Updating/downdating the NonNegative Matrix Factorization

Juan, Pablo San; Vidal, Antonio M.; Garcia-Mollá, Víctor M.

doi:10.1016/j.cam.2016.11.048

Cited by 3 publications

(1 citation statement)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There are also other factorizations whose update has been proposed and studied. However, the study of the update of the NMF was proposed first in [82] and extended in [83]. This work will be presented in the current Chapter.…”

Section: Introductionmentioning

confidence: 99%

HPC algorithms for nonnegative decompositions

Sebastián¹

View full text Add to dashboard Cite

Many real world-problems can be modelled as mathematical problems with nonnegative magnitudes, and, therefore, the solutions of these problems are meaningful only if their values are nonnegative. Examples of these nonnegative magnitudes are the concentration of components in a chemical compound, frequencies in an audio signal, pixel intensities on an image, etc. Some of these problems can be modelled to an overdetermined system of linear equations, that is, a system of equations with more equations than unknowns. When the solution of this system of equations should be constrained to nonnegative values, a new problem arises. This problem is called the Nonnegative Least Squares (NNLS) problem, and its solution has multiple applications in science and engineering, especially for solving optimization problems with nonnegative restrictions. Another important nonnegativity constrained decomposition is the Nonnegative Matrix Factorization (NMF). The NMF is a very popular tool in many fields such as document clustering, data mining, machine learning, image analysis, chemical analysis, and audio source separation. This factorization tries to approximate a nonnegative data matrix with the product of two smaller nonnegative matrices. Furthermore, this matrix decomposition usually creates parts based representations of the data in the original matrix. The algorithms that are designed to compute the solution of these two nonnegative problems have a high computational cost. Due to this high cost, these decompositions can benefit from the extra performance obtained using High Performance Computing (HPC) techniques. Nowadays, there are very powerful computational systems that offer high performance and can be used to solve extremely complex problems in science and engineering.

show abstract

Section: Introductionmentioning

confidence: 99%

HPC algorithms for nonnegative decompositions

Sebastián¹

View full text Add to dashboard Cite

show abstract

Parallel source separation system for heart and lung sounds

et al. 2021

View full text Add to dashboard Cite

An efficient parallel kernel based on Cholesky decomposition to accelerate Multichannel Non-Negative Matrix Factorization

Muñoz-Montoro

Carabias-Orti

Salvati

et al. 2022

Preprint

View full text Add to dashboard Cite

Multichannel Source Separation has been a popular topic, and recently proposed methods based on the local Gaussian model (LGM) have provided promising result despite its high computational cost when several sensors are used. The main reason being due to inversion of a spatial covariance matrix, with a complexity of \(O(I^3)\), being \(I\) the number of sensors. This drawback limits the practical application of this approach for tasks such as sound field reconstruction or virtual reality, among others. In this paper, we present a numerical approach to reduce the complexity of the Multichannel NMF to address the task of audio source separation for scenarios with a high number of sensors such as High Order Ambisonics (HOA) encoding. In particular, we propose a parallel multi-architecture driver to compute the multiplicative update rules in MNMF approaches. The proposed driver has been designed to work on both sequential and multi-core computers, as well as Graphics Processing Units (GPUs) and Intel Xeon coprocessors. The proposed software was written in C language and can be called from numerical computing environments. The proposed solution tries to reduce the computational cost of the multiplicative update rules by using the Cholesky decomposition and by solving several triangular equation systems.The proposal has been evaluated for different scenarios with promising results in terms of execution times for both CPU and GPU. To the best of our knowledge, our proposal is the first system that addresses the problem of reducing the computational cost of full-rank MNMF-based systems using parallel and high performance techniques.

show abstract

Updating/downdating the NonNegative Matrix Factorization

Cited by 3 publications

References 13 publications

HPC algorithms for nonnegative decompositions

HPC algorithms for nonnegative decompositions

Parallel source separation system for heart and lung sounds

An efficient parallel kernel based on Cholesky decomposition to accelerate Multichannel Non-Negative Matrix Factorization

Contact Info

Product

Resources

About