Nonnegative Matrix and Tensor Factorizations - Applications to Exploratory Multi-way Data Analysis and Blind Source Separation

By Andrzej S. Cichocki, Rafal Zdunek, Anh Huy Phan, Shun-ichi Amari. 2009

2,105 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Theory and Mathematics, Signal Processing

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Citations in the corpus

Nonparametric Divergence Estimation with Applications to Machine Learning on Distributions (2011, background): “, in Villmann and Haase (2010), Cichocki et al. (2009), and Wang et al.”
Sparse Overcomplete Word Vector Representations (2015, methodology): “Nonnegativity in the feature space has often been shown to correspond to interpretability (Lee and Seung, 1999; Cichocki et al., 2009; Murphy et al., 2012; Fyshe et al., 2014; Fyshe et al., 2015).”
The Sound of Pixels (2018, methodology): “Classical approaches include signal processing methods such as Nonnegative Matrix Factorization (NMF) [42,8,40].”
Temporal QoS-aware web service recommendation via non-negative tensor factorization (2014, methodology): “Tensor factorization is an important technique in many applications, such as data mining, dimensionality reduction, chemometrics, signal processing, neuroscience, and web analysis [7, 10, 26, 8].”
Hyperspectral Unmixing via $L_{1/2}$ Sparsity-Constrained Nonnegative Matrix Factorization (2011, methodology): “Note that NMF with sparsity constraints has been used as an effective tool for dimensionality reduction, feature extraction, and source separation [19].”
Global Optimality in Tensor Factorization, Deep Learning, and Beyond (2015, background): “More generally, tensor factorization models provide a natural extension to matrix factorization and have been employed in a wide variety of applications (Cichocki et al., 2009; Kolda and Bader, 2009).”
Information geometry of divergence functions (2010, background): “One of the original contribution of the present paper is to give a unified geometrical framework to various divergence functions, which have a lot of applications [2, 3].”
Low Complexity Damped Gauss-Newton Algorithms for CANDECOMP/PARAFAC (2012, methodology): “In practice, the factors A are often initialized using the mode-n singular vectors of the data tensor [5, 7, 14], then run over ALS (3.”
Limestone: High-throughput candidate phenotype generation via tensor factorization (2014, background): “These are problematic because, in certain domains, negative elements and/or negative combinations are not easily interpretable [42,43].”
Fast Nonnegative Matrix Factorization: An Active-Set-Like Method and Comparisons (2011, background): “As this problem indeed happens quite often, typically a small number ǫ ≈ 1e is used in places that are supposed to be zero [7, 10].”
Theoretical Analysis of Bayesian Matrix Factorization (2011, background): “Tensor factorization is a high-dimensional extension of matrix factorization, which gathers considerable attention recently as a novel data analysis tool (Cichocki et al., 2009).”
A Semi-NMF-PCA Unified Framework for Data Clustering (2017, background): “Some examples can be found in [2], [8], [13], [24].”