1 citations · 2 across the 12 of their papers we have counts for
12 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,…
Riemannian radial distributions on Riemannian symmetric spaces: Optimal rates of convergence for parameter estimation
Hengchao Chen
Manifold data analysis is challenging due to the lack of parametric distributions on manifolds. To address this, we introduce a series of Riemannian radial distributions on Riemann…
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…
Bounded Projection Matrix Approximation with Applications to Community Detection
Zheng Zhai, Hengchao Chen, Qiang Sun
Community detection is an important problem in unsupervised learning. This paper proposes to solve a projection matrix approximation problem with an additional entrywise bounded co…
Gradient descent in matrix factorization: Understanding large initialization
Hengchao Chen, Xin Chen, Mohamad Elmasri +1
Gradient Descent (GD) has been proven effective in solving various matrix factorization problems. However, its optimization behavior with large initial values remains less understo…
Statistical Analysis of Karcher Means for Random Restricted PSD Matrices
Hengchao Chen, Xiang Li, Qiang Sun
Non-asymptotic statistical analysis is often missing for modern geometry-aware machine learning algorithms due to the possibly intricate non-linear manifold structure. This paper s…
Quadratic Matrix Factorization with Applications to Manifold Learning
Zheng Zhai, Hengchao Chen, Qiang Sun
Matrix factorization is a popular framework for modeling low-rank data matrices. Motivated by manifold learning problems, this paper proposes a quadratic matrix factorization (QMF)…
Distributed Sparse Multicategory Discriminant Analysis
Hengchao Chen, Qiang Sun
This paper proposes a convex formulation for sparse multicategory linear discriminant analysis and then extend it to the distributed setting when data are stored across multiple si…