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Many applications in scientific computing and data science require the computation of a rank-revealing factorization of a large matrix. In many of these instances the classical algorithms for computing the singular value decomposition are…

Numerical Analysis · Mathematics 2018-12-17 Abinand Gopal , Per-Gunnar Martinsson

Many matrices associated with fast transforms posess a certain low-rank property characterized by the existence of several block partitionings of the matrix, where each block is of low rank. Provided that these partitionings are known,…

Numerical Analysis · Mathematics 2023-07-04 Léon Zheng , Gilles Puy , Elisa Riccietti , Patrick Pérez , Rémi Gribonval

Nonnegative matrix factorization (NMF) is widely used for clustering with strong interpretability. Among general NMF problems, symmetric NMF is a special one that plays an important role in graph clustering where each element measures the…

Machine Learning · Computer Science 2023-11-07 Mengyuan Zhang , Kai Liu

In this paper, we provide novel algorithms with identifiability guarantees for simplex-structured matrix factorization (SSMF), a generalization of nonnegative matrix factorization. Current state-of-the-art algorithms that provide…

Machine Learning · Computer Science 2021-05-12 Maryam Abdolali , Nicolas Gillis

In this paper we provide an algorithm, similar to the simplex algorithm, which determines a rational cp-factorization of a given matrix, whenever the matrix allows such a factorization. This algorithm can be used to show that every integral…

Optimization and Control · Mathematics 2021-04-27 Mathieu Dutour Sikirić , Achill Schürmann , Frank Vallentin

In this paper we develop algorithms for orthogonal similarity transformations of skew-symmetric matrices to simpler forms. The first algorithm is similar to the algorithm for the block antitriangular factorization of symmetric matrices, but…

Numerical Analysis · Mathematics 2020-05-05 Sanja Singer

In this paper, the Lorentz covariance of algorithms is introduced. Under Lorentz transformation, both the form and performance of a Lorentz covariant algorithm are invariant. To acquire the advantages of symplectic algorithms and Lorentz…

Plasma Physics · Physics 2017-09-13 Yulei Wang , Jian Liu , Hong Qin

This paper presents a new algorithm for generating random inverse-Wishart matrices that directly generates the Cholesky factor of the matrix without computing the factorization. Whenever parameterized in terms of a precision matrix…

Computation · Statistics 2023-10-25 Seth D. Axen

In this paper, two new stochastic algorithms for calculating parametric derivatives of the solution to the Smoluchowski coagulation equation are presented. It is assumed that the coagulation kernel is dependent on these parameters. The new…

Probability · Mathematics 2016-09-08 Peter L. W. Man , James R. Norris , Ismael F. Bailleul , Markus Kraft

Factorization of compact wavelet matrices into primitive ones has been known for more than 20 years. This method makes it possible to generate wavelet matrix coefficients and also to specify them by their first row. Recently, a new…

Numerical Analysis · Computer Science 2012-11-20 Nika Salia , Alexander Gamkrelidze , Lasha Ephremidze

Coupled matrix and tensor factorizations (CMTF) are frequently used to jointly analyze data from multiple sources, also called data fusion. However, different characteristics of datasets stemming from multiple sources pose many challenges…

Machine Learning · Computer Science 2021-04-21 Carla Schenker , Jeremy E. Cohen , Evrim Acar

The symmetric Nonnegative Matrix Factorization (NMF), a special but important class of the general NMF, has found numerous applications in data analysis such as various clustering tasks. Unfortunately, designing fast algorithms for the…

Machine Learning · Computer Science 2023-01-26 Xiao Li , Zhihui Zhu , Qiuwei Li , Kai Liu

A procedure for the construction and the classification of multilattices in arbitrary dimension is proposed. The algorithm allows to determine explicitly the location of the points of a multilattice given its space group, and to determine…

Mathematical Physics · Physics 2009-08-18 Giuliana Indelicato

In this work, we study a variant of nonnegative matrix factorization where we wish to find a symmetric factorization of a given input matrix into a sparse, Boolean matrix. Formally speaking, given $\mathbf{M}\in\mathbb{Z}^{m\times m}$, we…

Machine Learning · Computer Science 2022-01-14 Sitan Chen , Zhao Song , Runzhou Tao , Ruizhe Zhang

In this paper, we compute multiparticle form factors of local operators in 2d $\phi^4$ theory using a recently proposed method [1] for efficiently implementing the LSZ prescription with Hamiltonian Truncation methods, and we adopt Lightcone…

High Energy Physics - Theory · Physics 2023-08-23 A. Liam Fitzpatrick , Zhengxian Mei

In this paper we consider the stability of the QR factorization in an oblique inner product. The oblique inner product is defined by a symmetric positive definite matrix A. We analyze two algorithm that are based a factorization of A and…

Numerical Analysis · Mathematics 2014-01-22 Bradley R. Lowery , Julien Langou

In recent years it has been shown that for many linear algebra operations it is possible to create families of algorithms following a very systematic procedure. We do not refer to the fine tuning of a known algorithm, but to a methodology…

Mathematical Software · Computer Science 2014-10-03 Diego Fabregat-Traver , Paolo Bientinesi

Matrix factorization methods are important tools in data mining and analysis. They can be used for many tasks, ranging from dimensionality reduction to visualization. In this paper we concentrate on the use of matrix factorizations for…

Machine Learning · Computer Science 2017-07-28 Sanjar Karaev , Pauli Miettinen

We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…

Symbolic Computation · Computer Science 2019-01-31 Jean-Guillaume Dumas , Joris Van Der Hoeven , Clément Pernet , Daniel Roche

The application of binary matrices are numerous. Representing a matrix as a mixture of a small collection of latent vectors via low-rank decomposition is often seen as an advantageous method to interpret and analyze data. In this work, we…

Numerical Analysis · Mathematics 2021-11-03 Derek DeSantis , Erik Skau , Duc P. Truong , Boian Alexandrov