Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Effective Monotone Knowledge Integration in Kernel Support Vector Machines Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Unsupervised Component-Wise EM Learning for Finite Mixtures of Skew t-distributions

Authors : Sharon X. Lee, Geoffrey J. McLachlan

Published in: Advanced Data Mining and Applications

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In recent years, finite mixtures of skew distributions are gaining popularity as a flexible tool for modelling data with asymmetric distributional features. Parameter estimation for these mixture models via the traditional EM algorithm requires the number of components to be specified a priori. In this paper, we consider unsupervised learning of skew mixture models where the optimal number of components is estimated during the parameter estimation process. We adopt a component-wise EM algorithm and use the minimum message length (MML) criterion. For illustrative purposes, we focus on the case of a finite mixture of multivariate skew t distributions. The performance of the approach is demonstrated on a real dataset from flow cytometry, where our mixture model was used to provide an automated segmentation of cell populations.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter IPC Multi-label Classification Based on the Field Functionality of Patent Documents
next chapter Supervised Feature Selection by Robust Sparse Reduced-Rank Regression
Literature
1.
Abanto-Valle, C.A., Lachos, V.H., Dey, D.K.: Bayesian estimation of a skew-student-\(t\) stochastic volatility model. Methodol. Comput. Appl. Probab. 17, 721–738 (2015)MathSciNetCrossRefMATH
2.
3.
Asparouhov, T., Muthén, B.: Structural equation models and mixture models with continuous non-normal skewed distributions. Structural Equation Modeling (2015)
4.
Azzalini, A., Capitanio, A.: Distributions generated by perturbation of symmetry with emphasis on a multivariate skew \(t\)-distribution. J. Roy. Stat. Soc. B 65, 367–389 (2003)MathSciNetCrossRefMATH
5.
6.
Cabral, C.R.B., Lachos, V.H., Prates, M.O.: Multivariate mixture modeling using skew-normal independent distributions. Comput. Stat. Data Anal. 56, 126–142 (2012)MathSciNetCrossRefMATH
7.
Celeux, G., Chrétien, S., Forbes, F., MkhadrA.: A component-wise EM algorithm for mixtures. Journal of Computational and Graphical Statistics 10(4) (2001)
8.
Figueiredo, M.A.T., Jain, A.K.: Unsupervised learning of finite mixture models. IEEE Trans. Pattern Anal. Mach. Intell. 24, 3813 (2002)CrossRef
9.
Frühwirth-Schnatter, S., Pyne, S.: Bayesian inference for finite mixtures of univariate and multivariate skew-normal and skew-\(t\) distributions. Biostatistics 11, 317–336 (2010)CrossRef
10.
Hu, X., Kim, H., Brennan, P.J., Han, B., Baecher-Allan, C.M., Jager, P.L., Brenner, M.B., Raychaudhuri, S.: Application of user-guided automated cytometric data analysis to large-scale immunoprofiling of invariant natural killer t cells. In: Proceedings of the National Academy of Sciences USA, vol. 110, pp. 19030–19035 (2013)
11.
Lee, S., McLachlan, G.J.: Finite mixtures of multivariate skew \(t\)-distributions: Some recent and new results. Stat. Comput. 24, 181–202 (2014)MathSciNetCrossRefMATH
12.
Lee, S.X., McLachlan, G.J.: Model-based clustering and classification with non-normal mixture distributions. Stat. Methods Appl. 22, 427–454 (2013)MathSciNetCrossRefMATH
13.
Lee, S.X., McLachlan, G.J.: Modelling asset return using multivariate asym- metric mixture nodels with applications to wstimation of value-at-risk. In: MODSIM 2013, 20th International Congress on Modelling and Simulation, pp. 1228–1234, Adelaide, Australia (2013)
14.
15.
Lee, S.X., McLachlan, G.J.: Finite mixtures of canonical fundamental skew \(t\)-distributions: the unification of the restricted and unrestricted skew \(t\)-mixture models. Stat. Comput. 26, 573–589 (2016)MathSciNetCrossRefMATH
16.
Lee, S.X., McLachlan, G.J.: Risk measures based on multivariate skew normal and skew \(t\)-mixture models. In: Alcock, J., Satchell, S. (eds.) Asymmetric Dependence in Finance. Wiley, Hoboken, New Jersey (2016, to appear)
17.
Lee, S.X., McLachlan, G.J., Pyne, S.: Supervised classification of flow cytometric samples via the Joint Clustering and Matching (JCM) procedure. arXiv:​1411.​2820 [q-bio.QM] (2014)
18.
Lee, S.X., McLachlan, G.J., Pyne, S.: Modelling of inter-sample variation in flow cytometric data with the Joint Clustering and Matching (JCM) procedure. Cytometry A (2016)
19.
20.
Lin, T.I., Ho, H.J., Lee, C.R.: Flexible mixture modelling using the multivariate skew-\(t\)-normal distribution. Stat. Comput. 24, 531–546 (2014)MathSciNetCrossRefMATH
21.
Lin, T.I., McLachlan, G.J., Lee, S.X.: Extending mixtures of factor models using the restricted multivariate skew-normal distribution. J. Multivar. Anal. 143, 398–413 (2016)MathSciNetCrossRefMATH
22.
Lin, T.I., Wu, P.H., McLachlan, G.J., Lee, S.X.: A robust factor analysis model using the restricted skew \(t\)-distribution. TEST 24, 510–531 (2015)MathSciNetCrossRefMATH
23.
McLachlan, G.J., Lee, S.X.: Comment on “Comparing Two Formulations of Skew Distributions with Special Reference to Model-Based Clustering” by A. Azzalini, R. Browne, M. Genton, and P. McNicholas. arXiv:​1404.​1733 (2014)
24.
McLachlan, G.J., Lee, S.X.: Comment on “On nomenclature for, and the relative merits of, two formulations of skew distributions” by A. Azzalini, R. Browne, M. Genton, and P. McNicholas. Statistics and Probaility Letters 116, 1–5 (2016)MathSciNetCrossRefMATH
25.
Muthén, B., Asparouhov, T.: Growth mixture modeling with non-normal distributions. Stat. Med. 34, 1041–1058 (2014)MathSciNetCrossRef
26.
Pyne, S., Hu, X., Wang, K., Rossin, E., Lin, T.I., Maier, L.M., Baecher-Allan, C., McLachlan, G.J., Tamayo, P., Hafler, D.A., Jager, P.L., Mesirow, J.P.: Automated high-dimensional flow cytometric data analysis. In: Proceedings of the National Academy of Sciences USA, vol. 106, pp. 8519–8524 (2009)
27.
Pyne, S., Lee, S.X., Wang, K., Irish, J., Tamayo, P., Nazaire, M.D., Duong, T., Ng, S.K., Hafler, D., Levy, R., Nolan, G.P., Mesirov, J., McLachlan, G.: Joint modeling and registration of cell populations in cohorts of high-dimensional flow cytometric data. PLOS ONE 9, e100334 (2014)CrossRef
28.
Pyne, S., Lee, S., McLachlan, G.: Nature and man: The goal of bio-security in the course of rapid and inevitable human development. J. Indian Soc. Agric. Stat. 69, 117–125 (2015)MathSciNet
29.
Riggi, S., Ingrassia, S.: A model-based clustering approach for mass composition analysis of high energy cosmic rays. Astropart. Phys. 48, 86–96 (2013)CrossRef
30.
Sahu, S.K., Dey, D.K., Branco, M.D.: A new class of multivariate skew distributions with applications to Bayesian regression models. Can. J. Stat. 31, 129–150 (2003)MathSciNetCrossRefMATH
31.
Schaarschmidt, F., Hofmann, M., Jaki, T., Grün, B., Hothorn, L.A.: Statistical approaches for the determination of cut points in anti-drug antibody bioassays. J. Immunol. Methods 25, 295–306 (2015)
32.
Wallace, C.S., Boulton, D.M.: An information measure for classification. Comput. J. 11, 185–189 (1968)CrossRefMATH
33.
Wang, K., Ng, S.K., McLachlan, G.J.: Multivariate skew \(t\) mixture models: applications to fluorescence-activated cell sorting data. In: Proceedings of Conference of Digital Image Computing: Techniques and Applications, pp. 526–531, Los Alamitos, California (2009)
Metadata
Title
Unsupervised Component-Wise EM Learning for Finite Mixtures of Skew t-distributions
Authors
Sharon X. Lee
Geoffrey J. McLachlan
Copyright Year
2016
Book
Advanced Data Mining and Applications

Print ISBN: 978-3-319-49585-9

Electronic ISBN: 978-3-319-49586-6

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-49586-6_49

Premium Partner

    Image Credits