Related papers: Matrix sparsification and the sparse null space pr…
The problem of approximating a dense matrix by a product of sparse factors is a fundamental problem for many signal processing and machine learning tasks. It can be decomposed into two subproblems: finding the position of the non-zero…
We give a new proof for an equality of certain max-min and min-max approximation problems involving normal matrices. The previously published proofs of this equality apply tools from matrix theory, (analytic) optimization theory and…
This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which approximate inference corresponds to a matrix factorisation…
Stretching is a new sparse matrix method that makes matrices sparser by making them larger. Stretching has implications for computational complexity theory and applications in scientific and parallel computing. It changes matrix sparsity…
In this paper, we consider the matrices approximated in H2 format. The direct solution, as well as the preconditioning, of systems with such matrices is a challenging problem. We propose a non-extensive sparse factorization of the H2 matrix…
Efficient solutions of large-scale, ill-conditioned and indefinite algebraic equations are ubiquitously needed in numerous computational fields, including multiphysics simulations, machine learning, and data science. Because of their…
Nonnegative Matrix Factorization consists in (approximately) factorizing a nonnegative data matrix by the product of two low-rank nonnegative matrices. It has been successfully applied as a data analysis technique in numerous domains, e.g.,…
Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization…
Optimization problems are considered in the framework of tropical algebra to minimize and maximize a nonlinear objective function defined on vectors over an idempotent semifield, and calculated using multiplicative conjugate transposition.…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
Graphs arising in statistical problems, signal processing, large networks, combinatorial optimization, and data analysis are often dense, which causes both computational and storage bottlenecks. One way of \textit{sparsifying} a…
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…
Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of…
In light of recent data science trends, new interest has fallen in alternative matrix factorizations. By this, we mean various ways of factorizing particular data matrices so that the factors have special properties and reveal insights into…
Even distribution of irregular workload to processing units is crucial for efficient parallelization in many applications. In this work, we are concerned with a spatial partitioning called rectilinear partitioning (also known as generalized…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
Several applied problems may produce large sparse matrices with a small number of dense rows and/or columns, which can adversely affect the performance of commonly used direct solvers. By posing the problem as a saddle point system, an…
We consider list versions of sparse approximation problems, where unlike the existing results in sparse approximation that consider situations with unique solutions, we are interested in multiple solutions. We introduce these problems and…
The works presented in this habilitation concern the algorithmics of polynomials. This is a central topic in computer algebra, with numerous applications both within and outside the field - cryptography, error-correcting codes, etc. For…
Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an…