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Using underapproximations for sparse nonnegative matrix factorization

Nicolas Gillis, François Glineur
2010 Pattern Recognition  
Nonnegative Matrix Factorization consists in (approximately) factorizing a nonnegative data matrix by the product of two low-rank nonnegative matrices.  ...  We also prove that the underapproximation problem is NP-hard for any fixed factorization rank, using a reduction of the maximum edge biclique problem in bipartite graphs.  ...  The low-rank approximation problem with nonnegativity constraints is commonly called Nonnegative Matrix Factorization (NMF).  ... 
doi:10.1016/j.patcog.2009.11.013 fatcat:dwtoizx5sffinfgqknpgsyknsy

Nonlinear band expansion and nonnegative matrix underapproximation for unsupervised segmentation of a liver from a multi-phase CT image

Ivica Kopriva, Xinjian Chen, Jianhua Yao, Benoit M. Dawant, David R. Haynor
2011 Medical Imaging 2011: Image Processing  
The methodology exploits concentration and spatial diversities between organs present in the image and consists of nonlinear dimensionality expansion followed by matrix factorization that relies on sparseness  ...  A methodology is proposed for contrast enhanced unsupervised segmentation of a liver from a twodimensional multi-phase CT image.  ...  methods to factorize the NBE three-phase CT image (2): DCA and nonnegative matrix underapproximation (NMU).  ... 
doi:10.1117/12.876965 dblp:conf/miip/KoprivaCY11 fatcat:oy6mqtosy5bwvefuqdeibfuwry

Priors in sparse recursive decompositions of hyperspectral images

Nicolas Gillis, Robert J. Plemmons, Qiang Zhang, Sylvia S. Shen, Paul E. Lewis
2012 Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XVIII  
Nonnegative matrix factorization and its variants are powerful techniques for the analysis of hyperspectral images (HSI).  ...  Nonnegative matrix underapproximation (NMU) is a recent closely related model that uses additional underapproximation constraints enabling the extraction of features (e.g., abundance maps in HSI) in a  ...  Three-dimensional tensor factorization methods can also be used, 1, 2 but we concentrate here on matrix models.  ... 
doi:10.1117/12.918333 fatcat:2loktmjnavdwldlplcmutcyjhm

Sparseness constrained nonnegative matrix factorization for unsupervised 3D segmentation of multichannel images: demonstration on multispectral magnetic resonance image of the brain

Ivica Kopriva, Ante Jukić, Xinjian Chen, Sebastien Ourselin, David R. Haynor
2013 Medical Imaging 2013: Image Processing  
Interpretation of this model suggests that 3D segmentation of organs (tissues) can be implemented through sparseness constrained factorization of the nonnegative matrix obtained by mode-4 unfolding of  ...  Keywords: Multispectral magnetic resonance image, brain tumor delineation, unsupervised segmentation, sparseness, nonnegative matrix factorization. * ikopriva@irb.hr, phone: +385 1 4571 286; fax: +385  ...  INTRODUCTION The purpose of this paper is development of sparseness constrained nonnegative matrix factorization (NMF) method for unsupervised (a.k.a. blind or automatic) 3D (volume) segmentation of registered  ... 
doi:10.1117/12.2000529 dblp:conf/miip/KoprivaJC13 fatcat:3kpycrjg25catfrdw2zy5isjou

Nonnegative Matrix Underapproximation for Robust Multiple Model Fitting [article]

Mariano Tepper, Guillermo Sapiro
2017 arXiv   pre-print
In this work, we introduce a highly efficient algorithm to address the nonnegative matrix underapproximation (NMU) problem, i.e., nonnegative matrix factorization (NMF) with an additional underapproximation  ...  The proposed approach delivers state-of-the-art results for the estimation of multiple fundamental matrices and homographies, outperforming other alternatives in the literature and exemplifying the use  ...  Conclusions In this work, we first presented a highly efficient algorithm to address the nonnegative matrix underapproximation (NMU) problem.  ... 
arXiv:1611.01408v5 fatcat:faun5s2hgfh6fa3mwyb2yparzq

Dimensionality reduction, classification, and spectral mixture analysis using nonnegative underapproximation

Nicolas Gillis, Robert J. Plemmons, Sylvia S. Shen, Paul E. Lewis
2010 Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XVI  
Nonnegative Matrix Factorization (NMF) and its variants have recently been successfully used as dimensionality reduction techniques for identification of the materials present in hyperspectral images.  ...  In this paper, we present a new variant of NMF called Nonnegative Matrix Underapproximation (NMU): it is based on the introduction of underapproximation constraints which enables one to extract features  ...  SUMMARY AND FURTHER WORK In this paper, we have presented the approximate nonnegative matrix factorization problem with underapproximation constraints, called Nonnegative Matrix Underapproximation (NMU  ... 
doi:10.1117/12.849345 fatcat:xy6u4wktpfejxdpxty6sdpzmpe

Dimensionality reduction, classification, and spectral mixture analysis using non-negative underapproximation

Robert J. Plemmons
2011 Optical Engineering: The Journal of SPIE  
Nonnegative Matrix Factorization (NMF) and its variants have recently been successfully used as dimensionality reduction techniques for identification of the materials present in hyperspectral images.  ...  In this paper, we present a new variant of NMF called Nonnegative Matrix Underapproximation (NMU): it is based on the introduction of underapproximation constraints which enables one to extract features  ...  SUMMARY AND FURTHER WORK In this paper, we have presented the approximate nonnegative matrix factorization problem with underapproximation constraints, called Nonnegative Matrix Underapproximation (NMU  ... 
doi:10.1117/1.3533025 fatcat:jrmajhg2xzaknolr4nmnbpqeg4

Sparse nonnegative matrix underapproximation and its application to hyperspectral image analysis

Nicolas Gillis, Robert J. Plemmons
2011 2011 3rd Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS)  
In this paper we introduce sparse NMU by adding a sparsity constraint on the abundance matrix and use it to extract materials individually in a more efficient way than NMU.  ...  In hyperspectral image analysis, nonnegativity of the data can be taken into account, leading to an additive linear model called nonnegative matrix factorization (NMF), which improves interpretability  ...  At the first step of the recursion, the following problem, called (rank-one) nonnegative matrix underapproximation (NMU), min u≥0,v≥0 ||M − uv T || 2 F such that uv T ≤ M, (1.2) is solved, and a nonnegative  ... 
doi:10.1109/whispers.2011.6080923 dblp:conf/whispers/GillisP11 fatcat:shndjabdmnbyfha2npeqovurga

Sequential dimensionality reduction for extracting localized features

Gabriella Casalino, Nicolas Gillis
2017 Pattern Recognition  
In particular, nonnegative matrix factorization (NMF) has become very popular as it is able to extract sparse, localized and easily interpretable features by imposing an additive combination of nonnegative  ...  Nonnegative matrix underapproximation (NMU) is a closely related technique that has the advantage to identify features sequentially.  ...  Acknowledgment We would like to thank the reviewers for their insightful feedback that helped us improve the paper significantly. NG acknowledges the support by the F.R.S.  ... 
doi:10.1016/j.patcog.2016.09.006 fatcat:gpxirn4v3rc7zfogi3vb6jacfy

Single-Channel Sparse Non-Negative Blind Source Separation Method for Automatic 3-D Delineation of Lung Tumor in PET Images

Ivica Kopriva, Wei Ju, Bin Zhang, Fei Shi, Dehui Xiang, Kai Yu, Ximing Wang, Ulas Bagci, Xinjian Chen
2017 IEEE journal of biomedical and health informatics  
Afterwards, regularization free sparseness constrained nonnegative matrix factorization is used to separate tumor from other tissues.  ...  Index Terms-Single-channel blind source separation, nonnegative matrix factorization, sparseness, lung tumor delineation, positron emission tomography (PET).  ...  ACKNOWLEDGMENTS We want to thank Professors Milan Sonka for proofreading the paper and giving us useful suggestions.  ... 
doi:10.1109/jbhi.2016.2624798 pmid:27834658 fatcat:c6kbhcz3abcjnhzdwqcaxl5u4u

Nonnegative Matrix Underapproximation for Robust Multiple Model Fitting

Mariano Tepper, Guillermo Sapiro
2017 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)  
In this work, we introduce a highly efficient algorithm to address the nonnegative matrix underapproximation (NMU) problem, i.e., nonnegative matrix factorization (NMF) with an additional underapproximation  ...  The proposed approach delivers state-of-the-art results for the estimation of multiple fundamental matrices and homographies, outperforming other alternatives in the literature and exemplifying the use  ...  Conclusions In this work, we first presented a highly efficient algorithm to address the nonnegative matrix underapproximation (NMU) problem.  ... 
doi:10.1109/cvpr.2017.77 dblp:conf/cvpr/TepperS17 fatcat:jopzyd5b5nal5h6iu2jnbzqp6a

Nonlinear mixture-wise expansion approach to underdetermined blind separation of nonnegative dependent sources

Ivica Kopriva, Ivanka Jerić, Lidija Brkljačić
2013 Journal of Chemometrics  
The method performs nonlinear mixturewise mapping of observed data in high-dimensional reproducible kernel Hilbert space (RKHS) of functions and sparseness constrained nonnegative matrix factorization  ...  Thereby, analytes mimic complexity of components expected to be found in biological samples. kernel Hilbert spaces, Empirical kernel maps, Nonnegative matrix factorization. knowledge to evaluate the separation  ...  Thus nonnegativity and sparseness constrained factorization of (8) (8) is finite.  ... 
doi:10.1002/cem.2512 fatcat:xg326qf345anhgwsufe6kdjej4

Blind separation of analytes in nuclear magnetic resonance spectroscopy: Improved model for nonnegative matrix factorization

Ivica Kopriva, Ivanka Jerić
2014 Chemometrics and Intelligent Laboratory Systems  
We introduce improved model for sparseness constrained nonnegative matrix factorization (sNMF) of amplitude mixtures nuclear magnetic resonance (NMR) spectra into greater number of component spectra.  ...  Afterwards, the square roots of separated squares of components spectra and concentration matrix yield estimates of the true components amplitude spectra and of concentration matrix.  ...  While several methods are available for solving sparseness constrained NMF problem (6) [44-48], in the experiments reported below we have used the nonnegative matrix under-approximation (NMU) algorithm  ... 
doi:10.1016/j.chemolab.2014.06.004 fatcat:dlieb5m6wrcptemudce7act7ny

Empirical kernel map approach to nonlinear underdetermined blind separation of sparse nonnegative dependent sources: pure component extraction from nonlinear mixture mass spectra

Ivica Kopriva, Ivanka Jerić, Marko Filipović, Lidija Brkljačić
2014 Journal of Chemometrics  
Sparseness constrained nonnegative matrix factorizations (NMF) in RKHS yield sets of separated components. They are assigned to pure components from the library using maximal correlation criterion.  ...  This paper presents method for nonlinear underdetermined blind separation of nonnegative dependent sources that comply with sparse probabilistic model, i.e. sources are constrained to be sparse in support  ...  constrained nonnegative matrix factorization (NMF) in high-dimensional mapped space.  ... 
doi:10.1002/cem.2635 fatcat:73nxojwvt5hy3flmypqokrdkkq

Nonnegative Matrix Factorization: A Comprehensive Review

Yu-Xiong Wang, Yu-Jin Zhang
2013 IEEE Transactions on Knowledge and Data Engineering  
Nonnegative Matrix Factorization (NMF), a relatively novel paradigm for dimensionality reduction, has been in the ascendant since its inception.  ...  This survey aims to construct an integrated, state-of-the-art framework for NMF concept, from which the follow-up research may benefit.  ...  Le Li and the reviewers for their helpful comments and suggestions. This work was supported by National Natural Science Foundation of China under Grant 61171118.  ... 
doi:10.1109/tkde.2012.51 fatcat:ocxepl7gdrhszawqhsj36qhpme
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