Related papers: The WST-decomposition for partial matrices
A matrix is incomplete when some of its entries are missing. A Robinson incomplete symmetric matrix is an incomplete symmetric matrix whose non-missing entries do not decrease along rows and columns when moving toward the diagonal. A…
The low-rank matrix completion problem asks whether a given real matrix with missing values can be completed so that the resulting matrix has low rank or is close to a low-rank matrix. The completed matrix is often required to satisfy…
Matrix Completion is the problem of recovering an unknown real-valued low-rank matrix from a subsample of its entries. Important recent results show that the problem can be solved efficiently under the assumption that the unknown matrix is…
We study the problem of low-rank matrix completion for symmetric matrices. The minimum rank of a completion of a generic partially specified symmetric matrix depends only on the location of the specified entries, and not their values, if…
We investigate the problem of completing partial matrices to rank-one matrices in the standard simplex. The motivation for studying this problem comes from statistics: A lack of eligible completion can provide a falsification test for…
We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often…
In this paper, we consider matrix completion from non-uniformly sampled entries including fully observed and partially observed columns. Specifically, we assume that a small number of columns are randomly selected and fully observed, and…
Tensor completion can estimate missing values of a high-order data from its partially observed entries. Recent works show that low rank tensor ring approximation is one of the most powerful tools to solve tensor completion problem. However,…
A permutation representation of a Coxeter group $W$ naturally defines an absolute order. This family of partial orders (which includes the absolute order on $W$) is introduced and studied in this paper. Conditions under which the associated…
The top-quark, $W$ and $Z^0$ bosons have widths that are a sizable fraction of their masses and will be produced copiously at upcoming accelerators. Yet S-matrix theory cannot treat unstable particles as external states. Dealing with…
Given a large tensor, how can we decompose it to sparse core tensor and factor matrices such that it is easier to interpret the results? How can we do this without reducing the accuracy? Existing approaches either output dense results or…
The problem of matrix completion and decomposition in the cone of positive semidefinite (PSD) matrices is a well-understood problem, with many important applications in areas such as linear algebra, optimization, and control theory. This…
A simple matrix is a (0,1)-matrix with no repeated columns. For a (0,1)-matrix $F$, we say that a (0,1)-matrix $A$ has $F$ as a configuration if there is a submatrix of $A$ which is a row and column permutation of $F$ (trace is the set…
For $n\ge 2$ and fixed $k\ge 1$, we study when a square matrix $A$ over an arbitrary field $\mathbb{F}$ can be decomposed as $T+N$ where $T$ is a torsion matrix and $N$ is a nilpotent matrix with $N^k=0$. For fields of prime characteristic,…
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…
Every square matrix $A=(a_{uv})\in \mathcal{C}^{n\times n}$ can be represented as a digraph having $n$ vertices. In the digraph, a block (or 2-connected component) is a maximally connected subdigraph that has no cut-vertex. The determinant…
In many applications, e.g., recommender systems and traffic monitoring, the data comes in the form of a matrix that is only partially observed and low rank. A fundamental data-analysis task for these datasets is matrix completion, where the…
We propose a theory for matrix completion that goes beyond the low-rank structure commonly considered in the literature and applies to general matrices of low description complexity. Specifically, complexity of the sets of matrices…
The row (resp. column) rank profile of a matrix describes the stair-case shape of its row (resp. column) echelon form. We here propose a new matrix invariant, the rank profile matrix, summarizing all information on the row and column rank…
A $n\times n$ matrix $A$ has normal defect one if it is not normal, however can be embedded as a north-western block into a normal matrix of size $(n+1)\times (n+1)$. The latter is called a minimal normal completion of $A$. A construction…