Fuzzy Systems and its Applications

Fuzzy Systems and its Applications

A fuzzy classification method for mixture of nonlinear regression model

Document Type : Original Article

Author
Farzane Hashemi
Department of Statistics, Faculty of Mathematics Sciences, University of Kashan
10.22034/jfsa.2024.458851.1206
Abstract
Mixture regression models are widely used to obtain relationships between the response variable and one or more predictor variables from several non-homogeneous groups. Since many data have heavy tails in reality, using ordinary mixture regression models with normal errors can cause deviations in inference. The class of scale mixture normal distributions includes many symmetric distributions as special cases. In many studies, the EM algorithm is used to obtain the number of clusters and estimate the parameters. In this paper, a fuzzy approach is proposed to obtain the number of clusters and estimate the parameters in the mixture regression model based on normal scale mixture normal errors distribution. Extensive simulation studies and reals data analyses illustrate the efficacy and performance of the proposed methodologhy and EM-type algorithm.
Keywords
Nonlinear regression
Fuzzy classification
Finite mixture distribution
Fuzzy classification maximum
Subjects
[3]    A. Azzalini and A. D. Valle. The multivariate skew-normal distribution. Biome., vol. 83 (4), pp. 715–726.
[4]    J.C. Bezdek. “Pattern Recognition with Fuzzy Objective Function Algorithms”. Klu. Aca. Publ., Norwell, MA, USA, 1981.
[5]    R.D. Cook and S. Weisberg. “Residuals and Influence in Regression”. Chap and Hall, New York, 1982.
[6]    M. Davidian. “Nonlinear models for repeated measurement data”. Routledge, 2017.
[7]    A. P. Dempster, N. M. Laird and D. B. Rubin. “Maximum likelihood from incomplete data via the EM algorithm”. J. Roy. Stat. Soc.: Ser. B, vol. 39, 1977. pp. 1–22.
[8]    M. Geraci. “Modelling and estimation of nonlinear quantile regression with clustered data”. Comp. Stat. Dat. Anal., vol. 136, 2019, pp. 30–46.
[9]    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.
[10]    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”. App. Sof. Comp., vol. 82, 2019, 105539.
[11]    K.P. Lu and S.T. Chang. “A fuzzy classification approach to piecewise regression models”. App. Sof. Comp., vol. 69, 2018, pp. 671–688.
[12]    G. J. McLachlan and K.E.Basford. “Mixture Models: Inference and Applications to Clustering”. vol. 84, Marcel Dekker, 1988.
[13]    J.C. Pinheiro and D.M. Bates. “Mixed-Effects Models in S and S-PLUS”. Springer Verlag, New York, 2000.
[14]    A. Punzo and P.D. McNicholas. “Robust Clustering in Regression Analysis via the Contaminated Gaussian Cluster-Weighted Model”. J. Class., vol. 34, 2017, pp. 249–293.
[15]    W. Song, W. Yao and Y. Xing. “Robust mixture regression model fitting by Laplace distribution”. Comp. Stat. Dat. Anal., vol. 71, 2014, pp. 128–137.
[16]    W. Yao, Y. Wei and C. Yu. “Robust mixture regression using the t-distribution”. Comp. Stat. Dat. Anal., vol. 71, 2014, pp. 116–127.
[17]    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.
[18]    L. A. Zadeh. ‘Is there a need for fuzzy logic?”. Info. Scie., vol. 178, 2008, pp. 27
Fuzzy Systems and its Applications
Volume 7, Issue 2 - Serial Number 15
Open Access Statement
December 2024
Pages 13-32

  • Receive Date 22 May 2024
  • Revise Date 05 September 2024
  • Accept Date 06 October 2024