Zobrazeno 1 - 10
of 53
pro vyhledávání: '"Chen, Hengchao"'
Autor:
Chen, Hengchao, Sun, Qiang
This paper develops the first decentralized online Riemannian optimization algorithm on Hadamard manifolds. Our algorithm, the decentralized projected Riemannian gradient descent, iteratively performs local updates using projected Riemannian gradient
Externí odkaz:
http://arxiv.org/abs/2410.05128
Autor:
Chen, Hengchao
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 Riemannian symmetric spaces. By utilizing the symmetry, we show that for many
Externí odkaz:
http://arxiv.org/abs/2405.07852
Autor:
Chen, Hengchao
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 set of a spherical product manifold by an orthogonal group. We show t
Externí odkaz:
http://arxiv.org/abs/2401.03126
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 proves the inclusion relationship between ridges: $\cR(f\circ p)\subseteq \
Externí odkaz:
http://arxiv.org/abs/2306.05722
Gradient Descent (GD) has been proven effective in solving various matrix factorization problems. However, its optimization behavior with large initial values remains less understood. To address this gap, this paper presents a novel theoretical frame
Externí odkaz:
http://arxiv.org/abs/2305.19206
Community detection is an important problem in unsupervised learning. This paper proposes to solve a projection matrix approximation problem with an additional entrywise bounded constraint. Algorithmically, we introduce a new differentiable convex pe
Externí odkaz:
http://arxiv.org/abs/2305.15430
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 studies an intrinsic mean model on the manifold of restricted positive
Externí odkaz:
http://arxiv.org/abs/2302.12426
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) framework to learn the curved manifold on which the dataset lies. Unl
Externí odkaz:
http://arxiv.org/abs/2301.12965
Autor:
Chen, Hengchao, Sun, Qiang
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 sites. The key observation is that for the purpose of classification it
Externí odkaz:
http://arxiv.org/abs/2202.10913
Publikováno v:
In Journal of Constructional Steel Research November 2023 210
