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Fast and robust recursive algorithms for separable nonnegative matrix factorization. arXiv preprint arXiv:1208.1237
, 2012
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R.: Robust nearseparable nonnegative matrix factorization using linear optimization
 Journal of Machine Learning Research
, 2014
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Nonnegative matrix factorization revisited: Uniqueness and algorithm for symmetric decomposition
 IEEE TRANS. SIGNAL PROCESSING
, 2014
"... Nonnegative matrix factorization (NMF) has found numerous applications, due to its ability to provide interpretable decompositions. Perhaps surprisingly, existing results regarding its uniqueness properties are rather limited, and there is much room for improvement in terms of algorithms as well. ..."
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Cited by 8 (2 self)
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Nonnegative matrix factorization (NMF) has found numerous applications, due to its ability to provide interpretable decompositions. Perhaps surprisingly, existing results regarding its uniqueness properties are rather limited, and there is much room for improvement in terms of algorithms as well. Uniqueness aspects of NMF are revisited here from a geometrical point of view. Both symmetric and asymmetric NMF are considered, the former being tantamount to elementwise nonnegative squareroot factorization of positive semidefinite matrices. New uniqueness results are derived, e.g., it is shown that a sufficient condition for uniqueness is that the conic hull of the latent factors is a superset of a particular secondorder cone. Checking this condition is shown to be NPcomplete; yet this and other results offer insights on the role of latent sparsity in this context. On the computational side, a new algorithm for symmetric NMF is proposed, which is very different from existing ones. It alternates between Procrustes rotation and projection onto the nonnegative orthant to find a nonnegative matrix close to the span of the dominant subspace. Simulation results show promising performance with respect to the stateofart. Finally, the new algorithm is applied to a clustering problem for coauthorship data, yielding meaningful and interpretable results.
The why and how of nonnegative matrix factorization
 REGULARIZATION, OPTIMIZATION, KERNELS, AND SUPPORT VECTOR MACHINES. CHAPMAN & HALL/CRC
, 2014
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Nonnegative Blind Source Separation Algorithm based on Minimum Aperture Simplicial Cone
, 2014
"... Abstract—We address the problem of Blind Source Separation (BSS) when the hidden sources are Nonnegative (NBSS). In this case, the scatter plot of the mixed data is contained within the simplicial cone generated by the columns of the mixing matrix. The proposed method, termed SCSAUNS for Simplicia ..."
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Cited by 4 (0 self)
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Abstract—We address the problem of Blind Source Separation (BSS) when the hidden sources are Nonnegative (NBSS). In this case, the scatter plot of the mixed data is contained within the simplicial cone generated by the columns of the mixing matrix. The proposed method, termed SCSAUNS for Simplicial Cone Shrinking Algorithm for Unmixing Nonnegative Sources, aims at estimating the mixing matrix and the sources by fitting a Minimum Aperture Simplicial Cone (MASC) to the cloud of mixed data points. SCSAUNS is evaluated on both independent and correlated synthetic data and compared to other NBSS methods. Simulations are also performed on real Liquid ChromatographyMass Spectrum (LCMS) data for the metabolomic analysis of a chemical sample, and on real dynamic Positron Emission Tomography (PET) images, in order to study the pharmacokinetics of the [18F]FDG (FluoroDeoxyGlucose) tracer in the brain.
Hierarchical Clustering of Hyperspectral Images Using RankTwo Nonnegative Matrix Factorization
 IEEE, Transactions on Geoscience and Remote Sensing
, 2015
"... In this paper, we design a hierarchical clustering algorithm for highresolution hyperspectral images. At the core of the algorithm, a new ranktwo nonnegative matrix factorizations (NMF) algorithm is used to split the clusters, which is motivated by convex geometry concepts. The method starts with ..."
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In this paper, we design a hierarchical clustering algorithm for highresolution hyperspectral images. At the core of the algorithm, a new ranktwo nonnegative matrix factorizations (NMF) algorithm is used to split the clusters, which is motivated by convex geometry concepts. The method starts with a single cluster containing all pixels, and, at each step, (i) selects a cluster in such a way that the error at the next step is minimized, and (ii) splits the selected cluster into two disjoint clusters using ranktwo NMF in such a way that the clusters are well balanced and stable. The proposed method can also be used as an endmember extraction algorithm in the presence of pure pixels. The effectiveness of this approach is illustrated on several synthetic and realworld hyperspectral images, and shown to outperform standard clustering techniques such as kmeans, spherical kmeans and standard NMF.
A Vavasis, “Semidefinite programming based preconditioning for more robust nearseparable nonnegative matrix factorization,” arXiv preprint arXiv:1310.2273
, 2013
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Successive Nonnegative Projection Algorithm for Robust Nonnegative Blind Source Separation
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TheCAM Software for Nonnegative Blind Source Separation inRJava
"... We describe aRJava CAM (convex analysis of mixtures) package that provides comprehensive analytic functions and a graphic user interface (GUI) for blindly separating mixed nonnegative sources. This opensource multiplatform software implements recent and classic algorithms in the literature includi ..."
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We describe aRJava CAM (convex analysis of mixtures) package that provides comprehensive analytic functions and a graphic user interface (GUI) for blindly separating mixed nonnegative sources. This opensource multiplatform software implements recent and classic algorithms in the literature including Chan et al. (2008), Wang et al. (2010), Chen et al. (2011a) and Chen et al. (2011b). The CAM package offers several attractive features: (1) instead of using proprietary MATLAB, its analytic functions are written in R, which makes the codes more portable and easier to modify; (2) besides producing and plotting results in R, it also provides a Java GUI for automatic progress update and convenient visual monitoring; (3) multithread interactions between the R and Java modules are driven and integrated by a Java GUI, assuring that the whole CAM software runs responsively; (4) the package offers a simple mechanism to allow others to plugin additionalRfunctions.