scholarly journals Parameterized Nonlinear Least Squares for Unsupervised Nonlinear Spectral Unmixing

2019 ◽  
Vol 11 (2) ◽  
pp. 148 ◽  
Author(s):  
Risheng Huang ◽  
Xiaorun Li ◽  
Haiqiang Lu ◽  
Jing Li ◽  
Liaoying Zhao
Keyword(s):  
Least Squares ◽  
Optimization Problem ◽  
Nonnegative Matrix Factorization ◽  
Optimization Problems ◽  
State Of The Art ◽  
Synthetic Data ◽  
Nonnegative Matrix ◽  
Nonlinear Least Squares ◽  
Hyperspectral Data ◽  
Spectral Unmixing

This paper presents a new parameterized nonlinear least squares (PNLS) algorithm for unsupervised nonlinear spectral unmixing (UNSU). The PNLS-based algorithms transform the original optimization problem with respect to the endmembers, abundances, and nonlinearity coefficients estimation into separate alternate parameterized nonlinear least squares problems. Owing to the Sigmoid parameterization, the PNLS-based algorithms are able to thoroughly relax the additional nonnegative constraint and the nonnegative constraint in the original optimization problems, which facilitates finding a solution to the optimization problems . Subsequently, we propose to solve the PNLS problems based on the Gauss–Newton method. Compared to the existing nonnegative matrix factorization (NMF)-based algorithms for UNSU, the well-designed PNLS-based algorithms have faster convergence speed and better unmixing accuracy. To verify the performance of the proposed algorithms, the PNLS-based algorithms and other state-of-the-art algorithms are applied to synthetic data generated by the Fan model and the generalized bilinear model (GBM), as well as real hyperspectral data. The results demonstrate the superiority of the PNLS-based algorithms.

scholarly journals Accelerating Nonnegative Matrix Factorization Algorithms Using Extrapolation

2019 ◽  
Vol 31 (2) ◽  
pp. 417-439 ◽  
Author(s):  
Andersen Man Shun Ang ◽  
Nicolas Gillis
Keyword(s):  
Least Squares ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
State Of The Art ◽  
Gradient Methods ◽  
Nonnegative Matrix ◽  
Synthetic Image ◽  
Data Sets ◽  
Extrapolation Scheme ◽  
Factorization Algorithms

We propose a general framework to accelerate significantly the algorithms for nonnegative matrix factorization (NMF). This framework is inspired from the extrapolation scheme used to accelerate gradient methods in convex optimization and from the method of parallel tangents. However, the use of extrapolation in the context of the exact coordinate descent algorithms tackling the nonconvex NMF problems is novel. We illustrate the performance of this approach on two state-of-the-art NMF algorithms: accelerated hierarchical alternating least squares and alternating nonnegative least squares, using synthetic, image, and document data sets.

scholarly journals Accelerated Multiplicative Updates and Hierarchical ALS Algorithms for Nonnegative Matrix Factorization

2012 ◽  
Vol 24 (4) ◽  
pp. 1085-1105 ◽  
Author(s):  
Nicolas Gillis ◽  
François Glineur
Keyword(s):  
Data Analysis ◽  
Least Squares ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Computational Cost ◽  
Nonnegative Matrix ◽  
Careful Analysis ◽  
Hyperspectral Data ◽  
Projected Gradient Method ◽  
Multiplicative Updates

Nonnegative matrix factorization (NMF) is a data analysis technique used in a great variety of applications such as text mining, image processing, hyperspectral data analysis, computational biology, and clustering. In this letter, we consider two well-known algorithms designed to solve NMF problems: the multiplicative updates of Lee and Seung and the hierarchical alternating least squares of Cichocki et al. We propose a simple way to significantly accelerate these schemes, based on a careful analysis of the computational cost needed at each iteration, while preserving their convergence properties. This acceleration technique can also be applied to other algorithms, which we illustrate on the projected gradient method of Lin. The efficiency of the accelerated algorithms is empirically demonstrated on image and text data sets and compares favorably with a state-of-the-art alternating nonnegative least squares algorithm.

scholarly journals DISTRIBUTED UNMIXING OF HYPERSPECTRAL DATAWITH SPARSITY CONSTRAINT

2017 ◽  
Vol XLII-4/W4 ◽  
pp. 145-150 ◽  
Author(s):  
S. Khoshsokhan ◽  
R. Rajabi ◽  
H. Zayyani
Keyword(s):  
Nonnegative Matrix Factorization ◽  
Performance Metrics ◽  
Nonnegative Matrix ◽  
Hyperspectral Data ◽  
Spectral Unmixing ◽  
Single Node ◽  
Significant Challenge ◽  
Fractional Abundance ◽  
Simulation Results ◽  
Sparsity Constraint

Spectral unmixing (SU) is a data processing problem in hyperspectral remote sensing. The significant challenge in the SU problem is how to identify endmembers and their weights, accurately. For estimation of signature and fractional abundance matrices in a blind problem, nonnegative matrix factorization (NMF) and its developments are used widely in the SU problem. One of the constraints which was added to NMF is sparsity constraint that was regularized by L1/2 norm. In this paper, a new algorithm based on distributed optimization has been used for spectral unmixing. In the proposed algorithm, a network including single-node clusters has been employed. Each pixel in hyperspectral images considered as a node in this network. The distributed unmixing with sparsity constraint has been optimized with diffusion LMS strategy, and then the update equations for fractional abundance and signature matrices are obtained. Simulation results based on defined performance metrics, illustrate advantage of the proposed algorithm in spectral unmixing of hyperspectral data compared with other methods. The results show that the AAD and SAD of the proposed approach are improved respectively about 6 and 27 percent toward distributed unmixing in SNR=25dB.

Efficient Nonnegative Matrix Factorization by DC Programming and DCA

2016 ◽  
Vol 28 (6) ◽  
pp. 1163-1216 ◽  
Author(s):  
Hoai An Le Thi ◽  
Xuan Thanh Vo ◽  
Tao Pham Dinh
Keyword(s):  
Least Squares ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Synthetic Data ◽  
Nonnegative Matrix ◽  
Dc Programming ◽  
Selection Strategy ◽  
Sparse Regularization ◽  
Dc Algorithm ◽  
Difference Of Convex Functions

In this letter, we consider the nonnegative matrix factorization (NMF) problem and several NMF variants. Two approaches based on DC (difference of convex functions) programming and DCA (DC algorithm) are developed. The first approach follows the alternating framework that requires solving, at each iteration, two nonnegativity-constrained least squares subproblems for which DCA-based schemes are investigated. The convergence property of the proposed algorithm is carefully studied. We show that with suitable DC decompositions, our algorithm generates most of the standard methods for the NMF problem. The second approach directly applies DCA on the whole NMF problem. Two algorithms—one computing all variables and one deploying a variable selection strategy—are proposed. The proposed methods are then adapted to solve various NMF variants, including the nonnegative factorization, the smooth regularization NMF, the sparse regularization NMF, the multilayer NMF, the convex/convex-hull NMF, and the symmetric NMF. We also show that our algorithms include several existing methods for these NMF variants as special versions. The efficiency of the proposed approaches is empirically demonstrated on both real-world and synthetic data sets. It turns out that our algorithms compete favorably with five state-of-the-art alternating nonnegative least squares algorithms.

Nonnegative matrix factorization with region sparsity learning for hyperspectral unmixing

2017 ◽  
Vol 15 (06) ◽  
pp. 1750063
Author(s):  
Bin Qian ◽  
Lei Tong ◽  
Zhenmin Tang ◽  
Xiaobo Shen
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Spatial Information ◽  
State Of The Art ◽  
Nonnegative Matrix ◽  
Hyperspectral Data ◽  
Optimization Scheme ◽  
Hyperspectral Unmixing ◽  
Relationship Of ◽  
The Relationship

Hyperspectral unmixing is one of the most important techniques in the remote sensing image analysis tasks. In recent decades, nonnegative matrix factorization (NMF) has been shown to be effective for hyperspectral unmixing due to the strong discovery of the latent structure. Most NMFs put emphasize on the spectral information, but ignore the spatial information, which is very crucial for analyzing hyperspectral data. In this paper, we propose an improved NMF method, namely NMF with region sparsity learning (RSLNMF), to simultaneously consider both spectral and spatial information. RSLNMF defines a new sparsity learning model based on a small homogeneous region that is obtained via the graph cut algorithm. Thus RSLNMF is able to explore the relationship of spatial neighbor pixels within each region. An efficient optimization scheme is developed for the proposed RSLNMF, and its convergence is theoretically guaranteed. Experiments on both synthetic and real hyperspectral data validate the superiority of the proposed method over several state-of-the-art unmixing approaches.

scholarly journals Deep Nonnegative Dictionary Factorization for Hyperspectral Unmixing

2020 ◽  
Vol 12 (18) ◽  
pp. 2882
Author(s):  
Wenhong Wang ◽  
Hongfu Liu
Keyword(s):  
Nonnegative Matrix Factorization ◽  
State Of The Art ◽  
Nonnegative Matrix ◽  
Single Layer ◽  
Spectral Unmixing ◽  
Hyperspectral Unmixing ◽  
Hyperspectral Remote Sensing Images ◽  
Relationship Of ◽  
Structured Representation ◽  
Significant Superiority

As a powerful blind source separation tool, Nonnegative Matrix Factorization (NMF) with effective regularizations has shown significant superiority in spectral unmixing of hyperspectral remote sensing images (HSIs) owing to its good physical interpretability and data adaptability. However, the majority of existing NMF-based spectral unmixing methods only adopt the single layer factorization, which is not favorable for exploiting the complex and structured representation relationship of endmembers implied in HSIs. In order to overcome such an issue, we propose a novel two-stage Deep Nonnegative Dictionary Factorization (DNDF) approach with a sparseness constraint and self-supervised regularization for HSI unmixing. Beyond simply extending one-layer factorization to multi-layer, DNDF conducts fuzzy clustering to tackle the mixed endmembers of HSIs. Moreover, self-supervised regularization is integrated into our DNDF model to impose an effective constraint on the endmember matrix. Experimental results on three real HSIs demonstrate the superiority of DNDF over several state-of-the-art methods.

scholarly journals ENDMEMBER EXTRACTION OF HIGHLY MIXED DATA USING <i>L</i><sub>1</sub> SPARSITY-CONSTRAINED MULTILAYER NONNEGATIVE MATRIX FACTORIZATION

2018 ◽  
Vol XLII-3 ◽  
pp. 329-333 ◽  
Author(s):  
H. Fang ◽  
A. H. Li ◽  
H. X. Xu ◽  
T. Wang ◽  
K. Jiang ◽  
...  
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Synthetic Data ◽  
Nonnegative Matrix ◽  
Single Layer ◽  
Real Data ◽  
Hyperspectral Data ◽  
Mixed Data ◽  
Complex Data ◽  
Endmember Extraction

Due to the limited spatial resolution of remote hyperspectral sensors, pixels are usually highly mixed in the hyperspectral images. Endmember extraction refers to the process identifying the pure endmember signatures from the mixture, which is an important step towards the utilization of hyperspectral data. Nonnegative matrix factorization (NMF) is a widely used method of endmember extraction due to its effectiveness and convenience. While most NMF-based methods have single-layer structures, which may have difficulties in effectively learning the structures of highly mixed and complex data. On the other hand, multilayer algorithms have shown great advantages in learning data features and been widely studied in many fields. In this paper, we presented a <i>L</i><sub>1</sub> sparsityconstrained multilayer NMF method for endmember extraction of highly mixed data. Firstly, the multilayer NMF structure was obtained by unfolding NMF into a certain number of layers. In each layer, the abundance matrix was decomposed into the endmember matrix and abundance matrix of the next layer. Besides, to improve the performance of NMF, we incorporated sparsity constraints to the multilayer NMF model by adding a <i>L</i><sub>1</sub> regularizer of the abundance matrix to each layer. At last, a layer-wise optimization method based on NeNMF was proposed to train the multilayer NMF structure. Experiments were conducted on both synthetic data and real data. The results demonstrate that our proposed algorithm can achieve better results than several state-of-art approaches.

scholarly journals Maximum Likelihood Estimation Based Nonnegative Matrix Factorization for Hyperspectral Unmixing

2021 ◽  
Vol 13 (13) ◽  
pp. 2637
Author(s):  
Qin Jiang ◽  
Yifei Dong ◽  
Jiangtao Peng ◽  
Mei Yan ◽  
Yi Sun
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Objective Function ◽  
Least Squares ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Likelihood Estimation ◽  
Hyperspectral Data ◽  
Hyperspectral Unmixing

Hyperspectral unmixing (HU) is a research hotspot of hyperspectral remote sensing technology. As a classical HU method, the nonnegative matrix factorization (NMF) unmixing method can decompose an observed hyperspectral data matrix into the product of two nonnegative matrices, i.e., endmember and abundance matrices. Because the objective function of NMF is the traditional least-squares function, NMF is sensitive to noise. In order to improve the robustness of NMF, this paper proposes a maximum likelihood estimation (MLE) based NMF model (MLENMF) for unmixing of hyperspectral images (HSIs), which substitutes the least-squares objective function in traditional NMF by a robust MLE-based loss function. Experimental results on a simulated and two widely used real hyperspectral data sets demonstrate the superiority of our MLENMF over existing NMF methods.

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