8 papers
Mixture of Geodesic Factor Analyzers on Riemannian Homogeneous Spaces
Hengchao Chen, Yuanyao Tan, Chao Huang +2
This paper introduces Mixtures of Geodesic Factor Analyzers (MGFA) on Riemannian homogeneous spaces. MGFA uses a geodesic factor model within each mixture component, providing grea…
Distributional Matching for Vector Quantization: A Unified Theoretical and Empirical Framework
Xianghong Fang, Litao Guo, Hengchao Chen +8
The effectiveness of modern visual representation learning and autoregressive models critically depends on vector quantization (VQ), which discretizes continuous feature representa…
Enhancing Vector Quantization with Distributional Matching: A Theoretical and Empirical Study
Xianghong Fang, Litao Guo, Hengchao Chen +8
The success of autoregressive models largely depends on the effectiveness of vector quantization, a technique that discretizes continuous features by mapping them to the nearest co…
Decentralized Online Riemannian Optimization with Dynamic Environments
Hengchao Chen, Qiang Sun
This paper develops the first decentralized online Riemannian optimization algorithm on Hadamard manifolds. Our algorithm, the decentralized projected Riemannian gradient descent,…
Quotient geometry of bounded or fixed rank correlation matrices
Hengchao Chen
This paper studies the quotient geometry of bounded or fixed-rank correlation matrices. We establish a bijection between the set of bounded-rank correlation matrices and a quotient…
Ridge Estimation with Nonlinear Transformations
Zheng Zhai, Hengchao Chen, Zhigang Yao
Ridge estimation is an important manifold learning technique. The goal of this paper is to examine the effects of nonlinear transformations on the ridge sets. The main result prove…