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Composition Analysis and Identification of Ancient Glass Products Based on L1 Regularization Logistic Regression
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作者 Yuqiao Zhou Xinyang Xu Wenjing Ma 《Applied Mathematics》 2024年第1期51-64,共14页
In view of the composition analysis and identification of ancient glass products, L1 regularization, K-Means cluster analysis, elbow rule and other methods were comprehensively used to build logical regression, cluste... In view of the composition analysis and identification of ancient glass products, L1 regularization, K-Means cluster analysis, elbow rule and other methods were comprehensively used to build logical regression, cluster analysis, hyper-parameter test and other models, and SPSS, Python and other tools were used to obtain the classification rules of glass products under different fluxes, sub classification under different chemical compositions, hyper-parameter K value test and rationality analysis. Research can provide theoretical support for the protection and restoration of ancient glass relics. 展开更多
关键词 Glass Composition L1 Regularization logistic regression Model K-Means Clustering Analysis Elbow Rule Parameter Verification
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Adaptive Linearized Alternating Direction Method of Multipliers for Non-Convex Compositely Regularized Optimization Problems 被引量:5
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作者 Linbo Qiao Bofeng Zhang +1 位作者 Xicheng Lu Jinshu Su 《Tsinghua Science and Technology》 SCIE EI CAS CSCD 2017年第3期328-341,共14页
We consider a wide range of non-convex regularized minimization problems, where the non-convex regularization term is composite with a linear function engaged in sparse learning. Recent theoretical investigations have... We consider a wide range of non-convex regularized minimization problems, where the non-convex regularization term is composite with a linear function engaged in sparse learning. Recent theoretical investigations have demonstrated their superiority over their convex counterparts. The computational challenge lies in the fact that the proximal mapping associated with non-convex regularization is not easily obtained due to the imposed linear composition. Fortunately, the problem structure allows one to introduce an auxiliary variable and reformulate it as an optimization problem with linear constraints, which can be solved using the Linearized Alternating Direction Method of Multipliers (LADMM). Despite the success of LADMM in practice, it remains unknown whether LADMM is convergent in solving such non-convex compositely regularized optimizations. In this research, we first present a detailed convergence analysis of the LADMM algorithm for solving a non-convex compositely regularized optimization problem with a large class of non-convex penalties. Furthermore, we propose an Adaptive LADMM (AdaLADMM) algorithm with a line-search criterion. Experimental results on different genres of datasets validate the efficacy of the proposed algorithm. 展开更多
关键词 adaptive linearized alternating direction method of multipliers non-convex compositely regularizedoptimization cappled-ll regularized logistic regression
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Stochastic extra-gradient based alternating direction methods for graph-guided regularized minimization
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作者 Qiang LAN Lin-bo QIAO Yi-jie WANG 《Frontiers of Information Technology & Electronic Engineering》 SCIE EI CSCD 2018年第6期755-762,共8页
In this study, we propose and compare stochastic variants of the extra-gradient alternating direction method, named the stochastic extra-gradient alternating direction method with Lagrangian function(SEGL) and the s... In this study, we propose and compare stochastic variants of the extra-gradient alternating direction method, named the stochastic extra-gradient alternating direction method with Lagrangian function(SEGL) and the stochastic extra-gradient alternating direction method with augmented Lagrangian function(SEGAL), to minimize the graph-guided optimization problems, which are composited with two convex objective functions in large scale.A number of important applications in machine learning follow the graph-guided optimization formulation, such as linear regression, logistic regression, Lasso, structured extensions of Lasso, and structured regularized logistic regression. We conduct experiments on fused logistic regression and graph-guided regularized regression. Experimental results on several genres of datasets demonstrate that the proposed algorithm outperforms other competing algorithms, and SEGAL has better performance than SEGL in practical use. 展开更多
关键词 Stochastic optimization Graph-guided minimization Extra-gradient method Fused logistic regression Graph-guided regularized logistic regression
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A STOCHASTIC MOVING BALLS APPROXIMATION METHOD OVER A SMOOTH INEQUALITY CONSTRAINT
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作者 Leiwu Zhang 《Journal of Computational Mathematics》 SCIE CSCD 2020年第3期528-546,共19页
We consider the problem of minimizing the average of a large number of smooth component functions over one smooth inequality constraint.We propose and analyze a stochastic Moving Balls Approximation(SMBA)method.Like s... We consider the problem of minimizing the average of a large number of smooth component functions over one smooth inequality constraint.We propose and analyze a stochastic Moving Balls Approximation(SMBA)method.Like stochastic gradient(SG)met hods,the SMBA method's iteration cost is independent of the number of component functions and by exploiting the smoothness of the constraint function,our method can be easily implemented.Theoretical and computational properties of SMBA are studied,and convergence results are established.Numerical experiments indicate that our algorithm dramatically outperforms the existing Moving Balls Approximation algorithm(MBA)for the structure of our problem. 展开更多
关键词 Smooth convex constrained minimization.Large scale problem.Moving Balls Approximation regularized logistic regression
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