Related papers: Min-plus algebraic low rank matrix approximation: …
Over the past years Robust PCA has been established as a standard tool for reliable low-rank approximation of matrices in the presence of outliers. Recently, the Robust PCA approach via nuclear norm minimization has been extended to…
We present a fast randomized algorithm that computes a low rank LU decomposition. Our algorithm uses random projections type techniques to efficiently compute a low rank approximation of large matrices. The randomized LU algorithm can be…
Given a limited number of entries from the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, recovery of the low-rank and sparse components is a fundamental task subsuming…
The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…
We develop computational methods for approximating the solution of a linear multi-term matrix equation in low rank. We follow an alternating minimization framework, where the solution is represented as a product of two matrices, and…
The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem under the standard low rank assumption is NP-hard,…
We consider the problem of finding the best nonnegative rank-2 approximation of an arbitrary nonnegative matrix. We first revisit the theory, including an explicit parametrization of all possible nonnegative factorizations of a nonnegative…
In this paper, we consider optimal low-rank regularized inverse matrix approximations and their applications to inverse problems. We give an explicit solution to a generalized rank-constrained regularized inverse approximation problem,…
The importance of accurate recommender systems has been widely recognized by academia and industry. However, the recommendation quality is still rather low. Recently, a linear sparse and low-rank representation of the user-item matrix has…
Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems…
As a paradigm to recover unknown entries of a matrix from partial observations, low-rank matrix completion (LRMC) has generated a great deal of interest. Over the years, there have been lots of works on this topic but it might not be easy…
The method is based on the preliminary transformation of the traditionally used matrices or adjacency lists in the graph theory into refined projections free from redundant information, and their subsequent use in constructing shortest…
Hierarchical matrices approximate a given matrix by a decomposition into low-rank submatrices that can be handled efficiently in factorized form. $\mathcal{H}^2$-matrices refine this representation following the ideas of fast multipole…
Low-rank matrix is desired in many machine learning and computer vision problems. Most of the recent studies use the nuclear norm as a convex surrogate of the rank operator. However, all singular values are simply added together by the…
In this paper we address the problem of recovering a matrix, with inherent low rank structure, from its lower dimensional projections. This problem is frequently encountered in wide range of areas including pattern recognition, wireless…
Differentiable systems in this paper means systems of equations that are described by differentiable real functions in real matrix variables. This paper proposes algorithms for finding minimal rank solutions to such systems over (arbitrary…
Matrix rank minimization problems are gaining a plenty of recent attention in both mathematical and engineering fields. This class of problems, arising in various and across-discipline applications, is known to be NP-hard in general. In…
Modeling of multidimensional signal using tensor is more convincing than representing it as a collection of matrices. The tensor based approaches can explore the abundant spatial and temporal structures of the mutlidimensional signal. The…
Nowadays, low-rank approximations of matrices are an important component of many methods in science and engineering. Traditionally, low-rank approximations are considered in unitary invariant norms, however, recently element-wise…
We propose a novel linear discriminant analysis approach for the classification of high-dimensional matrix-valued data that commonly arises from imaging studies. Motivated by the equivalence of the conventional linear discriminant analysis…