Hu, Can, Fan, Wentao, Du, JiXiang and Bouguila, Nizar ORCID: https://orcid.org/0000000172247940 (2018) A Novel Statistical Approach for Clustering Positive Data Based on Finite Inverted BetaLiouville Mixture Models. Neurocomputing . ISSN 09252312 (In Press)
Text (application/pdf)
1MBANovelStatisticalApproachforClusteringPositiveDataBased_2018_Neuroco.pdf  Accepted Version Available under License Spectrum Terms of Access. 
Official URL: http://dx.doi.org/10.1016/j.neucom.2018.12.066
Abstract
Nowadays, a great number of positive data has been occurred naturally in many applications, however, it was not adequately analyzed. In this article, we propose a novel statistical approach for clustering multivariate positive data. Our approach is based on a finite mixture model of inverted BetaLiouville (IBL) distributions, which is proper choice for modeling and analysis of positive vector data. We develop two different approaches to learn the proposed mixture model. Firstly, the maximum likelihood (ML) is utilized to estimate parameters of the finite inverted BetaLiouville mixture model in which the right number of mixture components is determined according to the minimum message length (MML) criterion. Secondly, the variational Bayes (VB) is adopted to learn our model where the parameters and the number of mixture components can be determined simultaneously in a unified framework, without the requirement of using information criteria. We investigate the effectiveness of our model by conducting a series of experiments on both synthetic and real data sets.
Divisions:  Concordia University > Gina Cody School of Engineering and Computer Science > Concordia Institute for Information Systems Engineering 

Item Type:  Article 
Refereed:  Yes 
Authors:  Hu, Can and Fan, Wentao and Du, JiXiang and Bouguila, Nizar 
Journal or Publication:  Neurocomputing 
Date:  30 December 2018 
Funders: 

Digital Object Identifier (DOI):  10.1016/j.neucom.2018.12.066 
Keywords:  Clustering; Mixture models; Variational Bayes; Maximum likelihood; Minimum message; length; Inverted BetaLiouville 
ID Code:  984850 
Deposited By:  Michael Biron 
Deposited On:  10 Jan 2019 14:47 
Last Modified:  26 Dec 2020 02:00 
References:
C. Hu, W. Fan, J. Du, Y. Zeng Modelbased segmentation of image data using spatially constrained mixture models Neurocomputing, 283 (2018), pp. 214227A.K. Jain, R.P.W. Duin, J. Mao Statistical pattern recognition: A review IEEE Transactions on Pattern Analysis and Machine Intelligence, 22 (1) (2000), pp. 437
A.K. Jain, M.N. Murty, P.J. Flynn Data clustering: a review ACM Computing Surveys, 31 (3) (1999), pp. 264323
G.J. McLachlan, D. Peel Finite Mixture Models New York: Wiley (2000)
S. Boutemedjet, D. Ziou, N. Bouguila Modelbased subspace clustering of nongaussian data Neurocomputing, 73 (10) (2010), pp. 17301739
Y. Lai, Y. Ping, K. Xiao, B. Hao, X. ZhangVariational bayesian inference for a dirichlet process mixture of beta distributions and application Neurocomputing, 278 (2018), pp. 2333
G. Zhou, D. Zhu, Y. Wei, Z. Wang, Y. Zhou Realtime online learning of gaussian mixture model for opacity mapping Neurocomputing, 211 (2016), pp. 212220
W. Fan, N. Bouguila, D. Ziou Variational learning of finite Dirichlet mixture models using component splitting Neurocomputing, 129 (2014), pp. 316
W. Fan, N. Bouguila Online variational learning of generalized Dirichlet mixture models with feature selection Neurocomputing, 126 (2014), pp. 166179
T. Bdiri, N. Bouguila Positive vectors clustering using inverted Dirichlet finite mixture models Expert Systems with Applications, 39 (2) (2012), pp. 18691882
T. Bdiri, N. Bouguila Bayesian learning of inverted Dirichlet mixtures for SVM kernels generation Neural Computing and Applications, 23 (5) (2013), pp. 14431458
K.T. Fang, S. Kotz, K.W. Ng Symmetric Multivariate and Related Distributions Chapman and Hall (1990)
S. Ganesalingam Classification and mixture approaches to clustering via maximum likelihood Journal of the Royal Statistical Society, 38 (3) (1989), pp. 455466
G.J. Mclachlan, T. Krishnan The EM algorithm and extensions Biometrics, 382 (1) (1997), pp. 154156
H. Akaike A New Look at the Statistical Model Identification Springer New York (1974)
G. Schwarz Estimating dimension of a model Annals of Statistics (6) (1978), pp. 461464
J. Rissanen Modeling by shortest data description Pergamon Press, Inc. (1978)
C.S. Wallace, D.M. Boulton An information measure for classification Computer Journal, 11 (2) (1968), pp. 185194
M.A.T. Figueiredo, A.K. Jain Unsupervised learning of finite mixture models IEEE Transactions on Pattern Analysis and Machine Intelligence, 24 (3) (2002), pp. 381396
N. Bouguila, D. Ziou Highdimensional unsupervised selection and estimation of a finite generalized Dirichlet mixture model based on minimum message length IEEE Trans. Pattern Anal. Mach. Intell., 29 (10) (2007), pp. 17161731
N. Bouguila, D. Ziou Unsupervised selection of a finite Dirichlet mixture model: An MMLbased approach IEEE Trans. Knowl. Data Eng., 18 (8) (2006), pp. 9931009
H. Attias A variational Bayesian framework for graphical models International Conference on Neural Information Processing Systems (1999), pp. 209215
M.I. Jordan, Z. Ghahramani, T.S. Jaakkola, L.K. Saul An introduction to variational methods for graphical models Machine Learning, 37 (2) (1999), pp. 183233
C. Bishop Pattern Recognition and Machine Learning Springer (2006)
S. Konishi, G. Kitagawa Information Criteria and Statistical Modeling Springer New York (2008)
C.S. Wallace Statistical and Inductive Inference by Minimum Message Length SpringerVerlag New York (2005)
C.E. Shannon A mathematical theory of communication The Bell System Technical Journal, 27 (4) (1948), pp. 623656
W. Fan, N. Bouguila, D. Ziou Variational learning for finite Dirichlet mixture models and applications. IEEE Transactions on Neural Networks and Learning Systems, 23 (5) (2012), pp. 762774
C.M. Bishop, N. Lawrence, T. Jaakkola, M.I. Jordan Approximating posterior distributions in belief networks using mixtures Conference on Advances in Neural Information Processing Systems (1998), pp. 416422
N.D. Lawrence, C.M. Bishop, M.I. Jordan Mixture representations for inference and learning in boltzmann machines Fourteenth Conference on Uncertainty in Artificial Intelligence (1998), pp. 320327
M.M. Ichir, A. MohammadDjafari A mean field approximation approach to blind source separation with lp priors 13th European Signal Processing Conference (2005), pp. 14
P. Kasarapu, L. Allison Minimum message length estimation of mixtures of multivariate gaussian and von misesfisher distributions Machine Learning, 100 (2) (2015), pp. 333378
N. Nasios, A.G. Bors Variational learning for gaussian mixture models IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 36 (4) (2006), pp. 849862
N. Bouguila Hybrid generative/discriminative approaches for proportional data modeling and classification IEEE Trans. Knowl. Data Eng., 24 (12) (2012), pp. 21842202
W. Fan, N. Bouguila Learning finite BetaLiouville mixture models via variational Bayes for proportional data clustering Proceedings of the 23rd International Joint Conference on Artificial Intelligence (IJCAI) (2013), pp. 13231329
D. Mann, D. Zipes, P. Libby, R. Bonow Braunwald’s heart disease : a textbook of cardiovascular medicine (10th), Elsevier (2014)
R. Alizadehsani, J. Habibi, M.J. Hosseini, H. Mashayekhi, R. Boghrati, A. Ghandeharioun, B. Bahadorian, Z.A. SaniA data mining approach for diagnosis of coronary artery disease
Computer Methods and Programs in Biomedicine, 111 (1) (2013), pp. 5261
N.D. Singpurwalla, S.P. Wilson Software reliability modeling International Statistical Review, 62 (3) (1994), pp. 289317
M.R. Lyu Handbook of software reliability engineering McGrawHill, Inc. (1996)
F.A. Graybill Matrices With Applications in Statistics Wadsworth (1983)
C.S. Wallace, D.L. Dowe Mml mixture modelling of multistate, poisson, von mises circular and gaussian distributions Proc. 6th Int. Workshop on Artif. Intelligence and Statistics (1997), pp. 529536
R.A. Baxter, J.J. Oliver Finding overlapping components with MML Statistics and Computing, 10 (1) (2000), pp. 516
Repository Staff Only: item control page