Algorithms for Non-negative Matrix Factorization

By Daniel D. Lee, Hans-Jürgen Sebastian, S. y. 2000

9,381 citations recorded by the source corpus.

Subfields: Representation & Self-Supervised Learning, Optimization & Training

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Representation & Self-Supervised Learning

In Optimization & Training

Citations in the corpus

Efficient Content-Based Sparse Attention with Routing Transformers (2020, methodology): “This strategy draws inspiration from the application of k-means clustering to Non-negative Matrix Factorization (NMF) (Lee and Seung, 2001; Ding et al., 2005; Kim and Park, 2008), which is relevant to the sparsification of non-negative matrices like”
GAN Inversion: A Survey (2021, methodology): “DFF is the application of non-negative matrix factorization (NMF) [189], [190] to the ReLU feature activations of a pretrained neural network.”
Beyond CCA: Moment Matching for Multi-View Models (2016, positive): “…with the S-and T-cumulants) and DCCAg (implementation with the generalized S-covariance matrices and the processing points initialized as described in Appendix E.4) to DICA and the non-negative matrix factorization (NMF) algorithm with multiplicative updates for divergence (Lee & Seung, 2000).”
Measuring Bias in Contextualized Word Representations (2019, methodology): “We first extracted 20 major topics from the dataset using non-negative matrix factorization (Lee and Seung, 2001) (refer to Appendix for the list of topics).”
A Theory of Multiple-Source Adaptation with Limited Target Labeled Data (2020, methodology): “It is also equivalent to that of a non-negative factorization of the underlying distributions, often adopted in topic modelling or LDA (Hofmann, 2017; Lee and Seung, 2001).”
Explainable Recommendation: A Survey and New Perspectives (2018, background): “[2002]) and ROUGE (recall-oriented understudy for gisting evaluation) score (Lin [2004]).”
How algorithmic confounding in recommendation systems increases homogeneity and decreases utility (2017, background): “Non-negative matrix factorization [37] requires that these representations be non-negative.”
Natural-Parameter Networks: A Class of Probabilistic Neural Networks (2016, methodology): “Nonlinear Transformation : With the proxy natural parameters for the gamma distributions over o ( l ) , the mean a ( l ) m and variance a ( l ) s for the nonlinearly transformed distribution over a ( l ) would be obtained with Equation (4).”
Don’t count, predict! A systematic comparison of context-counting vs. context-predicting semantic vectors (2014, methodology): “The latter were obtained by applying the Singular Value Decomposition (Golub and Van Loan, 1996) or Non-negative Matrix Factorization (Lee and Seung, 2000), Lin (2007) algorithm, with reduced sizes ranging from 200 to 500 in steps of 100.”
Incremental Majorization-Minimization Optimization with Application to Large-Scale Machine Learning (2014, methodology): “Majorizing surrogates have also been used successfully in the signal processing literature about sparse estimation [11, 16, 26], linear inverse problems in image processing [1, 23], and matrix factorization [37, 40].”
Discriminative Improvements to Distributional Sentence Similarity (2013, background): “However, recent work has demonstrated the robustness of nonnegative matrix factorization (NMF; Lee and Seung, 2001) for text mining tasks (Xu et al., 2003; Arora et al., 2012); the difference from SVD is the addition of a non-negativity constraint in the latent representation based on…”
Neural Source-Filter Waveform Models for Statistical Parametric Speech Synthesis (2019, background): “Other common distances such as the Kullback-Leibler divergence (KLD) between spectra [33], [34] are also applicable.”
Multitalker Speech Separation With Utterance-Level Permutation Invariant Training of Deep Recurrent Neural Networks (2017, methodology): “Another popular technique for multi-talker speech separation is Non-negative Matrix Factorization (NMF) [11]–[14].”
Deep Unfolding: Model-Based Inspiration of Novel Deep Architectures (2014, methodology): “Despite the simplicity of its assumptions, this model, based on non-negative matrix factorization (NMF) [4, 5, 6], has no closed-form solution and relies on iterative inference methods, typically formulated as multiplicative updates.”
Online Learning for Matrix Factorization and Sparse Coding (2009, positive): “When applied to images, such as faces, Lee and Seung (2001) have shown that the learned features are more localized than the ones learned with a classical singular value decomposition.”
Neural Source-filter-based Waveform Model for Statistical Parametric Speech Synthesis (2018, background): “Kullback-Leibler For example, L s can be the square error or Kullback-Leibler divergence (KLD) of the spectral amplitudes [14, 15].”
A Hybrid Collaborative Filtering Model with Deep Structure for Recommender Systems (2017, background): “By specifying different L(·, ·), many matrix factorization models have been proposed, for example, non-negative matrix factorization (Lee and Seung 2001), probabilistic matrix factorization (Salakhutdinov and Mnih 2011), Bayesian probabilistic matrix factorization (Salakhutdinov and Mnih 2008), max-”