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**21 - 30**of**30**### Vtor Silvaa,d, Jose M. Bioucas-Diasa,e

"... Parallel hyperspectral unmixing problem is considered in this paper. A semisupervised approach is developed under the linear mixture model, where the abundance’s physical constraints are taken into account. The proposed approach relies on the increasing availability of spectral libraries of material ..."

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Parallel hyperspectral unmixing problem is considered in this paper. A semisupervised approach is developed under the linear mixture model, where the abundance’s physical constraints are taken into account. The proposed approach relies on the increasing availability of spectral libraries of materials measured on the ground instead of resorting to endmember extraction methods. Since Libraries are potentially very large and hyperspectral datasets are of high dimensionality a parallel implementation in a pixel-by-pixel fashion is derived to properly exploits the graphics processing units (GPU) architecture at low level, thus taking full advantage of the computational power of GPUs. Experimental results obtained for real hyperspectral datasets reveal significant speedup factors, up to 164 times, with regards to optimized serial implementation.

### Orthogonal NMF through Subspace Exploration

"... Abstract Orthogonal Nonnegative Matrix Factorization (ONMF) aims to approximate a nonnegative matrix as the product of two k-dimensional nonnegative factors, one of which has orthonormal columns. It yields potentially useful data representations as superposition of disjoint parts, while it has been ..."

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Abstract Orthogonal Nonnegative Matrix Factorization (ONMF) aims to approximate a nonnegative matrix as the product of two k-dimensional nonnegative factors, one of which has orthonormal columns. It yields potentially useful data representations as superposition of disjoint parts, while it has been shown to work well for clustering tasks where traditional methods underperform. Existing algorithms rely mostly on heuristics, which despite their good empirical performance, lack provable performance guarantees. We present a new ONMF algorithm with provable approximation guarantees. For any constant dimension k, we obtain an additive EPTAS without any assumptions on the input. Our algorithm relies on a novel approximation to the related Nonnegative Principal Component Analysis (NNPCA) problem; given an arbitrary data matrix, NNPCA seeks k nonnegative components that jointly capture most of the variance. Our NNPCA algorithm is of independent interest and generalizes previous work that could only obtain guarantees for a single component. We evaluate our algorithms on several real and synthetic datasets and show that their performance matches or outperforms the state of the art.

### Empirical-Bayes Approaches to Recovery of Structured Sparse Signals via . . .

, 2015

"... In recent years, there have been massive increases in both the dimensionality and sample sizes of data due to ever-increasing consumer demand coupled with relatively inexpensive sensing technologies. These high-dimensional datasets bring challenges such as complexity, along with numerous opportuniti ..."

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In recent years, there have been massive increases in both the dimensionality and sample sizes of data due to ever-increasing consumer demand coupled with relatively inexpensive sensing technologies. These high-dimensional datasets bring challenges such as complexity, along with numerous opportunities. Though many signals of interest live in a high-dimensional ambient space, they often have a much smaller inherent dimensionality which, if leveraged, lead to improved recoveries. For example, the notion of sparsity is a requisite in the compressive sensing (CS) field, which allows for accurate signal reconstruction from sub-Nyquist sampled measurements given certain conditions. When recovering a sparse signal from noisy compressive linear measurements, the distribution of the signal’s non-zero coefficients can have a profound effect on recov-ery mean-squared error (MSE). If this distribution is apriori known, then one could use computationally efficient approximate message passing (AMP) techniques that yield approximate minimum MSE (MMSE) estimates or critical points to the maxi-

### Elsevier on-line version:

"... of industrial source identification”, Applied Numerical Mathematics, vol. 85, ..."

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of industrial source identification”, Applied Numerical Mathematics, vol. 85,

### Scalable Methods for Nonnegative Matrix Factorizations of Near-separable Tall-and-skinny Matrices

"... • NMF Problem: X ∈ Rm×n+ is a matrix with nonnegative entries, and we want to compute a nonnegative matrix factorization (NMF) X = WH, where W ∈ Rm×r+ and H ∈ Rr×n+. When r < m, this problem is NP-hard. • A separable matrix is one that admits a nonnegative factorization where ..."

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• NMF Problem: X ∈ Rm×n+ is a matrix with nonnegative entries, and we want to compute a nonnegative matrix factorization (NMF) X = WH, where W ∈ Rm×r+ and H ∈ Rr×n+. When r < m, this problem is NP-hard. • A separable matrix is one that admits a nonnegative factorization where

### Contributions

, 2013

"... Recover low-rank matrix Z from noise-corrupted incomplete observations Y = PΩ ..."

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Recover low-rank matrix Z from noise-corrupted incomplete observations Y = PΩ

### unknown title

"... Hyperspectral image unmixing via bilinear generalized approximate message passing ..."

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Hyperspectral image unmixing via bilinear generalized approximate message passing