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International Workshop on Multimodal Brain Image Analysis

International Workshop on Mathematical Foundations of Computational Anatomy

MBIA 2019, MFCA 2019: Multimodal Brain Image Analysis and Mathematical Foundations of Computational Anatomy pp 196–208Cite as

Mixture Probabilistic Principal Geodesic Analysis

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Part of the book series: Lecture Notes in Computer Science ((LNIP,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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Author information

Authors and Affiliations

  1. Computer Science and Engineering, Lehigh University, Bethlehem, USA

    Youshan Zhang

  2. Electrical and Computer Engineering, University of Virginia, Charlottesville, USA

    Jiarui Xing & Miaomiao Zhang

  3. Computer Science, University of Virginia, Charlottesville, USA

    Miaomiao Zhang

Authors
  1. Youshan Zhang
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  2. Jiarui Xing
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  3. Miaomiao Zhang
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Corresponding author

Correspondence to Youshan Zhang .

Editor information

Editors and Affiliations

  1. The University of Texas at Arlington, Arlington, TX, USA

    Dajiang Zhu

  2. Indiana University – Purdue University Indianapolis, Indianapolis, IN, USA

    Jingwen Yan

  3. University of Pittsburgh, Pittsburgh, PA, USA

    Heng Huang

  4. University of Pennsylvania, Philadelphia, PA, USA

    Li Shen

  5. University of Southern California, Marina Del Rey, CA, USA

    Paul M. Thompson

  6. Harvard Medical School, Boston, MA, USA

    Carl-Fredrik Westin

  7. Inria Sophia-Antipolis, Sophia-Antipolis, France

    Xavier Pennec

  8. University of Utah, Salt Lake City, UT, USA

    Sarang Joshi

  9. University of Copenhagen, Copenhagen, Denmark

    Mads Nielsen

  10. University of Virginia, Charlottesville, VA, USA

    Tom Fletcher

  11. Inria, Paris, France

    Stanley Durrleman

  12. University of Copenhagen, Copenhagen, Denmark

    Stefan Sommer

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Zhang, Y., Xing, J., Zhang, M. (2019). Mixture Probabilistic Principal Geodesic Analysis. In: Zhu, D., et al. Multimodal Brain Image Analysis and Mathematical Foundations of Computational Anatomy. MBIA MFCA 2019 2019. Lecture Notes in Computer Science(), vol 11846. Springer, Cham. https://doi.org/10.1007/978-3-030-33226-6_21

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  • DOI: https://doi.org/10.1007/978-3-030-33226-6_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33225-9

  • Online ISBN: 978-3-030-33226-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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