相关论文: A Riemannian rank-adaptive method for higher-order…

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…

For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…

The existing matrix completion methods focus on optimizing the relaxation of rank function such as nuclear norm, Schatten-p norm, etc. They usually need many iterations to converge. Moreover, only the low-rank property of matrices is…

Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…

In this paper, we propose a novel approach to the rank minimization problem, termed rank residual constraint (RRC) model. Different from existing low-rank based approaches, such as the well-known nuclear norm minimization (NNM) and the…

This paper proposes a reduced-rank scheme for adaptive beamforming based on the constrained joint iterative optimization of filters. We employ this scheme to devise two novel reduced-rank adaptive algorithms according to the constant…

In the paper, we study a class of useful minimax problems on Riemanian manifolds and propose a class of effective Riemanian gradient-based methods to solve these minimax problems. Specifically, we propose an effective Riemannian gradient…

We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements. While the theoretical understanding of low rank…

The main aim of this paper is to develop a new algorithm for computing nonnegative low rank tensor approximation for nonnegative tensors that arise in many multi-dimensional imaging applications. Nonnegativity is one of the important…

Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries…

Tensor completion is an extension of matrix completion aimed at recovering a multiway data tensor by leveraging a given subset of its entries (observations) and the pattern of observation. The low-rank assumption is key in establishing a…

We propose a Riemannian optimization approach for computing low-rank solutions of the algebraic Riccati equation. The scheme alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is on the set of…

Multi-relational learning has received lots of attention from researchers in various research communities. Most existing methods either suffer from superlinear per-iteration cost, or are sensitive to the given ranks. To address both issues,…

A rank-adaptive integrator for the approximate solution of high-order tensor differential equations by tree tensor networks is proposed and analyzed. In a recursion from the leaves to the root, the integrator updates bases and then evolves…

This work presents cost-effective low-rank techniques for designing robust adaptive beamforming (RAB) algorithms. The proposed algorithms are based on the exploitation of the cross-correlation between the array observation data and the…

Recently, low-rank tensor completion has become increasingly attractive in recovering incomplete visual data. Considering a color image or video as a three-dimensional (3D) tensor, existing studies have put forward several definitions of…

Gradient descent methods are fundamental first-order optimization algorithms in both Euclidean spaces and Riemannian manifolds. However, the exact gradient is not readily available in many scenarios. This paper proposes a novel inexact…

This paper considers the problem of decentralized optimization on compact submanifolds, where a finite sum of smooth (possibly non-convex) local functions is minimized by $n$ agents forming an undirected and connected graph. However, the…

In this paper, we consider the tensor completion problem representing the solution in the tensor train (TT) format. It is assumed that tensor is high-dimensional, and tensor values are generated by an unknown smooth function. The assumption…

Random projection (RP) have recently emerged as popular techniques in the machine learning community for their ability in reducing the dimension of very high-dimensional tensors. Following the work in [30], we consider a tensorized random…