scholarly journals Analysis Sparse Representation for Nonnegative Signals Based on Determinant Measure by DC Programming

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Yujie Li ◽  
Benying Tan ◽  
Atsunori Kanemura ◽  
Shuxue Ding ◽  
Wuhui Chen
Keyword(s):  
Sparse Representation ◽  
Dictionary Learning ◽  
Optimization Problem ◽  
Learning Algorithm ◽  
State Of The Art ◽  
Optimization Methods ◽  
Dc Programming ◽  
Sparse Model ◽  
Alternative Approach ◽  
Difference Of Convex

Analysis sparse representation has recently emerged as an alternative approach to the synthesis sparse model. Most existing algorithms typically employ the l0-norm, which is generally NP-hard. Other existing algorithms employ the l1-norm to relax the l0-norm, which sometimes cannot promote adequate sparsity. Most of these existing algorithms focus on general signals and are not suitable for nonnegative signals. However, many signals are necessarily nonnegative such as spectral data. In this paper, we present a novel and efficient analysis dictionary learning algorithm for nonnegative signals with the determinant-type sparsity measure which is convex and differentiable. The analysis sparse representation can be cast in three subproblems, sparse coding, dictionary update, and signal update, because the determinant-type sparsity measure would result in a complex nonconvex optimization problem, which cannot be easily solved by standard convex optimization methods. Therefore, in the proposed algorithms, we use a difference of convex (DC) programming scheme for solving the nonconvex problem. According to our theoretical analysis and simulation study, the main advantage of the proposed algorithm is its greater dictionary learning efficiency, particularly compared with state-of-the-art algorithms. In addition, our proposed algorithm performs well in image denoising.

The smallest extraction problem

2021 ◽  
Vol 14 (11) ◽  
pp. 2445-2458
Author(s):  
Valerio Cetorelli ◽  
Paolo Atzeni ◽  
Valter Crescenzi ◽  
Franco Milicchio
Keyword(s):  
Unsupervised Learning ◽  
Optimization Problem ◽  
Learning Algorithm ◽  
State Of The Art ◽  
Data Extraction ◽  
Source Code ◽  
Web Data ◽  
Web Data Extraction ◽  
New Family ◽  
Context Free

We introduce landmark grammars , a new family of context-free grammars aimed at describing the HTML source code of pages published by large and templated websites and therefore at effectively tackling Web data extraction problems. Indeed, they address the inherent ambiguity of HTML, one of the main challenges of Web data extraction, which, despite over twenty years of research, has been largely neglected by the approaches presented in literature. We then formalize the Smallest Extraction Problem (SEP), an optimization problem for finding the grammar of a family that best describes a set of pages and contextually extract their data. Finally, we present an unsupervised learning algorithm to induce a landmark grammar from a set of pages sharing a common HTML template, and we present an automatic Web data extraction system. The experiments on consolidated benchmarks show that the approach can substantially contribute to improve the state-of-the-art.

Solving Mono- and Multi-Objective Problems Using Hybrid Evolutionary Algorithms and Nelder-Mead Method

2021 ◽  
Vol 12 (4) ◽  
pp. 98-116
Author(s):  
Noureddine Boukhari ◽  
Fatima Debbat ◽  
Nicolas Monmarché ◽  
Mohamed Slimane
Keyword(s):  
Convergence Rate ◽  
Optimization Problem ◽  
Optimization Problems ◽  
State Of The Art ◽  
Hybrid Approach ◽  
Optimization Methods ◽  
Global Optimum ◽  
Stochastic Methods ◽  
Local Optima ◽  
Portfolio Optimization Problem

Evolution strategies (ES) are a family of strong stochastic methods for global optimization and have proved their capability in avoiding local optima more than other optimization methods. Many researchers have investigated different versions of the original evolution strategy with good results in a variety of optimization problems. However, the convergence rate of the algorithm to the global optimum stays asymptotic. In order to accelerate the convergence rate, a hybrid approach is proposed using the nonlinear simplex method (Nelder-Mead) and an adaptive scheme to control the local search application, and the authors demonstrate that such combination yields significantly better convergence. The new proposed method has been tested on 15 complex benchmark functions and applied to the bi-objective portfolio optimization problem and compared with other state-of-the-art techniques. Experimental results show that the performance is improved by this hybridization in terms of solution eminence and strong convergence.

scholarly journals Nonlinear Kernel Dictionary Learning Algorithm Based on Analysis Sparse Model

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 212456-212466
Author(s):  
Zhuoyun Miao ◽  
Hongjuan Zhang ◽  
Shuang Ma
Keyword(s):  
Dictionary Learning ◽  
Learning Algorithm ◽  
Sparse Model

scholarly journals Optimization Methods for Redundancy Allocation in Large Systems

2020 ◽  
Vol 07 (03) ◽  
pp. 281-299
Author(s):  
Florin Leon ◽  
Petru Caşcaval ◽  
Costin Bădică
Keyword(s):  
Optimization Problem ◽  
Optimal Allocation ◽  
Optimization Methods ◽  
Fine Tuning ◽  
Hill Climbing ◽  
Cost Constraints ◽  
First Case ◽  
Alternative Approach ◽  
Cold Standby ◽  
Large Systems

This paper addresses the issue of optimal allocation of spare modules in large series-redundant systems in order to obtain a required reliability under cost constraints. Both cases of active and standby redundancy are considered. Moreover, for a subsystem with standby redundancy, two cases are examined: in the first case, all the spares are maintained in cold state (cold standby redundancy) and, in the second one, to reduce the time needed to put a spare into operation when the active one fails, one of the spares is maintained in warm conditions. To solve this optimization problem, for the simpler case of active redundancy an analytical method based on the Lagrange multipliers technique is first applied. Then the results are improved by using Pairwise Hill Climbing, an original fine-tuning algorithm. An alternative approach is an innovative evolutionary algorithm, RELIVE, in which an individual lives for several generations and improves its fitness based on local search. These methods are especially needed in case of very large systems.

scholarly journals Analysis K-SVD: A Dictionary-Learning Algorithm for the Analysis Sparse Model

2013 ◽  
Vol 61 (3) ◽  
pp. 661-677 ◽  
Author(s):  
Ron Rubinstein ◽  
Tomer Peleg ◽  
Michael Elad
Keyword(s):  
Dictionary Learning ◽  
Learning Algorithm ◽  
Sparse Model

Sparse angle CT reconstruction with weighted dictionary learning algorithm based on adaptive group-sparsity regularization

2021 ◽  
pp. 1-18
Author(s):  
Tiejun Yang ◽  
Lu Tang ◽  
Qi Tang ◽  
Lei Li
Keyword(s):  
Sparse Representation ◽  
Dictionary Learning ◽  
Learning Algorithm ◽  
Basic Unit ◽  
Ct Reconstruction ◽  
Group Sparsity ◽  
Sparsity Regularization ◽  
Smoothing Effects ◽  
Structural Details ◽  
Non Local

OBJECTIVE: In order to solve the blurred structural details and over-smoothing effects in sparse representation dictionary learning reconstruction algorithm, this study aims to test sparse angle CT reconstruction with weighted dictionary learning algorithm based on adaptive Group-Sparsity Regularization (AGSR-SART). METHODS: First, a new similarity measure is defined in which Covariance is introduced into Euclidean distance, Non-local image patches are adaptively divided into groups of different sizes as the basic unit of sparse representation. Second, the weight factor of the regular constraint terms is designed through the residuals represented by the dictionary, so that the algorithm takes different smoothing effects on different regions of the image during the iterative process. The sparse reconstructed image is modified according to the difference between the estimated value and the intermediate image. Last, The SBI (Split Bregman Iteration) iterative algorithm is used to solve the objective function. An abdominal image, a pelvic image and a thoracic image are employed to evaluate performance of the proposed method. RESULTS: In terms of quantitative evaluations, experimental results show that new algorithm yields PSNR of 48.20, the maximum SSIM of 99.06% and the minimum MAE of 0.0028. CONCLUSIONS: This study demonstrates that new algorithm can better preserve structural details in reconstructed CT images. It eliminates the effect of excessive smoothing in sparse angle reconstruction, enhances the sparseness and non-local self-similarity of the image, and thus it is superior to several existing reconstruction algorithms.

scholarly journals Optimal correction of infeasible equations system as Ax + B|x|= b using ℓ p-norm regularization

2022 ◽  
Vol 40 ◽  
pp. 1-16
Author(s):  
Fakhrodin Hashemi ◽  
Saeed Ketabchi
Keyword(s):  
Convex Functions ◽  
Regularization Method ◽  
High Performance ◽  
Optimization Problem ◽  
Dc Programming ◽  
Smoothing Technique ◽  
Optimal Correction ◽  
Difference Of Convex Functions ◽  
Difference Of Convex ◽  
Nonsmooth Optimization Problem

Optimal correction of an infeasible equations system as Ax + B|x|= b leads into a non-convex fractional problem. In this paper, a regularization method(ℓp-norm, 0 < p < 1), is presented to solve mentioned fractional problem. In this method, the obtained problem can be formulated as a non-convex and nonsmooth optimization problem which is not Lipschitz. The objective function of this problem can be decomposed as a difference of convex functions (DC). For this reason, we use a special smoothing technique based on DC programming. The numerical results obtained for generated problem show high performance and the effectiveness of the proposed method.

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