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Clustering High-Dimensional Landmark-Based Two-Dimensional Shape Data

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  • Chao Huang
  • Martin Styner
  • Hongtu Zhu

Abstract

An important goal in image analysis is to cluster and recognize objects of interest according to the shapes of their boundaries. Clustering such objects faces at least four major challenges including a curved shape space, a high-dimensional feature space, a complex spatial correlation structure, and shape variation associated with some covariates (e.g., age or gender). The aim of this article is to develop a penalized model-based clustering framework to cluster landmark-based planar shape data, while explicitly addressing these challenges. Specifically, a mixture of offset-normal shape factor analyzers (MOSFA) is proposed with mixing proportions defined through a regression model (e.g., logistic) and an offset-normal shape distribution in each component for data in the curved shape space. A latent factor analysis model is introduced to explicitly model the complex spatial correlation. A penalized likelihood approach with both adaptive pairwise fused Lasso penalty function and L 2 penalty function is used to automatically realize variable selection via thresholding and deliver a sparse solution. Our real data analysis has confirmed the excellent finite-sample performance of MOSFA in revealing meaningful clusters in the corpus callosum shape data obtained from the Attention Deficit Hyperactivity Disorder-200 (ADHD-200) study. Supplementary materials for this article are available online.

Suggested Citation

  • Chao Huang & Martin Styner & Hongtu Zhu, 2015. "Clustering High-Dimensional Landmark-Based Two-Dimensional Shape Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 946-961, September.
    • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:511:p:946-961
    DOI: 10.1080/01621459.2015.1034802
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    References listed on IDEAS

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    6. Xiaoyan Shi & Hongtu Zhu & Joseph G. Ibrahim & Faming Liang & Jeffrey Lieberman & Martin Styner, 2012. "Intrinsic Regression Models for Medial Representation of Subcortical Structures," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 12-23, March.
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    Cited by:

    1. Rabi Bhattacharya & Rachel Oliver, 2019. "Nonparametric Analysis of Non-Euclidean Data on Shapes and Images," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 1-36, February.
    2. Ruite Guo & Hwiyoung Lee & Vic Patrangenaru, 2023. "Test for Homogeneity of Random Objects on Manifolds with Applications to Biological Shape Analysis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1178-1204, August.
    3. Lizhen Lin & Brian St. Thomas & Hongtu Zhu & David B. Dunson, 2017. "Extrinsic Local Regression on Manifold-Valued Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1261-1273, July.

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