Online Program

M-GeoFARM: Mixture of Geodesic Factor Regression Model for Misaligned Pre-Shape Data Clustering Analysis (310012)

Keywords: Shape clustering, Riemannian Gaussian distribution, Geodesic regression

Due to the wide applications of shape data analysis in medical imaging, computer vision, and many other fields, it is of great interest to cluster objects and recover the underlying sub-group structure according to their shapes and covariates in Euclidean space (e.g., age and diagnostic status). However, this clustering task faces four challenges including (i) non-Euclidean space, (ii) misalignment of shapes due to pre-processing steps and imaging heterogeneity, (iii) complex spatial correlation structure, and (iv) geodesic variation associated with some covariates. In order to address these challenges, we propose a mixture of geodesic factor regression model (M-GeoFARM). In each cluster, a geodesic regression structure including covariates of interest and alignment step is established along with the Riemannian Gaussian distribution in the pre-shape space, and a latent factor model is built in the tangent space. In addition, a Monte Carlo EM algorithm is provided for the parameter estimation procedure. Finally, both simulation studies and real data analysis are conducted to compare the clustering performance of M-GeoFARM with other existing methods.