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Clustering via finite nonparametric ICA mixture models

Author

Listed:
  • Xiaotian Zhu

    (Natera Inc.)

  • David R. Hunter

    (Pennsylvania State University)

Abstract

We propose a novel extension of nonparametric multivariate finite mixture models by dropping the standard conditional independence assumption and incorporating the independent component analysis (ICA) structure instead. This innovation extends nonparametric mixture model estimation methods to situations in which conditional independence, a necessary assumption for the unique identifiability of the parameters in such models, is clearly violated. We formulate an objective function in terms of penalized smoothed Kullback–Leibler distance and introduce the nonlinear smoothed majorization-minimization independent component analysis algorithm for optimizing this function and estimating the model parameters. Our algorithm does not require any labeled observations a priori; it may be used for fully unsupervised clustering problems in a multivariate setting. We have implemented a practical version of this algorithm, which utilizes the FastICA algorithm, in the R package icamix. We illustrate this new methodology using several applications in unsupervised learning and image processing.

Suggested Citation

  • Xiaotian Zhu & David R. Hunter, 2019. "Clustering via finite nonparametric ICA mixture models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(1), pages 65-87, March.
  • Handle: RePEc:spr:advdac:v:13:y:2019:i:1:d:10.1007_s11634-018-0338-x
    DOI: 10.1007/s11634-018-0338-x
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    References listed on IDEAS

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    1. Hunter D.R. & Lange K., 2004. "A Tutorial on MM Algorithms," The American Statistician, American Statistical Association, vol. 58, pages 30-37, February.
    2. De Veaux, Richard D., 1989. "Mixtures of linear regressions," Computational Statistics & Data Analysis, Elsevier, vol. 8(3), pages 227-245, November.
    3. Eddelbuettel, Dirk & Sanderson, Conrad, 2014. "RcppArmadillo: Accelerating R with high-performance C++ linear algebra," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1054-1063.
    4. Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2016. "Non-parametric estimation of finite mixtures from repeated measurements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 211-229, January.
    5. Alessandra Guglielmi & Francesca Ieva & Anna M. Paganoni & Fabrizio Ruggeri & Jacopo Soriano, 2014. "Semiparametric Bayesian models for clustering and classification in the presence of unbalanced in-hospital survival," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(1), pages 25-46, January.
    6. Peña, Daniel & Prieto, Francisco J. & Viladomat, Júlia, 2010. "Eigenvectors of a kurtosis matrix as interesting directions to reveal cluster structure," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 1995-2007, October.
    7. Patrick Bajari & Jinyong Hahn & Han Hong & Geert Ridder, 2011. "A Note On Semiparametric Estimation Of Finite Mixtures Of Discrete Choice Models With Application To Game Theoretic Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(3), pages 807-824, August.
    8. Mian Huang & Runze Li & Shaoli Wang, 2013. "Nonparametric Mixture of Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 929-941, September.
    9. Cristina Butucea & Pierre Vandekerkhove, 2014. "Semiparametric Mixtures of Symmetric Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 227-239, March.
    10. Xiaotian Zhu & David R. Hunter, 2016. "Theoretical grounding for estimation in conditional independence multivariate finite mixture models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(4), pages 683-701, October.
    11. M. Levine & D. R. Hunter & D. Chauveau, 2011. "Maximum smoothed likelihood for multivariate mixtures," Biometrika, Biometrika Trust, vol. 98(2), pages 403-416.
    12. David Hunter & Derek Young, 2012. "Semiparametric mixtures of regressions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 19-38.
    13. repec:hal:spmain:info:hdl:2441/etefo8s8r89oamhnhiclqr530 is not listed on IDEAS
    14. Eddelbuettel, Dirk & Francois, Romain, 2011. "Rcpp: Seamless R and C++ Integration," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i08).
    15. Pierre Vandekerkhove, 2013. "Estimation of a semiparametric mixture of regressions model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(1), pages 181-208, March.
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