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Nonnegative matrix factorization (NMF) is a prominent technique for data dimensionality reduction that has been widely used for text mining, computer vision, pattern discovery, and bioinformatics. In this paper, a framework called ARkNLS…

Numerical Analysis · Mathematics 2020-07-14 Delin Chu , Wenya Shi , Srinivas Eswar , Haesun Park

In this work, we consider nonnegative matrix factorization (NMF) with a regularization that promotes small volume of the convex hull spanned by the basis matrix. We present highly efficient algorithms for three different volume…

Numerical Analysis · Computer Science 2020-01-14 M. S. Ang , Nicolas Gillis

Non-negative matrix factorization (NMF) is a dimensionality reduction technique which tends to produce a sparse representation of data. Commonly, the error between the actual and recreated matrices is used as an objective function, but this…

Machine Learning · Computer Science 2019-02-06 Steven Squires , Adam Prugel Bennett , Mahesan Niranjan

Non-negative matrix factorisation (NMF) has been extensively applied to the problem of corrupted image data. Standard NMF approach minimises Euclidean distance between data matrix and factorised approximation. The traditional NMF technique…

Computer Vision and Pattern Recognition · Computer Science 2023-05-02 Pengwei Yang , Chongyangzi Teng , Jack George Mangos

In this report, we discuss a simple model for RGB color and polarization images under a unified framework of quaternion nonnegative matrix factorization (QNMF) and present a hierarchical nonnegative least squares method to solve the factor…

Numerical Analysis · Mathematics 2024-07-23 Junjun Pan

Nowadays, nonnegative matrix factorization (NMF) based methods have been widely applied to blind spectral unmixing. Introducing proper regularizers to NMF is crucial for mathematically constraining the solutions and physically exploiting…

Computer Vision and Pattern Recognition · Computer Science 2020-10-12 Min Zhao , Tiande Gao , Jie Chen , Wei Chen

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

It is well known that good initializations can improve the speed and accuracy of the solutions of many nonnegative matrix factorization (NMF) algorithms. Many NMF algorithms are sensitive with respect to the initialization of W or H or…

Numerical Analysis · Computer Science 2014-07-29 Amy N. Langville , Carl D. Meyer , Russell Albright , James Cox , David Duling

Non-negative Matrix Factorization(NMF) algorithm can only be used to find low rank approximation of original non-negative data while Concept Factorization(CF) algorithm extends matrix factorization to single non-linear kernel space,…

Machine Learning · Computer Science 2024-10-29 Fei Li , Liang Du , Chaohong Ren

Symmetric nonnegative matrix factorization (symNMF) is a variant of nonnegative matrix factorization (NMF) that allows to handle symmetric input matrices and has been shown to be particularly well suited for clustering tasks. In this paper,…

Numerical Analysis · Mathematics 2020-03-11 François Moutier , Arnaud Vandaele , Nicolas Gillis

Symmetric nonnegative matrix factorization (SNMF) has demonstrated to be a powerful method for data clustering. However, SNMF is mathematically formulated as a non-convex optimization problem, making it sensitive to the initialization of…

Machine Learning · Computer Science 2021-03-03 Yuheng Jia , Hui Liu , Junhui Hou , Sam Kwong , Qingfu Zhang

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

Referring back to the original text in the course of hierarchical learning is a common human trait that ensures the right direction of learning. The models developed based on the concept of Non-negative Matrix Factorization (NMF), in this…

Machine Learning · Computer Science 2024-05-24 Prasun Dutta , Rajat K. De

Learning multi-view data is an emerging problem in machine learning research, and nonnegative matrix factorization (NMF) is a popular dimensionality-reduction method for integrating information from multiple views. These views often provide…

Machine Learning · Statistics 2023-04-26 Shuo Shuo Liu , Lin Lin

Deep Nonnegative Matrix Factorization (deep NMF) has recently emerged as a valuable technique for extracting multiple layers of features across different scales. However, all existing deep NMF models and algorithms have primarily centered…

Machine Learning · Computer Science 2025-01-10 Valentin Leplat , Le Thi Khanh Hien , Akwum Onwunta , Nicolas Gillis

Nonnegative Matrix Factorization (NMF) is the problem of approximating a given nonnegative matrix M through the product of two nonnegative low-rank matrices W and H. Traditionally NMF is tackled by optimizing a specific objective function…

Optimization and Control · Mathematics 2025-09-23 Flavia Esposito , Andersen Ang

Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization…

Machine Learning · Computer Science 2019-10-23 Yuejie Chi , Yue M. Lu , Yuxin Chen

In this paper, we consider the symmetric multi-type non-negative matrix tri-factorization problem (SNMTF), which attempts to factorize several symmetric non-negative matrices simultaneously. This can be considered as a generalization of the…

Data Structures and Algorithms · Computer Science 2020-12-14 Rok Hribar , Timotej Hrga , Gregor Papa , Gašper Petelin , Janez Povh , Nataša Pržulj , Vida Vukašinović

Nonnegative Matrix Factorization (NMF) is a versatile and powerful tool for discovering latent structures in data matrices, with many variations proposed in the literature. Recently, Leplat et al.\@ (2019) introduced a minimum-volume NMF…

Machine Learning · Statistics 2023-09-26 Duc Toan Nguyen , Eric C. Chi

Numerous algorithms are used for nonnegative matrix factorization under the assumption that the matrix is nearly separable. In this paper, we show how to make these algorithms efficient for data matrices that have many more rows than…

Machine Learning · Computer Science 2018-01-08 Austin R. Benson , Jason D. Lee , Bartek Rajwa , David F. Gleich