Related papers: Riemannian preconditioning for tensor completion

A matrix completion problem is to recover the missing entries in a partially observed matrix. Most of the existing matrix completion methods assume a low rank structure of the underlying complete matrix. In this paper, we introduce an…

In low-rank tensor completion tasks, due to the underlying multiple large-scale singular value decomposition (SVD) operations and rank selection problem of the traditional methods, they suffer from high computational cost and high…

Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due…

Tensor completion is a natural higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from sparse observations of its entries. Existing algorithms are either heuristic without provable guarantees,…

In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…

We propose a novel preconditioned inexact primal-dual interior point method for constrained convex quadratic programming problems. The algorithm we describe invokes the preconditioned conjugate gradient method on a new reduced Schur…

Several tensor networks are built of isometric tensors, i.e. tensors satisfying $W^\dagger W = \mathrm{I}$. Prominent examples include matrix product states (MPS) in canonical form, the multiscale entanglement renormalization ansatz (MERA),…

A Riemannian gradient descent algorithm and a truncated variant are presented to solve systems of phaseless equations $|Ax|^2=y$. The algorithms are developed by exploiting the inherent low rank structure of the problem based on the…

We propose an isogeometric solver for Poisson problems that combines i)low-rank tensor techniques to approximate the unknown solution and the system matrix, as a sum of a few terms having Kronecker product structure, ii) a Truncated…

This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its…

This work is concerned with the numerical solution of large-scale symmetric positive definite matrix equations of the form $A_1XB_1^\top + A_2XB_2^\top + \dots + A_\ell X B_\ell^\top = F$, as they arise from discretized partial differential…

Recovering a low rank matrix from a subset of its entries, some of which may be corrupted, is known as the robust matrix completion (RMC) problem. Existing RMC methods have several limitations: they require a relatively large number of…

Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors…

We introduce a new consistency-based approach for defining and solving nonnegative/positive matrix and tensor completion problems. The novelty of the framework is that instead of artificially making the problem well-posed in the form of an…

The recent low-rank prior based models solve the tensor completion problem efficiently. However, these models fail to exploit the local patterns of tensors, which compromises the performance of tensor completion. In this paper, we propose a…

In scientific computing and machine learning applications, matrices and more general multidimensional arrays (tensors) can often be approximated with the help of low-rank decompositions. Since matrices and tensors of fixed rank form smooth…

This paper proposes a Riemannian Multiobjective Proximal Gradient Method (RMPGM) for composite optimization problems on manifolds. Unlike scalarization-based approaches, the proposed framework directly handles vector-valued objectives and…

This paper focuses on minimizing a smooth function combined with a nonsmooth regularization term on a compact Riemannian submanifold embedded in the Euclidean space under a decentralized setting. Typically, there are two types of approaches…

Tensor ring (TR) decomposition has been successfully used to obtain the state-of-the-art performance in the visual data completion problem. However, the existing TR-based completion methods are severely non-convex and computationally…

The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…