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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 ...
Mahsa Shirmohammadi, Stefan Kiefer
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Nonnegative matrix factorization: When data is not nonnegative

2014 7th International Conference on Biomedical Engineering and Informatics, 2014
In this paper, we present a new variations of the popular nonnegative matrix factorization (NMF) approach to extend it to the data with negative values. When a NMF problem is formulated as μ ≈μμ, we try to develop a new method that only allows μ to contain nonnegative values, but allows both μ and μ to have both nonnegative and negative values. In this
Siyuan Wu, Jim Wang
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Elastic Nonnegative Matrix Factorization

2018 IEEE International Conference on Data Mining Workshops (ICDMW), 2018
Nonnegative Matrix Factorization factors a large matrix into smaller nonnegative components. Non-negative models are often more amenable to interpretation vis-a-vis standard principal component analysis where negative entries may not correspond to any physical process.
Peter Ballen, Sudipto Guha
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Labelwalking nonnegative matrix factorization

2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2015
Semi-supervised learning (SSL) utilizes plenty of unlabeled examples to boost the performance of learning from limited labeled examples. Due to its great discriminant power, SSL has been widely applied to various real-world tasks such as information retrieval, pattern recognition, and speech separa- tion.
Long Lan, Naiyang Guan, Xiang Zhang 0008, Xuhui Huang, Zhigang Luo   +4 more
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Nonnegative Discriminant Matrix Factorization

IEEE Transactions on Circuits and Systems for Video Technology, 2017
Nonnegative matrix factorization (NMF), which aims at obtaining the nonnegative low-dimensional representation of data, has received wide attention. To obtain more effective nonnegative discriminant bases from the original NMF, in this paper, a novel method called nonnegative discriminant matrix factorization (NDMF) is proposed for image classification.
Yuwu Lu, Zhihui Lai 0001, Yong Xu 0001, Xuelong Li 0001, David Zhang 0001, Chun Yuan 0003   +5 more
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Nonnegative Matrix Factorization With Regularizations

IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 2014
Matrix factorization techniques have been frequently applied in many fields. Among them, nonnegative matrix factorization (NMF) has received considerable attention for it aims to find a parts-based, linear representations of nonnegative data. Recently, many researchers propose various manifold learning algorithms to enhance learning performance by ...
Weiya Ren, Guohui Li, Dan Tu, Li Jia
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Unilateral Orthogonal Nonnegative Matrix Factorization

SIAM Journal on Control and Optimization, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jun Shang, Tongwen Chen
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Weighted nonnegative matrix factorization

2009 IEEE International Conference on Acoustics, Speech and Signal Processing, 2009
Nonnegative matrix factorization (NMF) is a widely-used method for low-rank approximation (LRA) of a nonnegative matrix (matrix with only nonnegative entries), where nonnegativity constraints are imposed on factor matrices in the decomposition. A large body of past work on NMF has focused on the case where the data matrix is complete.
Yong-Deok Kim, Seungjin Choi
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Nonnegative matrix factorization with matrix exponentiation

2010 IEEE International Conference on Acoustics, Speech and Signal Processing, 2010
Nonnegative matrix factorization (NMF) has been successfully applied to different domains as a technique able to find part-based linear representations for nonnegative data. However, when extra constraints are incorporated into NMF, simple gradient descent optimization can be inefficient for high-dimensional problems, due to the overhead to enforce the
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Elastic nonnegative matrix factorization

Pattern Recognition, 2019
Abstract Nonnegative matrix factorization (NMF) plays a vital role in data mining and machine learning fields. Standard NMF utilizes the Frobenius norm while robust NMF uses the robust l2,1-norm to measure the quality of factorization, given the assumption of i.i.d Gaussian noise model and i.i.d Laplacian noise model, respectively.
He Xiong, Deguang Kong
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