Mixture of Geodesic Factor Analyzers on Riemannian Homogeneous Spaces

arXiv:2608.06971 · stat.ML, cs.LG, math.ST, stat.ME, stat.TH · Submitted 2026-08-07 · Read on arXiv

Hengchao Chen, Yuanyao Tan, Chao Huang, Hongtu Zhu, Qiang Sun

stat.ML, cs.LG, math.ST, stat.ME, stat.TH

Submitted: 2026-08-07

Updated: 2026-08-10

Comments: 22 pages main, 49 pages appendix

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

Clustering — 100× in this paper · explained in 2 episodes
Hyperbolic Space — 19× in this paper · explained in 2 episodes
Robustness — 14× in this paper · explained in 6 episodes
Mixtures of Geodesic Factor Analyzers — 7× in this paper
Accuracy — 3× in this paper · explained in 1 episode
Consistency — 3× in this paper · explained in 3 episodes
Homogeneity — 3× in this paper · explained in 2 episodes
Objective Function — 3× in this paper · explained in 2 episodes
Stiefel Manifold — 3× in this paper · explained in 3 episodes
Clarity — 2× in this paper · explained in 3 episodes
Embeddings — 2× in this paper · explained in 2 episodes
Interpretability — 2× in this paper · explained in 15 episodes
K-means Clustering — 2× in this paper · explained in 3 episodes
Riemannian Optimization — 2× in this paper · explained in 3 episodes
Theoretical Guarantees — 2× in this paper · explained in 2 episodes
Benchmark — 1× in this paper · explained in 2 episodes
Computational Efficiency — 1× in this paper · explained in 2 episodes
Convergence Guarantees — 1× in this paper · explained in 3 episodes
Curse of Dimensionality — 1× in this paper · explained in 6 episodes
Orthogonal Projection — 1× in this paper · explained in 2 episodes
Regularization — 1× in this paper · explained in 3 episodes
Research Review — 1× in this paper · explained in 6 episodes
Rey Auditory Verbal Learning Test — 1× in this paper

Sources

Riemannian radial distributions on Riemannian symmetric spaces: Optimal rates of convergence for parameter estimation

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