Mixture of Geodesic Factor Analyzers on Riemannian Homogeneous Spaces
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 compe...
| Authors | Hengchao Chen, Yuanyao Tan, Chao Huang et al. |
|---|---|
| Primary category | stat.ML |
| Published | 7 August 2026 |
| Last updated at source | 7 August 2026 |
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