Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values†

By P. Paatero, U. Tapper. 1994

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Citations in the corpus

Group invariance principles for causal generative models (2017, methodology): “In order to assess whether the group invariance framework is useful to better infer the NMF generative process, we simulated the model by generating (20) data matrices using 5 NMF components: W matrices were generated with i.i.d. coefficients uniformly distributed on the unit interval, and sparse ma”
The Why and How of Nonnegative Matrix Factorization (2014, background): “NMF was ﬁrst introduced in 1994 by Paatero and Tapper [97] and gathered more and more interest after an article by Lee and Seung [79] in 1999.”
Unsupervised Discovery of Demixed, Low-Dimensional Neural Dynamics across Multiple Timescales through Tensor Component Analysis (2017, methodology): “Nonnegative TCA has been previously studied in the tensor decomposition literature [64, 96–98], and is a higher622 order generalization of nonnegative matrix factorization (NNMF) [60, 99].”
The Discrete Basis Problem (2006, methodology): “Early formulations of the NMF problem include those of Paatero and Tapper [6], where they call it “positive matrix factorization,” and Cohen and Rothblum [7].”
Music recommendation and discovery in the long tail (2008, methodology): “Singular Value Decomposition (SVD), and Non– negative Matrix Factorisation (NMF) (Paatero and Tapper, 1994; Lee and Seung, 1999) are the two most used methods in recommendation.”
Non-negative tensor factorization with applications to statistics and computer vision (2005, methodology): “Thus for example, the problem of finding a non-negative low rank decomposition of a set of images is a 3-NTF (the images forming the slices of a 3D cube) but can also be represented as an NMF problem by vectorizing the images (images forming columns of a matrix).”
Projected Gradient Methods for Nonnegative Matrix Factorization (2007, background): “Non-negative matrix factorization (NMF) (Paatero and Tapper, 1994; Lee and Seung, 1999) is useful for finding representations of non-negative data.”
Methods for estimating uncertainty in factor analytic solutions (2013, methodology): “The method is described in greater detail elsewhere (Paatero and Tapper, 1994; Paatero, 1997).”
A flexible R package for nonnegative matrix factorization (2010, unknown): “Since its formal definition in [1,2], the NMF approach has been applied successfully in several fields including image and pattern recognition, signal processing and text mining [3].”
Sparse Nonnegative Matrix Factorization for Clustering (2008, methodology): “Nonnegative Matrix Factorization (NMF) was introduced as a dimension reduction method for pattern analysis [14][ 16 ].”