Related papers: The CP-matrix completion problem
We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover…
The task of estimating a matrix given a sample of observed entries is known as the \emph{matrix completion problem}. Most works on matrix completion have focused on recovering an unknown real-valued low-rank matrix from a random sample of…
The low-rank matrix completion problem can be succinctly stated as follows: given a subset of the entries of a matrix, find a low-rank matrix consistent with the observations. While several low-complexity algorithms for matrix completion…
It is known that every complex square matrix with nonnegative determinant is the product of positive semi-definite matrices. There are characterizations of matrices that require two or five positive semi-definite matrices in the product.…
In this paper we consider the problem of how to computationally test whether a matrix inequality is positive semidefinite on a semialgebraic set. We propose a family of sufficient conditions using the theory of matrix Positivstellensatz…
The main purpose of this note is to investigate some kinds of nonlinear complementarity problems (NCP). For the structured tensors, such as, symmetric positive definite tensors and copositive tensors, we derive the existence theorems on a…
We present a novel method for matrix completion, specifically designed for matrices where one dimension is significantly larger than the other. Our Columns Selected Matrix Completion (CSMC) method combines Column Subset Selection with…
Matrix completion is a basic machine learning problem that has wide applications, especially in collaborative filtering and recommender systems. Simple non-convex optimization algorithms are popular and effective in practice. Despite recent…
We consider the problem of recovering the entries of diagonal matrices $\{U_a\}_a$ for $a = 1,\ldots,t$ from multiple "incomplete" samples $\{W_a\}_a$ of the form $W_a=PU_aQ$, where $P$ and $Q$ are unknown matrices of low rank. We devise…
Completing a data matrix X has become an ubiquitous problem in modern data science, with applications in recommender systems, computer vision, and networks inference, to name a few. One typical assumption is that X is low-rank. A more…
This article presents a class of modified new modulus-based iterative methods to process the large and sparse implicit complementarity problem (ICP). By using two positive diagonal matrices, we formulate a fixed-point equation which is…
It was recently pointed out that inclusive B^0(t) decays could show CP violation. The totally inclusive asymmetry is expected to be tiny [O(10^{-3})] because of large cancellations among the asymmetries in the charmless, single charm and…
A real square matrix $A$ is called a $Q$-matrix if the linear complementarity problem $LCP(A,q)$ has a solution for all $q \in \mathbb{R}^n$. This means that for every vector $q$ there exists a vector $x$ such that $x \geq 0, y=Ax+q\geq 0$…
Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system.…
In this paper, we study the popularly dubbed matrix completion problem, where the task is to "fill in" the unobserved entries of a matrix from a small subset of observed entries, under the assumption that the underlying matrix is of…
We study the complexity of algorithmic problems for matrices that are represented by multi-terminal decision diagrams (MTDD). These are a variant of ordered decision diagrams, where the terminal nodes are labeled with arbitrary elements of…
The inductive matrix completion (IMC) problem is to recover a low rank matrix from few observed entries while incorporating prior knowledge about its row and column subspaces. In this work, we make three contributions to the IMC problem:…
In this paper the geometric mean of partial positive definite matrices with missing entries is considered. The weighted geometric mean of two sets of positive matrices is defined, and we show whether such a geometric mean holds certain…
Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is…
This paper proposes an efficient algorithm for testing copositivity of homogeneous polynomials over the positive semidefinite cone. The algorithm is based on a novel matrix optimization reformulation and requires solving a hierarchy of…