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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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