzy Clustering and Its Applications, 155-192.
[5]    D'Urso, P., De Giovanni, L. (2014) Robust clustering of imprecise data. Chemometrics and Intelligent Laboratory Systems, 136, 58-80.
[6]    D'Urso, P., Leski, J. (2020) Fuzzy clustering of fuzzy data based on robust loss functions and ordered weighted averaging. Fuzzy Sets and Systems, 389, 1-28.
[7]    Eskandari, E., Khastan, A. (2023) A robust fuzzy clustering model for fuzzy data based on an adaptive weighted L, norm. Iranian Journal oj Fuzzy Systems, 20 (6), 1-20.
[8]    Eskandari, E., Khastan, A., Tomasiello, S. (2022) Improved determination of the weights in a clustering approach based on a weighted dissimilarity measure between fuzzy data. 2022 IEEE Int. Conj. Fuzzy Syst. (FUZZ-IEEE), Padua, Italy, 1-6.
[9]    Hullermeier, E., Rifqi, M., Henzgen, S., Senge, R. (2012) Comparing fuzzy partitions: a generalization of the Rand index and related measures. IEEE Transactions on Fuzzy Systems, 20 (3), 546-556.
[10]        Hung, W., Yang, M. (2005) Fuzzy clustering on LR-type fuzzy numbers with an application in Taiwanese tea evaluation. Fuzzy Sets and Systems, 150 (3), 561-577.
[11]    Jin, X., Han, J. (2010) K-medoids clustering. Encyclopedia oj Machine Learning, 697-700.
[12]        Sato, M., Sato, Y. (1995) Fuzzy clustering model for fuzzy data. Proceedings of 1995 IEEE International Conference on Fuzzy Systems, 4, 2123-2128.
[13]        Thrun, M. (2018) Projection-based clustering through self organization and swarm intelligence. Springer Vieweg, Wiesbaden.
[14]        Urbanowicz, R.J. [@DocUrbs]. (2018, Jun 15). New proposed field Iterm Venn diagram for an upcoming talk. My take on illustrating the relationship between #Data- Science, #MachineLearning, #ArtijicialIntelligence, #Statistics [Tweet]. Twitter. https://twitter.com/DocUrbs/status/1007375834347376642
[15]    Yang, M., Ko, C. (1996) On a class of fuzzy c-numbers clustering procedures for fuzzy data.  Fuzzy Sets and Systems, 84 (1), 49-60.
[16]        Yang, M., Liu, H. (1999) Fuzzy clustering procedures for conical fuzzy vector data. Fuzzy Sets and Systems, 106 (2), 189-200.
[17]        Zarandi, M., Razaee, Z. (2010) A fuzzy clustering model for fuzzy data with outliers. International Journal of Fuzzy System Applications (IJFSA), 1 (2), 29-42.
[18]        Zelnik-Manor, L., Perona, P. (2004) Self-tuning spectral clustering. Proceedings of the 17th International Conference on Neural Information Processing Systems, 17, 1601-1608.
Volume 7, Issue 1 - Serial Number 14
Open Access Statement
June 2024
Pages 109-123

  • Receive Date 12 October 2023
  • Revise Date 20 June 2024
  • Accept Date 18 August 2024