Non-Negative Matrix Factorization

Also known as NMF

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Overview

Non-negative matrix factorization represents data as a product of nonnegative factors, making components additive and often easier to interpret as topics, sources, communities, or biological signals. Researchers develop multiplicative updates, alternating least-squares and gradient methods, and structured variants that incorporate sparsity, graphs, temporal variation, or suitable count-data noise models. Applications include topic modeling, spectral unmixing, audio separation, clustering, and analysis of biological and network data. A central challenge is that factors may not be uniquely identifiable, especially with noisy or highly mixed observations, so work balances stronger recovery guarantees and useful structure against computational cost and assumptions that may not fit the data.

Latest papers

CardsList

34 papers5 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

  1. Controlled Block Proximal Linearized Method for Nonconvex and Nonsmooth Optimization

    Oct 25, 2026Weifeng YangProximal OptimizationTensor Decomposition

  2. Joint Estimation of Common-Slope Decay Rates and Spatial Amplitudes Using Parameterized Nonnegative Matrix Factorization

    Oct 4, 2026Jeremy B. Bai, Filip Elvander, Sebastian J. SchlechtNon-Negative Matrix FactorizationExpectation-Maximization

    Multimedia Comms. & Signal Proc., Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany · Dept. of Information and Communications Engineering, Aalto University, Finland

  3. Degree-Corrected Joint Matrix Factorization for Multilayer Community Detection

    Oct 1, 2026Alexandra Dache, Manon Rustin, Arnaud Vandaele +1Non-Negative Matrix FactorizationGraph Clustering

    Department of Mathematics and Operational Research, University of Mons, Mons, Belgium

  4. GEM-KMeans: Memory-Efficient and Accurate Clustering on Massive Scale with GPU Optimization

    Sep 28, 2026Peng Xu, Nihar Koganti, Volodymyr Kindratenko +1ClusteringNon-Negative Matrix Factorization

    Department of Statistics, University of Illinois Urbana-Champaign · Department of Electrical and Computer Engineering, University of Illinois Urbana-Champaign · National Center for Supercomputing Applications, University of Illinois Urbana-Champaign +3

  5. Singularities of Non-negative Matrix Factorization and their application to Bayesian inference

    Sep 28, 2026Naoki Hayashi, Yota Maeda, Yasushi EsakiNon-Negative Matrix FactorizationLow-Rank Matrix Decomposition

    Toyota Central R&D Labs., Inc.

  6. Identifiability of Nonnegative Tensor Decompositions via Positive Scattering

    Sep 10, 2026Haoming Wang, Ming YuanNon-Negative Matrix FactorizationTensor Decomposition

    Columbia University

  7. Separable Nonnegative Matrix Factorization Using Powered Ratio-of-Norms Regularization

    Aug 28, 2026Matthew McCarver, Jing QinNon-Negative Matrix FactorizationNonconvex Optimization

    Department of Mathematics, University of Kentucky, Lexington, KY 40506, USA

  8. Maximum-distance nonnegative matrix factorization for unmixing highly mixed grain-size distribution data

    Aug 24, 2026Qianqian Qi, Zhongming Chen, Peter G. M. van der HeijdenNon-Negative Matrix Factorization

    Hangzhou Dianzi University, China · Utrecht University, the Netherlands · University of Southampton, UK

  9. Exploiting chemical shift variability enables recovery of overlapping metabolites from 1H nuclear magnetic resonance spectra

    Aug 6, 2026Jesper Løve Hinrich, Pia Susan Mayer, Bekzod Khakimov +2Non-Negative Matrix FactorizationMagnetic Resonance Spectroscopy

    Department of Applied Mathematics and Computer Science, Technical University of Denmark, Richard Petersens Plads 321, Kgs. Lyngby, 2800, Denmark. · Department of Food Science, University of Copenhagen, Rolighedsvej 26, Frederiksberg, 1958, Denmark.

  10. Low-Rank Dependence Decomposition via Accelerated Symmetric Non-negative Matrix Factorization

    Jul 27, 2026Lavinia Ghita, Dhruv Desai, Jake Goldberg +1Non-Negative Matrix FactorizationLow-Rank Matrix Decomposition

    NVIDIA

  11. MemNMF: Memory-Augmented NMF on LPC Spectra for Anomalous Sound Detection

    Jul 24, 2026Phurich Saengthong, Takahiro ShinozakiMemory-Augmented Neural NetworksNon-Negative Matrix Factorization

    Institute of Science Tokyo, Japan

  12. Non--negative matrix factorization using the R package nnmf

    Jul 22, 2026Volkan Sevinç, Nikolas Kontemeniotis, Theodoros Perdikis +1Non-Negative Matrix FactorizationDimensionality Reduction

    Muğla Sıtkı Koçman University, Faculty of Science, Department of Statistics, Kötekli Kampüsü, Muğla, Türkiye · Department of Economics, University of Crete, Gallos Campus, Rethimno, Greece · Department of Tourism Studies, University of Piraeus, Piraeus, Greece +1

  13. An Efficient Newton Algorithm for Nonnegative Matrix Factorization with the Kullback-Leibler Divergence

    Jul 15, 2026Damien Lesens, Jérémy E. Cohen, Bora UçarNon-Negative Matrix FactorizationLow-Rank Matrix Decomposition

    ENS de Lyon · Univ. Lyon, INSA-Lyon, UCBL, UJM, CNRS, Inserm, CREATIS UMR 5220, U1294, F-69621, Lyon, France. · CNRS and LIP (UMR5668, Université de Lyon - ENS de Lyon - UCBL - CNRS - Inria), 46 allée d'Italie, Lyon, France.

  14. A Generalized Deep Non-negative Matrix Factorization Approach for SAR Automatic Target Recognition

    Jul 8, 2026Yunhong Zhang, Changjie Cao, Zhongli Zhou +4Non-Negative Matrix FactorizationRemote Sensing

  15. Non-negative Matrix Factorisation with Topological Regularisation

    Jun 16, 2026Matias de Jong van Lier, Shizuo Kaji, Keunsu KimNon-Negative Matrix Factorization

    Recursive Inc. · Tokyo, 150-0002, Japan · Graduate School of Science +5

  16. On solving symmetric multi-type orthogonal non-negative matrix tri-factorization problem

    Jun 6, 2026Rok Hribar, Gregor Papa, Janez Povh +1Non-Negative Matrix FactorizationGraph Clustering

    Computer Systems Department, Jožef Stefan Institute, Jamova cesta 39, Ljubljana, 1000, Slovenia. · Laboratory for Engineering Design, Faculty of Mechanical Engineering, University of Ljubljana, Aškerčeva cesta 6, Ljubljana, 1000, Slovenia. · Rudolfovo – Science and Technology Centre Novo mesto, Podbreznik 15, Novo mesto, 8000, Slovenia. +1

  17. Non-Negative Matrix Factorization for Event Data

    Jun 4, 2026Raphaël RomeroTemporal Point ProcessesLatent Variable Models

    Ghent University · Ghent, Belgium

  18. Graph Regularized Non-negative Reduced Biquaternion Matrix Factorization for Color Image Recognition

    Jun 2, 2026Hailang Wu, Yonghe Liu, Bingxuan Yu +1Non-Negative Matrix FactorizationMatrix Factorization

    School of Mathematics and Statistics, Yunnan University, Kunming, China.

  19. A Nonmonotone Gradient-Based Algorithm for Symmetric Nonnegative Matrix Factorization and Graph Clustering

    Jun 1, 2026Ryan Swart, Johannes BrustNon-Negative Matrix FactorizationGraph Clustering

    School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ

  20. An Exterior Method for Nonnegative Matrix Factorization

    May 19, 2026Qiujing Lu, Tonmoy Monsoor, Ehsan Ebrahimzadeh +2Non-Negative Matrix FactorizationLow-Rank Matrix Decomposition

    1ECE, UCLA · 2eBay Search Science Team

  21. Sparse Network Inference under Imperfect Detection and its Application to Ecological Networks

    Apr 20, 2026Aoran Zhang, Tianyao Wei, Maria J. Guerrero +1Sparse RecoveryNon-Negative Matrix Factorization

    Department of Electrical and Computer Engineering and the Ken Kennedy Institute, Rice University · Department of Computational and Applied Mathematics, Rice University

  22. Hyperspectral Unmixing Hierarchies

    Apr 18, 2026Joseph L. Garrett, P. S. Vishnu, Pauliina Salmi +4Non-Negative Matrix FactorizationRemote Sensing

    Department of Engineering Cybernetics, Norwegian University of Science and Technology · Department of Biology, Norwegian University of Science and Technology · Department of Automatic Control and Systems Engineering, University Politehnica Bucharest +1

  23. Audio Source Separation in Reverberant Environments using ββ-divergence based Nonnegative Factorization

    Apr 14, 2026Mahmoud Fakhry, Piergiorgio Svaizer, Maurizio OmologoAudio Source SeparationNon-Negative Matrix Factorization

    SHINE research unit - Center for Information and Communication Technology (ICT) - Fondazione Bruno Kessler (FBK), Via Sommarive 18, 38123 Trento, Italy.

  24. Shift- and stretch-invariant non-negative matrix factorization with an application to brain tissue delineation in emission tomography data

    Apr 9, 2026Anders S. Olsen, Miriam L. Navarro, Claus Svarer +3Non-Negative Matrix FactorizationMedical Imaging

    Neurobiology Research Unit, Copenhagen University Hospital Rigshospitalet, Copenhagen, Denmark · Department of Neuroscience, Faculty of Health and Medical Sciences, University of Copenhagen, Copenhagen, Denmark · Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kgs. Lyngby, Denmark +1

  25. Nonnegative Matrix Factorization in the Component-Wise L1 Norm for Sparse Data

    Mar 31, 2026Giovanni Seraghiti, Kévin Dubrulle, Arnaud Vandaele +1Non-Negative Matrix FactorizationMatrix Factorization

    University of Mons, Rue de Houdain 9, 7000 Mons, Belgium, and Dipartimento di Ingegneria Industriale, Università degli Studi di Firenze, Viale Morgagni 40/44, 50134 Firenze, Italia. Member of the INdAM Research Group GNCS. · University of Mons, Rue de Houdain 9, 7000 Mons, Belgium.

  26. Identification of NMF by choosing maximum-volume basis vectors

    Mar 25, 2026Qianqian Qi, Zhongming Chen, Peter G. M. van der HeijdenNon-Negative Matrix FactorizationRepresentation Identifiability

    Hangzhou Dianzi University, China · Utrecht University, the Netherlands and University of Southampton, UK

  27. MM-algorithms for traditional and convex NMF with Tweedie and Negative Binomial cost functions and empirical evaluation

    Mar 10, 2026Elisabeth Sommer James, Asger Hobolth, Marta PelizzolaNon-Negative Matrix Factorization

    Department of Mathematics, Aarhus University, Denmark

  28. Persistent Nonnegative Matrix Factorization via Multi-Scale Graph Regularization

    Feb 26, 2026Jichao Zhang, Ran Miao, Limin LiNon-Negative Matrix FactorizationMatrix Factorization

    School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi Province, 710049, China

  29. Disentangling Shared and Target-Enriched Topics via Background-Contrastive Non-negative Matrix Factorization

    Feb 25, 2026Yixuan Li, Archer Y. Yang, Yue LiNon-Negative Matrix FactorizationDisentangled Representation Learning

    Department of Mathematics and Statistics, McGill University, Montreal, QC, Canada · Mila – Quebec AI Institute, Montreal, QC, Canada · School of Computer Science, McGill University, Montreal, QC, Canada

  30. A New Family of Poisson Non-negative Matrix Factorization Methods Using the Shifted Log Link

    Jan 9, 2026Eric Weine, Peter Carbonetto, Rafael A. Irizarry +1Non-Negative Matrix FactorizationGeneralized Linear Models

    Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA · Department of Human Genetics, University of Chicago, Chicago, IL, USA · Department of Data Science, Dana-Farber Cancer Institute, Boston, MA, USA +1