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

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...

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Bibliographic Details
Published in:	Journal of the American Statistical Association 2015-09, Vol.110 (511), p.946-961
Main Authors:	Huang, Chao, Styner, Martin, Zhu, Hongtu
Format:	Article
Language:	eng
Subjects:	Alternating direction method of multipliers Applications and Case Studies Attention deficit disorder Attention deficit hyperactivity disorder cluster analysis Clustering Corpus callosum Differential analysis Discriminant analysis factor analysis gender image analysis mixing Normal distribution Offset-normal shape distribution Regression analysis Shape clustering Statistics
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Summary:	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.
ISSN:	1537-274X 0162-1459 1537-274X