Results 21 to 30 of about 137,800 (236)
Nonnegative matrix factorization of a correlation matrix
Linear Algebra and its Applications, 2009 AbstractWe present a dedicated algorithm for the nonnegative factorization of a correlation matrix from an application in financial engineering. We look for a low-rank approximation. The origin of the problem is discussed in some detail. Next to the description of the algorithm, we prove, by means of a counter example, that an exact nonnegative ...
P. Sonneveld +3 more
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On Rationality of Nonnegative Matrix Factorization [PDF]
Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, 2017 Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative n × m matrix M into a product of a nonnegative n × d matrix W and a nonnegative d × m matrix H. NMF has a wide variety of applications, including bioinformatics, chemometrics, communication complexity, machine learning, polyhedral combinatorics, among many others ...
Chistikov, Dmitry +4 more
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Adversarially-Trained Nonnegative Matrix Factorization [PDF]
IEEE Signal Processing Letters, 2021 We consider an adversarially-trained version of the nonnegative matrix factorization, a popular latent dimensionality reduction technique. In our formulation, an attacker adds an arbitrary matrix of bounded norm to the given data matrix. We design efficient algorithms inspired by adversarial training to optimize for dictionary and coefficient matrices ...
Ting Cai +2 more
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Nonnegativity Problems for Matrix Semigroups
, 2023 The matrix semigroup membership problem asks, given square matrices $M,M_1,\ldots,M_k$ of the same dimension, whether $M$ lies in the semigroup generated by $M_1,\ldots,M_k$. It is classical that this problem is undecidable in general but decidable in case $M_1,\ldots,M_k$ commute. In this paper we consider the problem of whether, given $M_1,\ldots,M_k$
D'Costa, Julian +2 more
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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 ...
Xiao Fu +2 more
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Nonnegative Matrix Factorization [PDF]
, 2013 Matrix factorization or factor analysis is an important task that is helpful in the analysis of high-dimensional real-world data. SVD is a classical method for matrix factorization, which gives the optimal low-rank approximation to a real-valued matrix in terms of the squared error.
Mallappa Kumara Swamy, Ke-Lin Du
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Cauchy nonnegative matrix factorization [PDF]
2015 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA), 2015 Nonnegative matrix factorization (NMF) is an effective and popular low-rank model for nonnegative data. It enjoys a rich background, both from an optimization and probabilistic signal processing viewpoint. In this study, we propose a new cost-function for NMF fitting, which is introduced as arising naturally when adopting a Cauchy process model for ...
Liutkus, Antoine +2 more
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Robust Graph Regularized Nonnegative Matrix Factorization
IEEE Access, 2022 Nonnegative Matrix Factorization (NMF) has become a popular technique for dimensionality reduction, and been widely used in machine learning, computer vision, and data mining. Existing unsupervised NMF methods impose the intrinsic geometric constraint on
Qi Huang +3 more
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Quantized nonnegative matrix factorization [PDF]
2014 19th International Conference on Digital Signal Processing, 2014 Even though Nonnegative Matrix Factorization (NMF) in its original form performs rank reduction and signal compaction implicitly, it does not explicitly consider storage or transmission constraints. We propose a Frobenius-norm Quantized Nonnegative Matrix Factorization algorithm that is 1) almost as precise as traditional NMF for decomposition ranks of
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On the Geometric Interpretation of the Nonnegative Rank [PDF]
, 2010 The nonnegative rank of a nonnegative matrix is the minimum number of nonnegative rank-one factors needed to reconstruct it exactly. The problem of determining this rank and computing the corresponding nonnegative factors is difficult; however it has ...
Aggarwal +31 more
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