Related papers: Fast matrix decomposition in F2
Low-rank approximations are essential in modern data science. The interpolative decomposition provides one such approximation. Its distinguishing feature is that it reuses columns from the original matrix. This enables it to preserve matrix…
In this work we describe an efficient implementation of a hierarchy of algorithms for the decomposition of dense matrices over the field with two elements (GF(2)). Matrix decomposition is an essential building block for solving dense…
In this paper we describe a parallel Gaussian elimination algorithm for matrices with entries in a finite field. Unlike previous approaches, our algorithm subdivides a very large input matrix into smaller submatrices by subdividing both…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
A Random SubMatrix method (RSM) is proposed to calculate the low-rank decomposition of large-scale matrices with known entry percentage \rho. RSM is very fast as the floating-point operations (flops) required are compared favorably with the…
We describe an efficient algorithm for computing the matrix vector products that appear in the numerical resolution of boundary integral equations in 2 space dimension. This work is an extension of the so-called Sparse Cardinal Sine…
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…
We consider the problem of computing the rank of an m x n matrix A over a field. We present a randomized algorithm to find a set of r = rank(A) linearly independent columns in \~O(|A| + r^\omega) field operations, where |A| denotes the…
Tensor ring (TR) decomposition has recently received increased attention due to its superior expressive performance for high-order tensors. However, the applicability of traditional TR decomposition algorithms to real-world applications is…
We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning,…
Given an irregular dense tensor, how can we efficiently analyze it? An irregular tensor is a collection of matrices whose columns have the same size and rows have different sizes from each other. PARAFAC2 decomposition is a fundamental tool…
We improve the current best running time value to invert sparse matrices over finite fields, lowering it to an expected $O\big(n^{2.2131}\big)$ time for the current values of fast rectangular matrix multiplication. We achieve the same…
Two methods to decompose block matrices analogous to Singular Matrix Decomposition are proposed, one yielding the so called economy decomposition, and other yielding the full decomposition. This method is devised to avoid handling matrices…
A large class of dense linear algebra operations, such as LU decomposition or inversion of a triangular matrix, are usually performed by blocked algorithms. For one such operation, typically, not only one but many algorithmic variants…
In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns),…
The nonnegative integer rank of a matrix is a variant of the classical nonnegative rank, introduced in the 1980s, where factorizations are required to have integer entries. While computing nonnegative integer rank is generally very hard, we…
In this work we describe an efficient implementation of a hierarchy of algorithms for Gaussian elimination upon dense matrices over the field with two elements. We discuss both well-known and new algorithms as well as our implementations in…
This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…
In this paper, we develop a polynomial time algorithm to compute a Dulmage-Mendelsohn-type decomposition of a matrix partitioned into submatrices of rank at most $1$.
Matrices are exceptionally useful in various fields of study as they provide a convenient framework to organize and manipulate data in a structured manner. However, modern matrices can involve billions of elements, making their storage and…