12 citations · 12 across the 1 of their papers we have counts for
6 papers
Near-Linear Time and Fixed-Parameter Tractable Algorithms for Tensor Decompositions
Arvind V. Mahankali, David P. Woodruff, Ziyu Zhang
We study low rank approximation of tensors, focusing on the tensor train and Tucker decompositions, as well as approximations with tree tensor networks and more general tensor netw…
Asymptotic Escape of Spurious Critical Points on the Low-rank Matrix Manifold
Thomas Y. Hou, Zhenzhen Li, Ziyun Zhang
We show that on the manifold of fixed-rank and symmetric positive semi-definite matrices, the Riemannian gradient descent algorithm almost surely escapes some spurious critical poi…
Fast Global Convergence for Low-rank Matrix Recovery via Riemannian Gradient Descent with Random Initialization
Thomas Y. Hou, Zhenzhen Li, Ziyun Zhang
In this paper, we propose a new global analysis framework for a class of low-rank matrix recovery problems on the Riemannian manifold. We analyze the global behavior for the Rieman…
Exponential convergence of Sobolev gradient descent for a class of nonlinear eigenproblems
Ziyun Zhang
We propose to use the Łojasiewicz inequality as a general tool for analyzing the convergence rate of gradient descent on a Hilbert manifold, without resorting to the continuous gra…
Analysis of Asymptotic Escape of Strict Saddle Sets in Manifold Optimization
Thomas Y. Hou, Zhenzhen Li, Ziyun Zhang
In this paper, we provide some analysis on the asymptotic escape of strict saddles in manifold optimization using the projected gradient descent (PGD) algorithm. One of our main co…
A Fast Hierarchically Preconditioned Eigensolver Based On Multiresolution Matrix Decomposition
Thomas Y. Hou, De Huang, Ka Chun Lam +1
In this paper we propose a new iterative method to hierarchically compute a relatively large number of leftmost eigenpairs of a sparse symmetric positive matrix under the multireso…