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Boolean matrix factorization is a natural and a popular technique for summarizing binary matrices. In this paper, we study a problem of Boolean matrix factorization where we additionally require that the factor matrices have consecutive…

Data Structures and Algorithms · Computer Science 2019-05-16 Nikolaj Tatti , Pauli Miettinen

We derive approximation algorithms for the nonnegative matrix factorization problem, i.e. the problem of factorizing a matrix as the product of two matrices with nonnegative coefficients. We form convex approximations of this problem which…

Optimization and Control · Mathematics 2012-07-03 Vijay Krishnamurthy , Alexandre d'Aspremont

In this paper, a method via sparse-sparse iteration for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix is proposed. The resulting factorized sparse approximate inverse is used as a…

Numerical Analysis · Mathematics 2008-08-03 Davod Khojasteh Salkuyeh , Faezeh Toutounian

In this article we develop an algorithm which computes a divisor of an integer $N$, which is assumed to be neither prime nor the power of a prime. The algorithm uses discrete time heat diffusion on a finite graph. If $N$ has $m$ distinct…

Quantum Physics · Physics 2023-01-24 Carlos A. Cadavid , Paulina Hoyos , Jay Jorgenson , Lejla Smajlović , Juan D. Vélez

The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…

Machine Learning · Computer Science 2016-03-30 Luc Le Magoarou , Rémi Gribonval

A symmetric nonnegative matrix factorization algorithm based on self-paced learning was proposed to improve the clustering performance of the model. It could make the model better distinguish normal samples from abnormal samples in an…

Machine Learning · Computer Science 2024-10-22 Lei Wang , Liang Du , Peng Zhou , Peng Wu

A novel approach to Boolean matrix factorization (BMF) is presented. Instead of solving the BMF problem directly, this approach solves a nonnegative optimization problem with the constraint over an auxiliary matrix whose Boolean structure…

Data Structures and Algorithms · Computer Science 2021-08-27 Duc P. Truong , Erik Skau , Derek Desantis , Boian Alexandrov

In addition to recent developments in computing speed and memory, methodological advances have contributed to significant gains in the performance of stochastic simulation. In this paper, we focus on variance reduction for matrix…

Machine Learning · Statistics 2023-03-28 Anant Mathur , Sarat Moka , Zdravko Botev

We analyse the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications such as dictionary learning, blind matrix…

Numerical Analysis · Computer Science 2016-07-19 Yoshiyuki Kabashima , Florent Krzakala , Marc Mézard , Ayaka Sakata , Lenka Zdeborová

This manuscript describes a technique for computing partial rank-revealing factorizations, such as, e.g, a partial QR factorization or a partial singular value decomposition. The method takes as input a tolerance $\varepsilon$ and an…

Numerical Analysis · Mathematics 2015-06-19 Per-Gunnar Martinsson , Sergey Voronin

New algorithms for prime factorization that outperform the existing ones or take advantage of particular properties of the prime factors can have a practical impact on present implementations of cryptographic algorithms that rely on the…

Cryptography and Security · Computer Science 2022-09-26 Alberto Montina , Stefan Wolf

This paper presents low-complexity tensor completion algorithms and their efficient implementation to reconstruct highly oscillatory operators discretized as $n\times n$ matrices. The underlying tensor decomposition is based on the…

Numerical Analysis · Mathematics 2026-02-17 Navjot Singh , Edgar Solomonik , Xiaoye Sherry Li , Yang Liu

In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…

Numerical Analysis · Mathematics 2022-08-11 Andrew V. Terekhov

We present and analyse a Monte-Carlo algorithm to compute the minimal polynomial of an $n\times n$ matrix over a finite field that requires $O(n^3)$ field operations and O(n) random vectors, and is well suited for successful practical…

Rings and Algebras · Mathematics 2008-04-07 Max Neunhoeffer , Cheryl E. Praeger

We show that assuming the availability of the processor with variable precision arithmetic, we can compute matrix-by-matrix multiplications in $O(N^2log_2N)$ computational complexity. We replace the standard matrix-by-matrix multiplications…

Data Structures and Algorithms · Computer Science 2025-08-19 Maciej Paszyński

We offer multiplication method for factoring big natural numbers which extends the group of the Fermat's and Lehman's factorization algorithms and has run-time complexity $O(n^{1/3})$. This paper is argued the finiteness of proposed…

Data Structures and Algorithms · Computer Science 2019-04-01 Igor Nesiolovskiy , Artem Nesiolovskiy

We present an approximate algorithm for matrix multiplication based on matrix sketching techniques. First one of the matrix is chosen and sparsified using the online matrix sketching algorithm, and then the matrix product is calculated…

Numerical Analysis · Computer Science 2014-06-12 Huan Wang , Christos Boutsidis , Edo Liberty , Daniel Hsu

A butterfly-based direct combined-field integral equation (CFIE) solver for analyzing scattering from electrically large, perfect electrically conducting objects is presented. The proposed solver leverages the butterfly scheme to compress…

Numerical Analysis · Mathematics 2017-10-11 Han Guo , Yang Liu , Jun Hu , Eric Michielssen

A convergent algorithm for nonnegative matrix factorization with orthogonality constraints imposed on both factors is proposed in this paper. This factorization concept was first introduced by Ding et al. with intent to further improve…

Machine Learning · Computer Science 2018-11-16 Andri Mirzal

Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two low rank, binary matrices: one containing meaningful patterns, the other quantifying how the observations can be expressed as a…

Machine Learning · Statistics 2017-02-28 Tammo Rukat , Chris C. Holmes , Michalis K. Titsias , Christopher Yau