Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Partial Fractions01:28

Partial Fractions

A partial fraction is a component of a rational expression represented as the sum of simpler fractions. When a rational function is expressed as a ratio of two polynomials, it can often be decomposed into a sum of fractions whose denominators are simpler polynomials, typically linear or irreducible quadratic factors. This process is called partial fraction decomposition, and it is used to simplify complex expressions for integration, solving equations, or analysis.Partial fraction decomposition...
Linearization and Approximation01:26

Linearization and Approximation

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
Fast Fourier Transform01:10

Fast Fourier Transform

The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...
Quadratic Models01:23

Quadratic Models

Quadratic models are mathematical representations used to describe relationships in which the rate of change changes at a constant rate. These models appear in a wide variety of natural and engineered systems, especially those involving motion, forces, and optimization. One common application is analyzing the vertical motion of objects influenced by gravity, such as a ball thrown into the air.In such scenarios, the object's height changes over time in a curved pattern, rising to a maximum point...
Methods of Medium Optimization01:28

Methods of Medium Optimization

Optimizing growth media enhances microbial proliferation and maximizes product yield. Statistical experimental design methodologies provide structured and reproducible approaches, offering progressively higher levels of robustness and efficiency.The One-Factor-at-a-Time (OFAT) MethodThe One-Factor-at-a-Time (OFAT) method involves adjusting a single variable while keeping all others constant. However, it cannot detect interactions between variables, often leading to suboptimal outcomes when...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Deep Nonnegative Matrix Factorization With Beta Divergences.

Neural computation·2024
Same author

Real-time image-guided treatment of mobile tumors in proton therapy by a library of treatment plans: a simulation study.

Medical physics·2022
Same author

Distributionally Robust and Multi-Objective Nonnegative Matrix Factorization.

IEEE transactions on pattern analysis and machine intelligence·2021
Same author

Generalized Separable Nonnegative Matrix Factorization.

IEEE transactions on pattern analysis and machine intelligence·2019
Same author

Orthogonal joint sparse NMF for microarray data analysis.

Journal of mathematical biology·2019
Same author

Extended Formulations for Order Polytopes through Network Flows.

Journal of mathematical psychology·2019
Same journal

A Model-Free Reinforcement Learning Implementation of Decision Making Under Uncertainty by Sequential Sampling.

Neural computation·2026
Same journal

DROP: Distributional and Regular Optimism and Pessimism for Reinforcement Learning.

Neural computation·2026
Same journal

Hierarchical Active Inference Using Successor Representations.

Neural computation·2026
Same journal

W-Kernel and Its Principal Space for Frequentist Evaluation of Bayesian Estimators.

Neural computation·2026
Same journal

A Hidden Markov Model-Inspired Sequence Classification Method for Hyperdimensional Computing.

Neural computation·2026
Same journal

Sparse Graphical Modeling for Electrophysiological Phase-Based Connectivity Using Circular Statistics.

Neural computation·2026
See all related articles

Related Experiment Video

Updated: May 26, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Accelerated multiplicative updates and hierarchical ALS algorithms for nonnegative matrix factorization.

Nicolas Gillis1, François Glineur

  • 1University of Waterloo, Department of Combinatorics and Optimization, Waterloo, Ontario N2L 3G1, Canada. ngillis@uwaterloo.ca

Neural Computation
|December 16, 2011
PubMed
Summary
This summary is machine-generated.

We present a simple acceleration technique for Nonnegative Matrix Factorization (NMF) algorithms, significantly speeding up computations. This method enhances convergence properties and works across various NMF applications like image and text analysis.

Related Experiment Videos

Last Updated: May 26, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Area of Science:

  • Data Science
  • Machine Learning
  • Computational Mathematics

Background:

  • Nonnegative Matrix Factorization (NMF) is a versatile data analysis technique.
  • NMF finds applications in diverse fields including text mining, image processing, and computational biology.
  • Existing NMF algorithms, such as multiplicative updates and hierarchical alternating least squares, can be computationally intensive.

Purpose of the Study:

  • To propose a novel method for accelerating existing Nonnegative Matrix Factorization (NMF) algorithms.
  • To maintain the convergence properties of NMF algorithms while improving their computational efficiency.
  • To demonstrate the applicability of the acceleration technique to various NMF algorithms and datasets.

Main Methods:

  • Analysis of computational cost per iteration for NMF algorithms.
  • Development of a simple acceleration technique based on computational cost analysis.
  • Empirical validation of the accelerated algorithms on image and text datasets.
  • Comparison with a state-of-the-art alternating nonnegative least squares algorithm.

Main Results:

  • The proposed technique significantly accelerates the convergence of multiplicative updates and hierarchical alternating least squares NMF algorithms.
  • The acceleration method preserves the convergence properties of the original algorithms.
  • The efficiency of the accelerated algorithms was empirically demonstrated on real-world image and text data.
  • The accelerated NMF methods showed favorable performance compared to a state-of-the-art algorithm.

Conclusions:

  • A simple and effective acceleration technique for Nonnegative Matrix Factorization (NMF) has been developed.
  • This method offers significant computational speedups for NMF algorithms without compromising convergence.
  • The technique is broadly applicable, enhancing the efficiency of NMF in various data analysis tasks.