title: Clustering High-Dimensional Landmark-based Two-dimensional Shape Data‡.
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 paper 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 fusion Lasso penalty function andL2penalty 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.
authors.affiliation: Department of Biostatistics and Biomedical Research Imaging Center, University of North Carolina at Chapel Hill, NC 27599-7420, USA.
authors.forename: Chao
authors.initials: C
authors.lastname: Huang
authors.affiliation: Department of Biostatistics and Biomedical Research Imaging Center, University of North Carolina at Chapel Hill, NC 27599-7420, USA.
authors.forename: Martin
authors.initials: M
authors.lastname: Styner
authors.affiliation: Department of Biostatistics and Biomedical Research Imaging Center, University of North Carolina at Chapel Hill, NC 27599-7420, USA.
authors.forename: Hongtu
authors.initials: H
authors.lastname: Zhu
keywords: Alternating direction method of multipliers; Attention deficit hyperactivity disorder; Corpus callosum; Offset-normal shape distribution; Shape clustering