Learning-based fuzzy c-means clustering using finite mixtures of scale mixture normal distributions with missing information

Document Type : Original Article

Authors

1 Army Command and Staff University

2 Army command and staff University‎, ‎Tehran‎, ‎Iran

Abstract

One of the most widely used models for data clustering, which has been considered by many researchers in recent years, is finite mixture models. Clustering is generally a process in which each observation is assigned to one of the specified groups. Although the main idea in mixture models is based on normal distribution, but in recent years with the introduction of other distributions of mixture models based on these distributions has been considered by many researchers. In the articles, the EM algorithm and its extensions are used for estimation. However, it is possible that the EM algorithm does not provide good results for clustering because in this method each member of the observation belongs to one class. This limitation led to the use of the fuzzy clustering approach in this type of problem. In this paper is proposed a clustering algorithm‎, ‎based on a fuzzy treatment of finite mixtures‎ of multivariate scale mixture of normal distribution, ‎using Learning-based fuzzy c-means (LB-FCM) algorithm as well as missing data‎. ‎We construct a robust LB-FCM framework for handling missing data assuming the finite mixture of multivariate scale mixture of normal distribution. Comparisons between LB-FCM and EM-type algorithms are made‎. ‎Experimental‎ results and comparisons actually demonstrate the advantage of the proposed LB-FCM‎.

Keywords

References

[1] D.R. Andrews and C.L. Mallows, Scale mixture of normal distributions, J. Roy. Stat. Soc. B 36, 1974, pp. 99–102
 
[2] LA. García-Escudero, F. Greselin and AM. Iscar. “Robust, fuzzy, and parsimonious clustering, based on mixtures of factor analyzers”. Inter. Jou. Appr. Reas., vol. 94, 2018, pp. 60–75.
 
[3] LA. García-Escudero, D. Rivera-García, AM. Iscar and J. Ortega. “Cluster analysis with cellwise trimming and applications for the robust clustering of curves”. Info. Scie. vol. 573, 2021, pp. 100–124.
 
[4] D. E. Gustafson and W.C. Kessel. “Fuzzy clustering with a fuzzy covariance matrix”. IEEE conf. on deci. and conto. inclu. the 17th sympo. on adap. proc., 1979, pp. 761–766.
 
[5] F. Hashemi, M. Naderi and M. Mashinchi. “Clustering right-skewed data stream via Birnbaum–Saunders mixture models: A flexible approach based on fuzzy clustering algorithm”. Appl. Sof. Compu., vol. 82, 2019, 105539.
 
[6] Z. Ju and H. Liu. “Fuzzy gaussian mixture models”. Patt. Recog. vol. 45, 2012, pp. 1146–1158.
 
[7] T. I. Lin, J. C. Lee and H. J. Ho. “On fast supervised learning for normal mixture models with missing information”. Patt. Recog., vol. 39, 2006, pp. 1177–1187.
 
[8] Quost, B., Denoeux, T., 2016. “Clustering and classification of fuzzy data using the fuzzy EM algorithm”. Fuz. Set. and Sys., vol. 286, 2016, pp. 134–156.
 
[9] H. Wang, Q. bing Zhang, B. Luo and S. Wei. “Robust mixture modelling using multivariate t-distribution with missing information”. Patt. Recog., vol. 25, 2004, pp. 701–710.
 
[10] WL. Wang, A. Jamalizadeh, and TI, Lin. “Finite mixtures of multivariate scaleshape mixtures of skew-normal distributions”. Stat Papers, vol. 61, 2020, pp. 2643–2670.
 
[11] M. S. Yang, and Y. Nataliani. “Robust-learning fuzzy c-means clustering algorithm with unknown number of clusters”. Patt. Recog., vol. 71, 2017, pp. 45–59.
 
[12] L. A. Zadeh. “Fuzzy sets”. Info. and cont. vol. 8, 1965, pp. 338–353.
Fuzzy Systems and its Applications
Volume 5, Issue 2 - Serial Number 11
January 2023
Pages 203-225

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History

  • Receive Date: 27 April 2022
  • Revise Date: 02 November 2022
  • Accept Date: 11 January 2023

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