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 and L2 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.

STGP: Spatio-temporal Gaussian process models for longitudinal neuroimaging data

“…We can estimate ε i ( d,t ij ) by using ${\widehat{\epsilon }}_{i}false(d,t_{ij}false)=y_{i}false(d,t_{ij}false)-\hat{\mu }false(d,{\mathbf{x}}_{i}false(t_{ij}false)false)-{\sum }_{l=1}^{L_0}{\widehat{\xi }}_{i,l}{\widehat{\psi }}_{l}false(d,t_{ij}false)$ and concatenate them into a vector ε̂ ( d ) = ( ε̂ i ( d , t ij ) : i = 1, …, n ; j = 1, …, m i ) T for each voxel. Specifically, we use a penalized likelihood approach with an L 1 penalty function for a Gaussian mixture model to cluster all residual vectors { ε̂ ( d ) : d ∈ 𝒟} into K homogeneous regions [Pan and Shen, 2007, Huang et al, 2015]. …”

A geodesic deployment and radial shaped clustering (RSC) algorithm with statistical aggregation in sensor networks

“…However, for translations, scaling and rotations of the nodes, this metric has to be replaced by the shape space according to Huang et.al [13].…”

The Offset Normal Shape Distribution for Dynamic Shape Analysis

“…The approach involves working with the original distribution of the landmark coordinates but treating the rotation and scale as missing/hidden variables. Huang et al (2015) have recently used the algorithm to consider a mixture of offset-normal shape factor analyzers (MOSFA) and Brombin et al (2016) have further explored the use of the EM algorithm in a dynamic setting by discussing its limitations when Laguerre polynomials are used to evaluate the offset-normal shape distribution. The methodology has also been extended to 3D shape and size-and-shape analysis by Kume et al (2017).…”