Related papers: A note on column subset selection
The Boolean matrix factorization problem consists in approximating a matrix by the Boolean product of two smaller Boolean matrices. To obtain optimal solutions when the matrices to be factorized are small, we propose SAT and MaxSAT…
We show that any $n\times m$ matrix $A$ can be approximated in operator norm by a submatrix with a number of columns of order the stable rank of $A$. This improves on existing results by removing an extra logarithmic factor in the size of…
Many machine learning applications such as in vision, biology and social networking deal with data in high dimensions. Feature selection is typically employed to select a subset of features which im- proves generalization accuracy as well…
In this paper the problem of maximizing the distance to a given fixed point over an intersection of balls is considered. It is known that this problem is NP complete in the general case, since any subset sum problem can be solved upon…
This paper addresses matrix approximation problems for matrices that are large, sparse and/or that are representations of large graphs. To tackle these problems, we consider algorithms that are based primarily on coarsening techniques,…
This paper delves into the spectral norm aspect of the Generalized Column and Row Subset Selection (GCRSS) problem. Given a target matrix $\mathbf{A}\in \mathbb{R}^{n\times d}$, the objective of GCRSS is to select a column submatrix…
The problem of diagonalizing a class of complicated matrices, to be called ultrametric matrices, is investigated. These matrices appear at various stages in the description of disordered systems with many equilibrium phases by the technique…
We show in this paper that after proper scalings, the characteristic polynomial of a random unitary matrix converges almost surely to a random analytic function whose zeros, which are on the real line, form a determinantal point process…
We prove the decomposition of arbitrary diagonal operators into tensor and matrix products of smaller matrices, focusing on the analytic structure of the resulting formulas and their inherent symmetries. Diagrammatic representations are…
The article is devoted to the development of algorithmic methods ensuring efficient complexity bounds for strongly convex-concave saddle point problems in the case when one of the groups of variables is high-dimensional, and the other is…
We study the problem of maximizing a monotone submodular function subject to a matroid constraint and present a deterministic algorithm that achieves (1/2 + {\epsilon})-approximation for the problem. This algorithm is the first…
We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…
Consider the collection of all binary matrices having a specific sequence of row and column sums and consider sampling binary matrices uniformly from this collection. Practical algorithms for exact uniform sampling are not known, but there…
A CUR approximation of a matrix $A$ is a particular type of low-rank approximation $A \approx C U R$, where $C$ and $R$ consist of columns and rows of $A$, respectively. One way to obtain such an approximation is to apply column subset…
Motivated by recent works on statistics of matrices over sets of number theoretic interest, we study matrices with entries from arbitrary finite subsets $\mathcal A$ of finite rank multiplicative groups infields of characteristic zero. We…
In this paper, we introduce the Maximum Matrix Contraction problem, where we aim to contract as much as possible a binary matrix in order to maximize its density. We study the complexity and the polynomial approximability of the problem.…
In this paper we study the extraction of representative elements in the data stream model in the form of submodular maximization. Different from the previous work on streaming submodular maximization, we are interested only in the recent…
Decision-making problems are commonly formulated as optimization problems, which are then solved to make optimal decisions. In this work, we consider the inverse problem where we use prior decision data to uncover the underlying…
We use a deterministic particle method to produce numerical approximations to the solutions of an evolution cross-diffusion problem for two populations. According to the values of the diffusion parameters related to the intra and…
In the construction of low-rank matrix approximation and maximum element search it is effective to use maxvol algorithm. Nevertheless, even in the case of rank 1 approximation the algorithm does not always converge to the maximum matrix…