Related papers: On the equivalence between low rank matrix complet…
Rank-metric codes are subspaces of matrices over finite fields endowed with the rank metric and admit a natural tensorial representation. The tensor rank provides a measure of the minimal size of a decomposition of a code into rank-one…
The minimum rank problem is to determine for a graph $G$ the smallest rank of a Hermitian (or real symmetric) matrix whose off-diagonal zero-nonzero pattern is that of the adjacency matrix of $G$. Here $G$ is taken to be a circulant graph,…
The low-rank approximation is a complexity reduction technique to approximate a tensor or a matrix with a reduced rank, which has been applied to the simulation of high dimensional problems to reduce the memory required and computational…
This study aims to solve the over-reliance on the rank estimation strategy in the standard tensor factorization-based tensor recovery and the problem of a large computational cost in the standard t-SVD-based tensor recovery. To this end, we…
We study low T-phase-rank approximation of sectorial third-order tensors $\mathscr{A}\in\mathbb{C}^{n\times n\times p}$ under the tensor T-product. We introduce canonical T-phases and T-phase rank, and formulate the approximation task as…
In this paper, we describe a low-rank matrix completion method based on matrix decomposition. An incomplete matrix is decomposed into submatrices which are filled with a proposed trimming step and then are recombined to form a low-rank…
We analyze low rank tensor completion (TC) using noisy measurements of a subset of the tensor. Assuming a rank-$r$, order-$d$, $N \times N \times \cdots \times N$ tensor where $r=O(1)$, the best sampling complexity that was achieved is…
We study three fundamental problems of Linear Algebra, lying in the heart of various Machine Learning applications, namely: 1)"Low-rank Column-based Matrix Approximation". We are given a matrix A and a target rank k. The goal is to select a…
Matrix completion is about recovering a matrix from its partial revealed entries, and it can often be achieved by exploiting the inherent simplicity or low dimensional structure of the target matrix. For instance, a typical notion of matrix…
Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion…
Currently, low-rank tensor completion has gained cumulative attention in recovering incomplete visual data whose partial elements are missing. By taking a color image or video as a three-dimensional (3D) tensor, previous studies have…
A well studied problem in algebraic complexity theory is the determination of the complexity of problems relying on evaluations of bilinear maps. One measure of the complexity of a bilinear map (or 3-tensor) is the optimal number of…
We consider the problem of finding the smallest or largest entry of a tensor of order N that is specified via its rank decomposition. Stated in a different way, we are given N sets of R-dimensional vectors and we wish to select one vector…
Low-rank matrix completion has been studied extensively under various type of categories. The problem could be categorized as noisy completion or exact completion, also active or passive completion algorithms. In this paper we focus on…
Consider a movie recommendation system where apart from the ratings information, side information such as user's age or movie's genre is also available. Unlike standard matrix completion, in this setting one should be able to predict…
Low-rank tensor completion (LRTC) aims to recover a complete low-rank tensor from incomplete observed tensor, attracting extensive attention in various practical applications such as image processing and computer vision. However, current…
The problem of partitioning a large and sparse tensor is considered, where the tensor consists of a sequence of adjacency matrices. Theory is developed that is a generalization of spectral graph partitioning. A best rank-$(2,2,\lambda)$…
We consider robust low rank matrix estimation as a trace regression when outputs are contaminated by adversaries. The adversaries are allowed to add arbitrary values to arbitrary outputs. Such values can depend on any samples. We deal with…
Affine matrix rank minimization problem is a fundamental problem with a lot of important applications in many fields. It is well known that this problem is combinatorial and NP-hard in general. In this paper, a continuous promoting low rank…
Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…