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Nonnegative Matrix Factorization Requires Irrationality [PDF]
SIAM Journal on Applied Algebra and Geometry, 2017 Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative $n \times m$ matrix $M$ into a product of a nonnegative $n \times d$ matrix $W$ and a nonnegative $d \times m$ matrix $H$. A longstanding open question, posed by Cohen and Rothblum in 1993, is whether a rational matrix $M$ always has an NMF of minimal inner ...
Dmitry Chistikov +2 more
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Sparse Deep Nonnegative Matrix Factorization [PDF]
Big Data Mining and Analytics, 2020 Nonnegative Matrix Factorization (NMF) is a powerful technique to perform dimension reduction and pattern recognition through single-layer data representation learning. However, deep learning networks, with their carefully designed hierarchical structure,
Zhenxing Guo, Shihua Zhang
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On the Complexity of Nonnegative Matrix Factorization [PDF]
SIAM Journal on Optimization, 2010 Version 2 corrects small typos; adds ref to Cohen & Rothblum; adds ref to Gillis; clarifies reduction of NMF to int ...
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Coseparable Nonnegative Matrix Factorization
SIAM Journal on Matrix Analysis and Applications, 2023 Nonnegative matrix factorization (NMF) is a popular model in the field of pattern recognition. It aims to find a low rank approximation for nonnegative data M by a product of two nonnegative matrices W and H. In general, NMF is NP-hard to solve while it can be solved efficiently under separability assumption, which requires the columns of factor matrix
Michael Ng, Junjun Pan
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On Identifiability of Nonnegative Matrix Factorization [PDF]
IEEE Signal Processing Letters, 2018 In this letter, we propose a new identification criterion that guarantees the recovery of the low-rank latent factors in the nonnegative matrix factorization (NMF) model, under mild conditions. Specifically, using the proposed criterion, it suffices to identify the latent factors if the rows of one factor are \emph{sufficiently scattered} over the ...
Nicholas Sidiropoulos +2 more
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Predicting epileptic seizures using nonnegative matrix factorization. [PDF]
PLoS ONE, 2020 This paper presents a procedure for the patient-specific prediction of epileptic seizures. To this end, a combination of nonnegative matrix factorization (NMF) and smooth basis functions with robust regression is applied to power spectra of intracranial ...
Olivera Stojanović +2 more
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Robust Structured Convex Nonnegative Matrix Factorization for Data Representation
IEEE Access, 2021 Nonnegative Matrix Factorization (NMF) is a popular technique for machine learning. Its power is that it can decompose a nonnegative matrix into two nonnegative factors whose product well approximates the nonnegative matrix.
Qing Yang +3 more
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On a Guided Nonnegative Matrix Factorization [PDF]
ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2021 Fully unsupervised topic models have found fantastic success in document clustering and classification. However, these models often suffer from the tendency to learn less-than-meaningful or even redundant topics when the data is biased towards a set of features.
Joshua Vendrow +3 more
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Matrix Factorization Techniques in Machine Learning, Signal Processing, and Statistics
Mathematics, 2023 Compressed sensing is an alternative to Shannon/Nyquist sampling for acquiring sparse or compressible signals. Sparse coding represents a signal as a sparse linear combination of atoms, which are elementary signals derived from a predefined dictionary ...
Ke-Lin Du +3 more
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Randomized nonnegative matrix factorization [PDF]
Pattern Recognition Letters, 2018 This is an extended and revised version of the paper which appeared in ...
N. Benjamin Erichson +3 more
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