Algorithms and applications for approximate nonnegative matrix factorization

By Michael W. Berry, Murray Browne, Amy Nicole Langville, V. P. Pauca, Robert J. Plemmons. 2007

1,648 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Computer Vision and Pattern Recognition

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Citations in the corpus

Explaining Explanations: An Overview of Interpretability of Machine Learning (2018, methodology): “The problem of separating latent factors is an old problem that has previously been attacked using a variety of techniques such as Principal Component Analysis [61], Independent Component Analysis [62], and Nonnegative Matrix Factorization [63].”
Scalable Temporal Latent Space Inference for Link Prediction in Dynamic Social Networks (2014, methodology): “One of the most widely used methods for inferring lowrank latent space in networks is via matrix factorization with the “block-coordinate gradient descent (BCGD)” algorithm [20], [21], which has been successfully applied in community detection for static networks [22].”
Unifying Heterogeneous Classifiers With Distillation (2019, methodology): “This formulation can be regarded as a non-negative matrix factorisation problem [24], which we solve using Alternating Least Squares (ALS) [2] where we normalise u to sum to 1 in each iteration3.”
Asynchronous Distributed ADMM for Consensus Optimization (2014, methodology): “In this section, we demonstrate the effectiveness of the proposed async-ADMM on one such nonconvex problem, namely, low-rank matrix factorization (Berry et al., 2007).”
On the Convergence of Multiplicative Update Algorithms for Nonnegative Matrix Factorization (2007, background): “Theorem 1 [5, Th. 1]: If has neither zero column nor row, and and , , then and We hope that any limit point of is stationary as a local minimum must be a stationary point.”
An alternating direction algorithm for matrix completion with nonnegative factors (2011, background): “stering, as well as spectral data analysis. It started to appear in [24, 22, 23] and has become popular since the publication of [18] in 1999. More information on NMF can be found in the survey paper [1], as well as books [8, 9]. Unlike NMF, NMFC assumes that the underlying matrix is incompletely sa”
Nonnegative Matrix Factorization: A Comprehensive Review (2013, methodology): “[10] recommended ALS NMF algorithm by computing the solutions to the subproblems as unconstrained LS problems with multiple right-hand sides and maintaining nonnegativity via setting negative values to zero per iteration.”
Nonnegative Matrix Factorization with the Itakura-Saito Divergence: With Application to Music Analysis (2009, methodology): “This is stressed by Berry et al. (2007) for EUC-NMF but holds for IS-NMF/MU as well.”
Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis (2007, methodology): “For feature extraction, principal component analysis (PCA), linear discriminant analysis (LDA) and non-negative matrix factorization (NMF) have been widely used.”
An Efficient Non-Negative Matrix-Factorization-Based Approach to Collaborative Filtering for Recommender Systems (2014, background): “It is initially designed for learning part-based object representations in computer vision [25], [26], [31], [32]; and then applied to CF problems [27]–[30].”
Explaining Explanations: An Approach to Evaluating Interpretability of Machine Learning (2018, methodology): “The problem of separating latent factors is an old problem that has previously been attacked using a variety of techniques such as Principal Component Analysis [61], Independent Component Analysis [62], and Nonnegative Matrix Factorization [63].”
The Why and How of Nonnegative Matrix Factorization (2014, background): “For other comparisons of NMF algorithms and more numerical experiments, we refer the reader to the book [28], the theses [63, 47], the survey [6], and the references therein.”
A flexible R package for nonnegative matrix factorization (2010, methodology): “See [14] for a review of some existing methods.”
Deciphering Signatures of Mutational Processes Operative in Human Cancer (2013, positive): “Algorithms implementing this and other constraints have been previously developed (Berry et al., 2007; Gao and Church, 2005; Peharz and Pernkopf, 2012; Zheng et al., 2006) and could be applied to cancer genomics data.”