Mixture of Geodesic Factor Analyzers on Riemannian Homogeneous Spaces

• URL: http://arxiv.org/abs/2608.06971v1
• Date: Fri, 07 Aug 2026 08:46:11 GMT
• Title: Mixture of Geodesic Factor Analyzers on Riemannian Homogeneous Spaces
• Abstract summary: We introduce Mixtures of Geodesic Factor Analyzers (MGFA) on homogeneous spaces.<n>MGFA uses a geodesic factor model within each mixture component.<n>We establish root-$n$ consistency for the MGFA maximum likelihood estimator (MLE)<n>We also propose an iterative estimation algorithm and implement it on spheres, shape spaces, and hyperbolic spaces.
• Score: 18.04564201305071
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper introduces Mixtures of Geodesic Factor Analyzers (MGFA) on Riemannian homogeneous spaces. MGFA uses a geodesic factor model within each mixture component, providing greater expressiveness than mixtures of Riemannian radial distributions and enabling clustering of manifold-valued data with anisotropic subpopulations. We establish root-$n$ consistency for the MGFA maximum likelihood estimator (MLE), thereby filling a theoretical gap for mixtures of Riemannian radial distributions as a special case. We also propose an iterative estimation algorithm and implement it on spheres, shape spaces, and hyperbolic spaces. Numerical experiments show that MGFA substantially outperforms competing methods in well-specified regimes while remaining robust under model misspecification. Finally, case studies on corpus callosum and left hippocampus shape datasets demonstrate MGFA's effectiveness for both 2D contour and 3D shape analysis.

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