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MaxMin-L2-SVC-NCH: A novel approach for support vector classifier training and parameter selection

NEUROCOMPUTING 2025年 623卷

作者： Luo, Linkai Yang, Qiaoling Peng, Hong Wang, Yiding Chen, Ziyang Xiamen Univ Dept Automat Xiamen 361102 Peoples R China Xiamen Key Lab Big Data Intelligent Anal & Decis M Xiamen 361102 Peoples R China

The selection of Gaussian kernel parameters plays an important role in the applications of support vector classification (SVC). A commonly used method is the k-fold cross validation with grid search (CV), which is extremely time-consuming because it needs to train a large number of SVC models. In this paper, a new approach is proposed to train SVC and optimize the selection of Gaussian kernel parameters. We first formulate the training and the parameter selection of SVC as a minimax optimization problem named as MaxMin-L2-SVCNCH, in which the minimization problem is an optimization problem of finding the closest points between two normal convex hulls (L2-SVC-NCH) while the maximization problem is an optimization problem of finding the optimal Gaussian kernel parameters. A lower time complexity can be expected in MaxMin-L2-SVC-NCH because CV is not needed. We then propose a projected gradient algorithm (PGA) for the training of L2-SVC-NCH. It is revealed that the famous sequential minimal optimization (SMO) algorithm is a special case of the PGA. Thus, the PGA can provide more flexibility than the SMO. Furthermore, the solution of the maximization problem is done by a gradient ascent algorithm with dynamic learning rate. The comparative experiments between MaxMin-L2-SVC-NCH and the previous best approaches on public datasets show that MaxMin-L2-SVC-NCH greatly reduces the number of models to be trained while maintaining competitive test accuracy. These findings indicate that MaxMin-L2-SVC-NCH is a better choice for SVC tasks.

关键词： Support vector classification The selection of kernel parameters Minimax optimization Closest points Normal convex hull projected gradient algorithm

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Joint dictionary and deep learning for cosparse recovery of the millimeter wave massive MIMO channels

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JOURNAL OF ENGINEERING-JOE 2022年第3期2022卷 371-376页

作者： Hajjaj, Moufida Univ Carthage Higher Sch Commun Tunis Innov COM Lab Ariana 2083 Tunisia

The channel estimation (CE) for millimeter wave (mmW) massive multiple input multiple output (mMIMO) is a challenging task because of the important number of transmit and receive antennas, which results in high pilot overhead. In conventional CE algorithms, the channel is modeled using pre-constructed dictionary. This often leads to a suboptimal solution which cannot guarantee CE accuracy. In this paper, an iterative two-stage CE algorithm is presented. In the first stage, training measurements under different conditions are collected and it is proposed to estimate the virtual sparse mmW mMIMO channel using a deep residual learning based orthogonal approximate message passing (DRL-OAMP) algorithm from these measurements. The estimated channel is used in the second stage to learn the dictionary via a projected gradient algorithm. Simulation results show that the proposal improves the CE accuracy with low pilot overhead.

关键词： low pilot overhead two-stage CE algorithm millimeter wave massive MIMO channels conventional CE algorithms virtual sparse mmW mMIMO channel 5G mobile communication joint dictionary high pilot overhead deep learning receiving antennas projected gradient algorithm learning (artificial intelligence) estimated channel gradient methods wireless channels millimetre wave communication deep learning (artificial intelligence) deep residual learning channel estimation cosparse recovery MIMO communication message passing telecommunication computing CE accuracy millimeter wave massive multiple input multiple output

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Learning Multiple Quantiles With Neural Networks

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2021年第4期30卷 1238-1248页

作者： Moon, Sang Jun Jeon, Jong-June Lee, Jason Sang Hun Kim, Yongdai Univ Seoul Dept Stat Seoul South Korea Univ Seoul Dept Phys Seoul South Korea Seoul Natl Univ Dept Stat Seoul South Korea

We present a neural network model for estimation of multiple conditional quantiles that satisfies the noncrossing property. Motivated by linear noncrossing quantile regression, we propose a noncrossing quantile neural network model with inequality constraints. In particular, to use the first-order optimization method, we develop a new algorithm for fitting the proposed model. This algorithm gives a nearly optimal solution without the projected gradient step that requires polynomial computation time. We compare the performance of our proposed model with that of existing neural network models on simulated and real precipitation data. for this article are available online.

关键词： Deep learning Feed-forward neural network Interior point algorithm projected gradient algorithm Quantile regression

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Generalized conditional gradient method for elastic-net regularization

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2022年第0期403卷 113872-113872页

作者： Li, Hailong Ding, Liang Northeast Forestry Univ Dept Math Harbin 150040 Peoples R China

Iterative soft thresholding algorithm (ISTA) has a simple formulation and it can easily be implemented. Nevertheless, ISTA is limited to well-conditioned problems, e.g. compressive sensing. In this paper, we present an ISTA type algorithm based on the generalized conditional gradient method (GCGM) to solve elastic-net regularization which is commonly adopted in ill-conditioned problems. Furthermore, we propose a projected gradient (PG) method to accelerate the ISTA type algorithm. In addition, we discuss the existence of the radius R and we give a strategy to determine the radius R of the l1-ball constraint in the PG method by Morozov's discrepancy principle (MDP). Numerical results are reported to illustrate the efficiency of the proposed approach. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Ill-posed problem Elastic-net regularization Generalized conditional gradient method projected gradient algorithm

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H2 Model Reduction of Linear Network Systems by Moment Matching and Optimization

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2020年第12期65卷 5328-5335页

作者： Necoara, Ion Ionescu, Tudor C. Univ Politehn Bucuresti Dept Automat Control & Syst Engn Bucharest 060042 Romania Romanian Acad G Mihoc C Iacob Inst Math Stat & Appl Math Bucharest 050711 Romania

In this article, we compute the reduced-order stable approximation of a linear network system, preserving the topology and optimal w.r.t. the H-2-norm of the approximation error. Our approach is based on time-domain moment matching, where we optimize over families of parameterized reduced-order models, matching moments at arbitrary interpolation points. The low-order models are parametrized in the free parameters (i.e., the elements of the input matrix) and the interpolation matrix. We formulate an optimization-based problem with the H-2-norm of the error as the objective function and with structural and physical properties as the constraints. The problem is nonconvex and we write it in terms of the Gramians of the error system. We propose two solutions. The first solution assumes that the error system admits a block diagonal observability Gramian, allowing for a simple convex reformulation as semidefinite programming, but at the cost of some performance loss. We also derive the sufficient conditions to guarantee the block diagonalization of the Gramian. The second solution employs a gradient projection method for a smooth reformulation, yielding the (locally) optimal interpolation points and free parameters. The potential of the methods is illustrated on a positive network and a power network.

关键词： Reduced order systems Interpolation Time-domain analysis Observability Stability analysis Network topology Linear systems Network systems model reduction optimal H2 norm moment matching nonconvex optimization projected gradient algorithm

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Fractional spectral collocation method for optimal control problem governed by space fractional diffusion equation

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APPLIED MATHEMATICS AND COMPUTATION 2019年 350卷 331-347页

作者： Li, Shengyue Zhou, Zhaojie Shandong Normal Univ Sch Math & Stat Jinan Shandong Peoples R China

In this paper, we mainly investigate the fractional spectral collocation discretization of optimal control problem governed by a space-fractional diffusion equation. Existence and uniqueness of the solution to optimal control problem is proved. The continuous first order optimality condition is derived. The eigenfunctions of two classes of fractional Strum-Liouville problems are used as basis functions to approximate state variable and adjoint state variable, respectively. The fractional spectral collocation scheme for the control problem is constructed based on 'first optimize, then discretize' approach. Note that the solutions of fractional differential equations are usually singular near the boundary, a generalized fractional spectral collocation scheme for the control problem is proposed based on 'first optimize, then discretize' approach. A projected gradient algorithm is designed based on the discrete optimality condition. Numerical experiments are carried out to verify the effectiveness of the proposed numerical schemes and algorithm. (C) 2019 Elsevier Inc. All rights reserved.

关键词： Fractional spectral collocation method Optimal control problem Space-fractional diffusion equation Optimality condition projected gradient algorithm

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Real-time Traffic Information Based Load Forecasting and Economical Dispatch of Electric Vehicles 31

Real-time Traffic Information Based Load Forecasting and Eco...

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31st Chinese Control And Decision Conference (CCDC)

作者： Dou, Chunxia Zhang, Yong Zhang, Tengfei Nanjing Univ Posts & Telecommun Inst Avanced Technol Nanjing 210023 Peoples R China Nanjing Univ Posts & Telecommun Sch Automat Nanjing 210023 Peoples R China

ISBN: (纸本)9781728101057

With the popularity of electric vehicles, the charging load of electric vehicles has gradually become a challenge to the power grid's stability. Therefore, the load forecasting of the electric vehicle is the premise of analyzing the influence of the electric vehicle to the power grid, and it is also the basis of the power grid operation and dispatch. Traditional prediction methods need the support of large data and the prediction results are weak in pertinence. Therefore, a method is proposed to further optimize the results by combining Bureau of Public Road path resistance function(BPR) and the extreme learning machine, so as to make the prediction results effective. Finally, the projected gradient algorithm is used to optimize the dispatch plan of the power grid containing wind power based on the predicted power demand of the electric vehicles, so as to achieve the most economical operation of the power grid.

关键词： electric vehicles load forecasting Extreme Learning Machine projected gradient algorithm economic dispatch

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Legendre pseudo-spectral method for optimal control problem governed by a time-fractional diffusion equation

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2018年第6-7期95卷 1308-1325页

作者： Li, Shengyue Zhou, Zhaojie Shandong Normal Univ Coll Math & Stat Jinan Shandong Peoples R China

This paper presents a numerical scheme for optimal control problem governed by a time-fractional diffusion equation based on a Legendre pseudo-spectral method for space discretization and a finite difference method for time discretization. Lagrange interpolating basis polynomials are used to approximate the state, and the differentiation matrix is derived to discrete the spatial derivative. We also discuss the fully discrete scheme for the control problem. A finite difference method developed in Lin and Xu [Finite difference/spectral approximations for the time-fractional diffusion equation, J. Comput. Phys. 225 (2007), pp. 1533-1552] is used to discretize the time-fractional derivative. A fully discrete first-order optimality condition is developed based on the first discretize, then optimize' approach. Furthermore, we design the projected gradient algorithm based on the fully discrete optimality conditions. Numerical examples are given to illustrate the feasibility of the proposed method.

关键词： Legendre pseudo-spectral method optimal control problem time-fractional diffusion equation optimality conditions projected gradient algorithm

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An alternating projected gradient algorithm for nonnegative matrix factorization

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APPLIED MATHEMATICS AND COMPUTATION 2011年第24期217卷 9997-10002页

作者： Lin, Lu Liu, Zhong-Yun Xiamen Univ Sch Math Sci Xiamen 361005 Peoples R China Changsha Univ Sci & Technol Sch Math Changsha 410076 Hunan Peoples R China

Due to the extensive applications of nonnegative matrix factorizations (NMFs) of nonnegative matrices, such as in image processing, text mining, spectral data analysis, speech processing, etc., algorithms for NMF have been studied for years. In this paper, we propose a new algorithm for NMF, which is based on an alternating projected gradient (APG) approach. In particular, no zero entries appear in denominators in our algorithm which implies no breakdown occurs, and even if some zero entries appear in numerators new updates can always be improved in our algorithm. It is shown that the effect of our algorithm is better than that of Lee and Seung's algorithm when we do numerical experiments on two known facial databases and one iris database. (C) 2011 Elsevier Inc. All rights reserved.

关键词： Nonnegative matrix factorization projected gradient algorithm Multiplicative updating method Low-rank decomposition

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Spectral Minimal Partitions for a Family of Tori

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EXPERIMENTAL MATHEMATICS 2017年第4期26卷 381-395页

作者： Bonnaillie-Noel, Virginie Lena, Corentin PSL Res Univ CNRS ENS Paris Dept Math & Leurs Applicat Paris France Univ Torino Dipartimento Matemat Giuseppe Peano Via Carlo Alberto 10 I-10123 Turin TO Italy

We study partitions of the two-dimensional flat torus into k domains, with b a real parameter in (0, 1] and k an integer. We look for partitions which minimize the energy, defined as the largest first eigenvalue of the Dirichlet Laplacian on the domains of the partition. We are in particular interested in the way these minimal partitions change when b is varied. We present here an improvement, when k is odd, of the results on transition values of b established by B. Helffer and T. Hoffmann-Ostenhof (2014) and state a conjecture on those transition values. We establish an improved upper bound of the minimal energy by explicitly constructing hexagonal tilings of the torus. These tilings are close to the partitions obtained from a systematic numerical study based on an optimization algorithm adapted from B. Bourdin, D. Bucur, and E. Oudet (2009). These numerical results also support our conjecture concerning the transition values and give better estimates near those transition values.

关键词： Dirichlet-Laplacian eigenvalues finite difference method minimal partitions projected gradient algorithm shape optimization

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