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Most state-of-the-art top-N collaborative recommender systems work by learning embeddings to jointly represent users and items. Learned embeddings are considered to be effective to solve a variety of tasks. Among others, providing and…

Information Retrieval · Computer Science 2021-04-14 Giovanni Gabbolini , Edoardo D'Amico , Cesare Bernardis , Paolo Cremonesi

Tensor factorization models are widely used in many applied fields such as chemometrics, psychometrics, computer vision or communication networks. Real life data collection is often subject to errors, resulting in missing data. Here we…

Signal Processing · Electrical Eng. & Systems 2022-03-23 Amaury Durand , François Roueff , Jean-Marc Jicquel , Nicolas Paul

Nonnegative matrix factorization (NMF) is a powerful technique for dimension reduction, extracting latent factors and learning part-based representation. For large datasets, NMF performance depends on some major issues: fast algorithms,…

Optimization and Control · Mathematics 2015-07-01 Duy-Khuong Nguyen , Tu-Bao Ho

Learning approaches rely on hyperparameters that impact the algorithm's performance and affect the knowledge extraction process from data. Recently, Nonnegative Matrix Factorization (NMF) has attracted a growing interest as a learning…

Numerical Analysis · Mathematics 2023-06-29 Nicoletta Del Buono , Flavia Esposito , Laura Selicato , Rafal Zdunek

Nonnegative matrix factorization (NMF) has been widely studied in recent years due to its effectiveness in representing nonnegative data with parts-based representations. For NMF, a sparser solution implies better parts-based…

Machine Learning · Computer Science 2022-04-25 Chong Peng , Yiqun Zhang , Yongyong Chen , Zhao Kang , Chenglizhao Chen , Qiang Cheng

Linear dimensionality reduction techniques are powerful tools for image analysis as they allow the identification of important features in a data set. In particular, nonnegative matrix factorization (NMF) has become very popular as it is…

Computer Vision and Pattern Recognition · Computer Science 2016-10-07 Gabriella Casalino , Nicolas Gillis

As Machine Learning (ML) applications rapidly grow, concerns about adversarial attacks compromising their reliability have gained significant attention. One unsupervised ML method known for its resilience to such attacks is Non-negative…

Machine Learning · Computer Science 2024-08-08 Minh Vu , Ben Nebgen , Erik Skau , Geigh Zollicoffer , Juan Castorena , Kim Rasmussen , Boian Alexandrov , Manish Bhattarai

Non-negative matrix factorization (NMF) is widely used as a feature extraction technique for matrices with non-negative entries, such as image data, purchase histories, and other types of count data. In NMF, a non-negative matrix is…

Computation · Statistics 2026-01-01 Ryo Ohashi , Hiroyasu Abe , Fumitake Sakaori

Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors $W$ and $H$, for the given input matrix $A$, such that $A \approx W H$. NMF is a useful tool for many applications in different domains…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-10-01 Ramakrishnan Kannan , Grey Ballard , Haesun Park

Nonnegative matrix factorization (NMF) under the separability assumption can provably be solved efficiently, even in the presence of noise, and has been shown to be a powerful technique in document classification and hyperspectral unmixing.…

Machine Learning · Statistics 2015-04-02 Nicolas Gillis , Stephen A. Vavasis

This paper introduces an algorithm for the nonnegative matrix factorization-and-completion problem, which aims to find nonnegative low-rank matrices X and Y so that the product XY approximates a nonnegative data matrix M whose elements are…

Information Theory · Computer Science 2015-11-23 Yangyang Xu , Wotao Yin , Zaiwen Wen , Yin Zhang

We show that, for a certain class of scaling matrices including the commonly used inverse square-root of the conditional Fisher Information, score-driven factor models are identifiable up to a multiplicative scalar constant under very mild…

Econometrics · Economics 2024-12-03 Giuseppe Buccheri , Fulvio Corsi , Emilija Dzuverovic

Sparse matrix factorization is the problem of approximating a matrix $\mathbf{Z}$ by a product of $J$ sparse factors $\mathbf{X}^{(J)} \mathbf{X}^{(J-1)} \ldots \mathbf{X}^{(1)}$. This paper focuses on identifiability issues that appear in…

Machine Learning · Computer Science 2021-11-18 Léon Zheng , Elisa Riccietti , Rémi Gribonval

Non-negative matrix factorization (NMF) is a powerful tool for dimensionality reduction and clustering. Unfortunately, the interpretation of the clustering results from NMF is difficult, especially for the high-dimensional biological data…

Machine Learning · Computer Science 2021-04-28 Wenwen Min , Taosheng Xu , Xiang Wan , Tsung-Hui Chang

We study a nonlinear factor model in which observed responses depend on low-rank latent factors through an unknown monotone link function. This setting is challenging and largely underexplored due to severe nonconvexity and identifiability…

Machine Learning · Statistics 2026-05-27 Yutong Chao , Resat Gökhan , Jalal Etesami , Ali Habibnia

This article introduces quaternion non-negative matrix factorization (QNMF), which generalizes the usual non-negative matrix factorization (NMF) to the case of polarized signals. Polarization information is represented by Stokes parameters,…

Signal Processing · Electrical Eng. & Systems 2020-06-24 Julien Flamant , Sebastian Miron , David Brie

Matrix factorization techniques, especially Nonnegative Matrix Factorization (NMF), have been widely used for dimensionality reduction and interpretable data representation. However, existing NMF-based methods are inherently single-scale…

Machine Learning · Computer Science 2026-02-27 Jichao Zhang , Ran Miao , Limin Li

Tensor decompositions have become a central tool in data science, with applications in areas such as data analysis, signal processing, and machine learning. A key property of many tensor decompositions, such as the canonical polyadic…

Numerical Analysis · Mathematics 2025-05-20 Subhayan Saha , Giovanni Barbarino , Nicolas Gillis

We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices. A salient feature of the proposed factorization scheme is it decouples the…

Machine Learning · Statistics 2018-06-18 Pratik Jawanpuria , Bamdev Mishra

Nonnegative matrix factorization (NMF) is a widely used linear dimensionality reduction technique for nonnegative data. NMF requires that each data point is approximated by a convex combination of basis elements. Archetypal analysis (AA),…

Signal Processing · Electrical Eng. & Systems 2020-03-31 Pierre De Handschutter , Nicolas Gillis , Arnaud Vandaele , Xavier Siebert