scholarly journals Double Regression-Based Sparse Unmixing for Hyperspectral Images

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Shuaiyang Zhang ◽  
Wenshen Hua ◽  
Gang Li ◽  
Jie Liu ◽  
Fuyu Huang ◽  
...  
Keyword(s):  
Computational Complexity ◽  
Clustering Algorithm ◽  
Real Data ◽  
Alternating Direction Method ◽  
Threshold Function ◽  
Joint Sparsity ◽  
Alternating Direction ◽  
Sparsity Constraints ◽  
The Cost ◽  
Unmixing Model

Sparse unmixing has attracted widespread attention from researchers, and many effective unmixing algorithms have been proposed in recent years. However, most algorithms improve the unmixing accuracy at the cost of large calculations. Higher unmixing accuracy often leads to higher computational complexity. To solve this problem, we propose a novel double regression-based sparse unmixing model (DRSUM), which can obtain better unmixing results with lower computational complexity. DRSUM decomposes the complex objective function into two simple formulas and completes the unmixing process through two sparse regressions. The unmixing result of the first sparse regression is added as a constraint to the second. DRSUM is an open model, and we can add different constraints to improve the unmixing accuracy. In addition, we can perform appropriate preprocessing to further improve the unmixing results. Under this model, a specific algorithm called double regression-based sparse unmixing via K -means ( DRSU M K − means ) is proposed. The improved K -means clustering algorithm is first used for preprocessing, and then we impose single sparsity and joint sparsity (using l 2 , 0 norm to control the sparsity) constraints on the first and second sparse unmixing, respectively. To meet the sparsity requirement, we introduce the row-hard-threshold function to solve the l 2 , 0 norm directly. Then, DRSU M K − means can be efficiently solved under alternating direction method of multipliers (ADMM) framework. Simulated and real data experiments have proven the effectiveness of DRSU M K − means .

scholarly journals Remote Sensing Image Stripe Detecting and Destriping Using the Joint Sparsity Constraint with Iterative Support Detection

2019 ◽  
Vol 11 (6) ◽  
pp. 608 ◽  
Author(s):  
Yun-Jia Sun ◽  
Ting-Zhu Huang ◽  
Tian-Hui Ma ◽  
Yong Chen
Keyword(s):  
Remote Sensing ◽  
Real Data ◽  
Total Variation Regularization ◽  
Joint Sparsity ◽  
Alternating Direction ◽  
Proposed Model ◽  
Comparison Results ◽  
Wide Range ◽  
Image Edges ◽  
Full Consideration

Remote sensing images have been applied to a wide range of fields, but they are often degraded by various types of stripes, which affect the image visual quality and limit the subsequent processing tasks. Most existing destriping methods fail to exploit the stripe properties adequately, leading to suboptimal performance. Based on a full consideration of the stripe properties, we propose a new destriping model to achieve stripe detection and stripe removal simultaneously. In this model, we adopt the unidirectional total variation regularization to depict the directional property of stripes and the weighted ℓ 2 , 1 -norm regularization to depict the joint sparsity of stripes. Then, we combine the alternating direction method of multipliers and iterative support detection to solve the proposed model effectively. Comparison results on simulated and real data suggest that the proposed method can remove and detect stripes effectively while preserving image edges and details.

scholarly journals Theoretical and Experimental Analyses of Tensor-Based Regression and Classification

2016 ◽  
Vol 28 (4) ◽  
pp. 686-715 ◽  
Author(s):  
Kishan Wimalawarne ◽  
Ryota Tomioka ◽  
Masashi Sugiyama
Keyword(s):  
Real Data ◽  
Optimization Methods ◽  
Alternating Direction Method ◽  
Trace Norm ◽  
Method Of Multipliers ◽  
Computationally Efficient ◽  
Learning Methods ◽  
Alternating Direction ◽  
Training Samples ◽  
Tensor Norm

We theoretically and experimentally investigate tensor-based regression and classification. Our focus is regularization with various tensor norms, including the overlapped trace norm, the latent trace norm, and the scaled latent trace norm. We first give dual optimization methods using the alternating direction method of multipliers, which is computationally efficient when the number of training samples is moderate. We then theoretically derive an excess risk bound for each tensor norm and clarify their behavior. Finally, we perform extensive experiments using simulated and real data and demonstrate the superiority of tensor-based learning methods over vector- and matrix-based learning methods.

Alternating direction method of multiplier for solving electromagnetic inverse scattering problems

2020 ◽  
Vol 12 (8) ◽  
pp. 790-796
Author(s):  
Jian Liu ◽  
Huilin Zhou ◽  
Liangbing Chen ◽  
Tao Ouyang
Keyword(s):  
Cost Function ◽  
Inverse Scattering ◽  
Source Function ◽  
Alternating Direction Method ◽  
Scattering Problems ◽  
Contrast Function ◽  
Inverse Scattering Problems ◽  
Alternating Direction ◽  
Dual Variables ◽  
The Cost

AbstractIn this paper, a novel alternating direction method of multiplier (ADMM) is proposed to solve the inverse scattering problems. The proposed method is suitable for a wide range of applications with electromagnetic detection. In order to solve the internal ill-posed problem of the integral equation and make the reconstructed images more closer to the ground truth, first, the augmented Lagrangian method is introduced to transform the complex constrained optimization problem into the extremum problem of unconstrained cost function. Therefore, two artificial regularization factors of the cost function are optimized. Then, this proposed method decomposes the unconstrained global problem in the inversion process into three linear sub-problem forms of contrast source function, contrast function, and dual variables. And the form of the updated algebra for each sub-problem is not complicated. By cross-iterating and updating contrast source function, contrast function, and dual variables, the global minimization of the cost function can be accurately found. Finally, the proposed method is compared with the existing well-known iterative method for solving the inverse scattering problem. Both the numerical and experimental tests verify the validity and accuracy of the proposed ADMM.

Solving Constrained TV2L1-L2 MRI Signal Reconstruction via an Efficient Alternating Direction Method of Multipliers

2017 ◽  
Vol 10 (4) ◽  
pp. 895-912 ◽  
Author(s):  
Tingting Wu ◽  
David Z. W. Wang ◽  
Zhengmeng Jin ◽  
Jun Zhang
Keyword(s):  
Fourier Transforms ◽  
Signal Reconstruction ◽  
Alternating Direction Method ◽  
Method Of Multipliers ◽  
Closed Form Solutions ◽  
Alternating Direction ◽  
Mri Reconstruction ◽  
Constrained Model ◽  
Magnetic Resonance Imaging Mri ◽  
The Cost

AbstractHigh order total variation (TV2) and ℓ1 based (TV2L1) model has its advantage over the TVL1 for its ability in avoiding the staircase; and a constrained model has the advantage over its unconstrained counterpart for simplicity in estimating the parameters. In this paper, we consider solving the TV2L1 based magnetic resonance imaging (MRI) signal reconstruction problem by an efficient alternating direction method of multipliers. By sufficiently utilizing the problem's special structure, we manage to make all subproblems either possess closed-form solutions or can be solved via Fast Fourier Transforms, which makes the cost per iteration very low. Experimental results for MRI reconstruction are presented to illustrate the effectiveness of the new model and algorithm. Comparisons with its recent unconstrained counterpart are also reported.

scholarly journals Parameter Estimation with the Ordered ℓ2 Regularization via an Alternating Direction Method of Multipliers

2019 ◽  
Vol 9 (20) ◽  
pp. 4291 ◽  
Author(s):  
Mahammad Humayoo ◽  
Xueqi Cheng
Keyword(s):  
Parameter Estimation ◽  
Large Scale ◽  
Scale Up ◽  
Synthetic Data ◽  
Real Data ◽  
Alternating Direction Method ◽  
Training Data ◽  
Accurate Estimation ◽  
Method Of Multipliers ◽  
Alternating Direction

Regularization is a popular technique in machine learning for model estimation and for avoiding overfitting. Prior studies have found that modern ordered regularization can be more effective in handling highly correlated, high-dimensional data than traditional regularization. The reason stems from the fact that the ordered regularization can reject irrelevant variables and yield an accurate estimation of the parameters. How to scale up the ordered regularization problems when facing large-scale training data remains an unanswered question. This paper explores the problem of parameter estimation with the ordered ℓ 2 -regularization via Alternating Direction Method of Multipliers (ADMM), called ADMM-O ℓ 2 . The advantages of ADMM-O ℓ 2 include (i) scaling up the ordered ℓ 2 to a large-scale dataset, (ii) predicting parameters correctly by excluding irrelevant variables automatically, and (iii) having a fast convergence rate. Experimental results on both synthetic data and real data indicate that ADMM-O ℓ 2 can perform better than or comparable to several state-of-the-art baselines.

Pareto Set as a Model for Dispatching Resources in Emergency Centres (Preprint)

2018 ◽  
Author(s):  
Ricardo Guedes ◽  
Vasco Furtado ◽  
Tarcísio Pequeno ◽  
Joel Rodrigues
Keyword(s):  
Operational Research ◽  
Real Data ◽  
Pareto Set ◽  
Multi Objective Optimization ◽  
Pareto Dominance ◽  
Four Dimensions ◽  
Multi Objective ◽  
The Best Approximation ◽  
One Year ◽  
The Cost

UNSTRUCTURED The article investigates policies for helping emergency-centre authorities for dispatching resources aimed at reducing goals such as response time, the number of unattended calls, the attending of priority calls, and the cost of displacement of vehicles. Pareto Set is shown to be the appropriated way to support the representation of policies of dispatch since it naturally fits the challenges of multi-objective optimization. By means of the concept of Pareto dominance a set with objectives may be ordered in a way that guides the dispatch of resources. Instead of manually trying to identify the best dispatching strategy, a multi-objective evolutionary algorithm coupled with an Emergency Call Simulator uncovers automatically the best approximation of the optimal Pareto Set that would be the responsible for indicating the importance of each objective and consequently the order of attendance of the calls. The scenario of validation is a big metropolis in Brazil using one-year of real data from 911 calls. Comparisons with traditional policies proposed in the literature are done as well as other innovative policies inspired from different domains as computer science and operational research. The results show that strategy of ranking the calls from a Pareto Set discovered by the evolutionary method is a good option because it has the second best (lowest) waiting time, serves almost 100% of priority calls, is the second most economical, and is the second in attendance of calls. That is to say, it is a strategy in which the four dimensions are considered without major impairment to any of them.

scholarly journals ALPINE: Active Link Prediction Using Network Embedding

2021 ◽  
Vol 11 (11) ◽  
pp. 5043
Author(s):  
Xi Chen ◽  
Bo Kang ◽  
Jefrey Lijffijt ◽  
Tijl De Bie
Keyword(s):  
Active Learning ◽  
Protein Interactions ◽  
Link Prediction ◽  
Prediction Accuracy ◽  
Real Data ◽  
Network Embedding ◽  
Protein Protein Interactions ◽  
Additional Information ◽  
The Cost ◽  
Active Link

Many real-world problems can be formalized as predicting links in a partially observed network. Examples include Facebook friendship suggestions, the prediction of protein–protein interactions, and the identification of hidden relationships in a crime network. Several link prediction algorithms, notably those recently introduced using network embedding, are capable of doing this by just relying on the observed part of the network. Often, whether two nodes are linked can be queried, albeit at a substantial cost (e.g., by questionnaires, wet lab experiments, or undercover work). Such additional information can improve the link prediction accuracy, but owing to the cost, the queries must be made with due consideration. Thus, we argue that an active learning approach is of great potential interest and developed ALPINE (Active Link Prediction usIng Network Embedding), a framework that identifies the most useful link status by estimating the improvement in link prediction accuracy to be gained by querying it. We proposed several query strategies for use in combination with ALPINE, inspired by the optimal experimental design and active learning literature. Experimental results on real data not only showed that ALPINE was scalable and boosted link prediction accuracy with far fewer queries, but also shed light on the relative merits of the strategies, providing actionable guidance for practitioners.

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