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Clustering via finite nonparametric ICA mixture models

  • Xiaotian Zhu
  • David R. HunterEmail author
Regular Article

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.

Keywords

Independent component analysis Kernel density estimation Nonparametric estimation Penalized smoothed likelihood Unsupervised learning 

Mathematics Subject Classification

62H30 62G07 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Natera Inc.San CarlosUSA
  2. 2.Department of StatisticsPennsylvania State UniversityUniversity ParkUSA

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