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Mixture Probabilistic Principal Geodesic Analysis

  • Youshan ZhangEmail author
  • Jiarui Xing
  • Miaomiao Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11846)

Abstract

Dimensionality reduction on Riemannian manifolds is challenging due to the complex nonlinear data structures. While probabilistic principal geodesic analysis (PPGA) has been proposed to generalize conventional principal component analysis (PCA) onto manifolds, its effectiveness is limited to data with a single modality. In this paper, we present a novel Gaussian latent variable model that provides a unique way to integrate multiple PGA models into a maximum-likelihood framework. This leads to a well-defined mixture model of probabilistic principal geodesic analysis (MPPGA) on sub-populations, where parameters of the principal subspaces are automatically estimated by employing an Expectation Maximization algorithm. We further develop a mixture Bayesian PGA (MBPGA) model that automatically reduces data dimensionality by suppressing irrelevant principal geodesics. We demonstrate the advantages of our model in the contexts of clustering and statistical shape analysis, using synthetic sphere data, real corpus callosum, and mandible data from human brain magnetic resonance (MR) and CT images.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Computer Science and EngineeringLehigh UniversityBethlehemUSA
  2. 2.Electrical and Computer EngineeringUniversity of VirginiaCharlottesvilleUSA
  3. 3.Computer ScienceUniversity of VirginiaCharlottesvilleUSA

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