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A robust fuzzy clustering model for fuzzy data based on an adaptive weighted L1 norm | ||
Iranian Journal of Fuzzy Systems | ||
دوره 20، شماره 6، بهمن و اسفند 2023، صفحه 1-20 اصل مقاله (495.89 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2023.43284.7606 | ||
نویسندگان | ||
Elham Eskandari* ؛ Alireza Khastan | ||
Department of Mathematics, Institute for Advanced Studies in Basic Sciences, Zanjan, Iran | ||
چکیده | ||
The imprecision related to measurements can be managed in terms of fuzzy features, which are characterized by two components: center and spread. Outliers affect the outcome of the clustering models. In trying to overcome this problem, this paper proposes a fuzzy clustering model for L-R fuzzy data, which is based on a dissimilarity measure between each pair of fuzzy data defined as an adaptive weighted sum of the L1-norms of the centers and the spreads. The proposed method is robust based on the metric and weighting approaches. It estimates the weight of a given fuzzy feature on a given fuzzy cluster by considering the relevance of that feature to the cluster; if outlier fuzzy features are present in the dataset, it tends to assign them weights close to 0. To deeply investigate the capability of our model, i.e., alleviating undesirable effects of outlier fuzzy data, we provide a wide simulation study. We consider the ability to classify correctly and the ability to recover the true prototypes, both in the presence of outliers. The comparison made with other existing robust methods indicates that the proposed methodology is more robust to the presence of outliers than other methods. Moreover, the performance of our method decreases more slowly than others when the percentage of outliers increases. An application of the suggested method to a real-world categorical dataset is also provided. | ||
کلیدواژهها | ||
L-R fuzzy data؛ Robust fuzzy clustering؛ L1 norm؛ Outlier | ||
مراجع | ||
[1] J. R. Alharbi, W. S. Alhalabi, Hybrid approach for sentiment analysis of twitter posts using a dictionary-based approach and fuzzy logic methods: Study case on cloud service providers, International Journal on Semantic Web and Information Systems (IJSWIS), 16(1) (2020), 116-145. [2] M. A. Alsmirat, Y. Jararweh, M. Al-Ayyoub, M. A. Shehab, B. B. Gupta, Accelerating compute intensive medical imaging segmentation algorithms using hybrid CPU-GPU implementations, Multimedia Tools and Applications, 76 (2017), 3537-3555. [3] J. C. Bezdek, Pattern recognition with fuzzy objective function algorithm, Plenum Press, New York, 1981.
[4] P. Bloomfield, W. L. Steiger, Least absolute deviations, Birkh Iuser, Boston, MA, 1983.
[5] L. Bobrowski, J. C. Bezdek, C-means clustering with the l1 and l1 norms, IEEE Transactions on Systems, Man, and Cybernetics, 21(3) (1991), 545-554. [6] A. M. Bowcock, A. Ruiz-Linares, J. Tomfohrde, E. Minch, J. R. Kidd, L. L. Cavalli-Sforza, High resolution of human evolutionary trees with polymorphic microsatellites, Nature, 368 (1994), 455-457. [7] B. S. Butkiewicz, Robust fuzzy clustering with fuzzy data, in: P. S. Szczepaniak, J. Kacprzyk, A. Niewiadomski (Eds.), Proceedings of Advances in Web Intelligence, Third International Atlantic Web Intelligence Conference, AWIC 2005, Lecture Notes in Computer Science, Vol. 3528, Springer, Berlin, Heidelberg, (2005), 76-82. [8] R. J. G. B. Campello, A fuzzy extension of the Rand index and other related indexes for clustering and classification assessment, Pattern Recognition Letters, 28(7) (2007), 833-841. [9] R. Coppi, P. D’Urso, P. Giordani, Fuzzy and possibilistic clustering for fuzzy data, Computational Statistics and Data Analysis, 56(4) (2012), 915-927. [10] R. N. Dave, Characterization and detection of noise in clustering, Pattern Recognition Letters, 12(11) (1991), 657-664. [11] F. de A. T. De Carvalho, E. C. Simoes, Fuzzy clustering of interval-valued data with City-Block and Hausdorff distances, Neurocomputing, 266 (2017), 659-673. [12] M. Deveci, D. Pamucar, I. Gokasar, M. Köppen, B. B. Gupta, Personal mobility in metaverse with autonomous vehicles using Q-rung orthopair fuzzy sets based OPA-RAFSI model, IEEE Transactions on Intelligent Transportation Systems, (2022), 1-10. [13] P. D’Urso, L. De Giovanni, Robust clustering of imprecise data, Chemometrics and Intelligent Laboratory Systems, 136 (2014), 58-80. [14] P. D’Urso, M. Disegna, R. Massari, Fuzzy clustering in travel and tourism analytics, in: Business and Consumer Analytics: New Ideas, Springer, (2019), 839-863. [15] P. D’Urso, P. Giordani, A weighted fuzzy c-means clustering model for fuzzy data, Computational Statistics and Data Analysis, 50(6) (2006), 1496-1523. [16] P. D’Urso, J. M. Leski, Fuzzy clustering of fuzzy data based on robust loss functions and ordered weighted averaging, Fuzzy Sets and Systems, 389 (2020), 1-28. [17] E. Eskandari, A. Khastan, S. Tomasiello, Improved determination of the weights in a clustering approach based on a weighted dissimilarity measure between fuzzy data, 2022 IEEE Int. Conf. Fuzzy Syst. (FUZZ-IEEE), Padua, Italy, (2022), 1-6. [18] M. B. Ferraro, P. Giordani, Possibilistic and fuzzy clustering methods for robust analysis of non-precise data, International Journal of Approximate Reasoning, 88 (2017), 23-38. [19] P. Franck, E. Cameron, G. Good, J. Y. Rasplus, B. Oldroyd, Nest architecture and genetic differentiation in a species complex of Australian stingless bees, Molecular Ecology, 13(8) (2004), 2317-2331. [20] R. J. Hathaway, J. C. Bezdek, Y. K. Hu, Generalized fuzzy c-means clustering strategies using Lp norm distances, IEEE Transactions on Fuzzy Systems, 8(5) (2000), 576-582. [21] C. Hennig, How many bee species? A case study in determining the number of clusters, in: M. Spiliopoulou, L. Schmidt-Thieme, R. Janning (Eds.), Data Analysis, Machine Learning and Knowledge Discovery, Studies in Classification, Data Analysis, and Knowledge Organization, Springer, (2014), 41-49. [22] E. Hullermeier, M. Rifqi, S. Henzgen, R. Senge, Comparing fuzzy partitions: A generalization of the Rand index and related measures, IEEE Transactions on Fuzzy Systems, 20(3) (2012), 546-556. [23] W. Hung, M. Yang, Fuzzy clustering on LR-type fuzzy numbers with an application in Taiwanese tea evaluation, Fuzzy Sets and Systems, 150(3) (2005), 561-577. [24] W. Hung, M. Yang, E. Lee, A robust clustering procedure for fuzzy data, Computers and Mathematics with Applications, 60 (2010), 151-165. [25] K. Jajuga, L1-norm based fuzzy clustering, Fuzzy Sets and Systems, 39 (1991), 43-50.
[26] S. Jin, A bidirectional reasoning based on fuzzy interpolation, International Journal of Software Science and Computational Intelligence (IJSSCI), 12(1) (2020), 1-14.
[27] L. Kaufman, P. J. Rousseeuw, Finding groups in data: An introduction to cluster analysis, Wiley, Hoboken, NJ, 2005. [28] V. D. Minh, T. T. Ngan, T. M. Tuan, V. T. Duong, N. T. Cuong, An improvement in integrating clustering method and neural network to extract rules and application in diagnosis support, Iranian Journal of Fuzzy Systems, 19(5) (2022), 147-165. [29] N. M. Ralevic, M. Delic, Lj. Nedovic, Aggregation of fuzzy metrics and its application in image segmentation, Iranian Journal of Fuzzy Systems, 19(3) (2022), 19-37. [30] A. B. Ramos-Guajardo, M. B. Ferraro, A fuzzy clustering approach for fuzzy data based on a generalized distance, Fuzzy Sets and Systems, 389 (2020), 29-50. [31] W. Rhmann, An ensemble of hybrid search-based algorithms for software effort prediction, International Journal of Software Science and Computational Intelligence (IJSSCI), 13(3) (2021), 28-37. [32] S. Sathe, C. C. Aggarwal, LODES: Local density meets spectral outlier detection, in: Proceedings of the 2016 SIAM International Conference on Data Mining (SDM), (2016), 171-179. [33] M. Sato, Y. Sato, Fuzzy clustering model for fuzzy data, in: Fuzzy Systems, 1995. International Joint Conference of the Fourth IEEE International Conference on Fuzzy Systems and the Second International Fuzzy Engineering Symposium, Proceedings of 1995 IEEE Int., Vol. 4, IEEE, (1995), 2123-2128. [34] B. Sinova, M. A. Gil, A. Colubi, S. Van Aelst, The median of a random fuzzy number. The 1-norm distance approach, Fuzzy Sets and Systems, 200 (2012), 99-115. [35] B. Sinova, S. R. de Saa, M. A. Gil, A generalized L1-type metric between fuzzy numbers for an approach to central tendency of fuzzy data, Information Sciences, 242 (2013), 22-34. [36] V. V. Tai, L. D. Nghiep, Interpolating time series based on fuzzy cluster analysis problem, Iranian Journal of Fuzzy Systems, 17(3) (2020), 151-161. [37] M. C. Thrun, Projection based clustering through self-organization and swarm intelligence, Springer, Heidelberg, 2018. [38] M. C. Thrun, A. Ultsch, Clustering benchmark datasets exploiting the fundamental clustering problems, Data in Brief, 30 (2020), 105501. [39] E. J. Wood, The encyclopedia of molecular biology, Biochemical Education, 23(2) (1995), 1165. [40] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353. [41] M. F. Zarandi, Z. S. Razaee, A fuzzy clustering model for fuzzy data with outliers, International Journal of Fuzzy System Applications (IJFSA), 1(2) (2010), 29-42. | ||
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