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REDUCED-RANK MODELING FOR HIGH-DIMENSIONAL MODEL-BASED CLUSTERING

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Journal of Computational mathematics 2018年第3期36卷 426-440页

作者： Lei Yang Junhui Wang Shiqian ma Department of Environmental Medicine New York University New York NY USA Department of mathematics City University of Hong Kong Kowloon Tong Hong Kong Department of mathematics University of California Davis CA 95616 USA

Model-based clustering is popularly used in statistical literature, which often models the data with a Gaussian mixture model. As a consequence, it requires estimation of a large amount of parameters, especially when the data dimension is relatively large, in this paper, reduced-rank model and group-sparsity regularization are proposed to equip with the model-based clustering, which substantially reduce the number of parameters and thus facilitate the high-dimensional clustering and variable selection simultaneously. We propose an EM algorithm for this task, in which the M-step is solved using alternating minimization. One of the alternating steps involves both nonsmooth function and nonconvex constraint, and thus we propose a linearized alternating direction method of multipliers （ADMM） for solving it. This leads to an efficient algorithm whose subproblems are all easy to solve. In addition, a model selection criterion based on the concept of clustering stability is developed for tuning the clustering model. The effectiveness of the proposed method is supported in a variety of simulated and real examples, as well as its asymptotic estimation and selection consistencies.

关键词： Clustering Gaussian mixture model Group Lasso ADMM Reduced-rankmodel

Adaptive composite frequency control of power systems using reinforcement learning

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CAAI Transactions on Intelligence Technology 2022年第4期7卷 671-684页

作者： Chaoxu Mu Ke Wang Shiqian ma Zhiqiang Chong Zhen Ni School of Electrical and Information Engineering Tianjin UniversityTianjinChina State Grid Tianjin Electric Power Company Electric Power Research Institute TianjinChina Department of Electrical Engineering and Computer Science Florida Atlantic UniversityBoca RatonFLUSA

With the incorporation of renewable energy,load frequency control(LFC)becomes more challenging due to uncertain power generation and changeable load demands.The electric vehicle(EV)has been a popular transportation and can also provide flexible options to play a role in frequency regulation.In this paper,a novel adaptive composite controller is designed to solve the LFC problem for the interconnected power system with electric vehicles and wind turbine.EVs are used as regulation resources to effectively compensate the power mismatch.First,the sliding mode controller is developed to reduce the random influences caused by the wind turbine generation system.Second,an auxiliary controller with reinforcement learning is proposed to produce adaptive control signals,which will be attached to the primary proportion-integration-differentiation control signal in a realtime manner.Finally,by considering random wind power,load disturbances and output constraints,the proposed scheme is verified on a two-area power system under four different cases.Simulation results demonstrate that the proposed adaptive composite frequency control scheme has a competitive performance with regard to dynamic performance.

关键词： power composite attached

Alternating Direction Method of Multipliers for Sparse Principal Component Analysis

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Journal of the Operations Research Society of China 2013年第2期1卷 253-274页

作者： Shiqian ma Department of Systems Engineering and Engineering management The Chinese University of Hong KongShatinNTHong Kong

We consider a convex relaxation of sparse principal component analysisproposed by d' Aspremont et al. (SIAM Rev. 49:434 448, 2007). This convex relax-ation is a nonsmooth semidefinite programming problem in which the ξ1 norm of thedesired matrix is imposed in either the objective function or the constraint to improvethe sparsity of the resulting matrix. The sparse principal component is obtained by arank- one decomposition of the resulting sparse matrix. We propose an alternating di-rection method based on a variable-splitting technique and an augmented I agrangianframework for solving this nonsmooth semidefinite programming problem. In con-trast to the first-order method proposed in d' Aspremont et al. (SIAM Rev. 49:434448, 2007), which solves approximately the dual problem of the original semidefiniteprogramming problem, our method deals with the primal problem directly and solvesit exactly, which guarantees that the resulting matrix is a sparse matrix. A globalconvergence result is established for the proposed method. Numerical results on bothsynthetic problems and the real applications from classification of text data and senatevoting data are reported to demonstrate the efficacy of our method.

关键词： Sparse PCA Semidefinite programming Alternating direction method Augmented L agrangian method Deflation Projection onto the simplex

A Novel Design Framework for Smart Operating Robot in Power System

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IEEE/CAA Journal of Automatica Sinica 2018年第2期5卷 531-538页

作者： Qiang Wang Xiaojing Yang Zhigang Huang Shiqian ma Qiao Li David Wenzhong Gao Fei-Yue Wang State Grid Tianjin Electric Power Company Tianjin 300010 China State Grid Tianjin Electric Power Research Institute Tianjin 300384 China University of Denver Denver Colorado 80210 USA Institute of Automation Chinese Academy of Sciences Beijing 100190 China IEEE

This paper proposes the concept and framework of smart operating system based on the artificial intelligence(AI)techniques. The demands and the potential applications of AI technologies in power system control centers is discussed in the beginning of the paper. The discussion is based on the results of a field study in the Tianjin Power System Control Center in China. According to the study, one problem in power systems is that the power system analysis system in the control center is not fast and powerful enough to help the operators in time to deal with the incidents in the power system. Another issue in current power system control center is that the operation tickets are compiled manually by the operators, so that it is less efficient and human errors cannot be avoided. Based on these problems, a framework of the smart operating robot is proposed in this paper, which includes an intelligent power system analysis system and a smart operation ticket compiling system to solve the two problems in power system control centers. The proposed framework is mainly based on the AI techniques, especially the neural network with deep learning, since it is faster and more capable of dealing with the highly nonlinear and complex power system.

关键词： Artificial intelligence deep learning human-inthe-loop power system control center power system operating robot machine learning

Dual-stage constructed random graph algorithm to generate random graphs featuring the same topological characteristics with power grids

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Journal of Modern Power Systems and Clean Energy 2017年第5期5卷 683-695页

作者： Shiqian ma Yixin YU Lei ZHAO State Grid Tianjin Electric Power Research Institute Tianjin 300384China Key Laboratory of Smart Grid of Ministry of Education Tianjin UniversityTianjin 300072China

It is a common practice to simulate some historical or test systems to validate the efficiency of new methods or concepts. However, there are only a small number of existing power system test cases, and validation and evaluation results, obtained using such a limited number of test cases, may not be deemed sufficient or convincing. In order to provide more available test cases, a new random graph generation algorithm, named ‘‘dualstage constructed random graph’’ algorithm, is proposed to effectively model the power grid topology. The algorithm generates a spanning tree to guarantee the connectivity of random graphs and is capable of controlling the number of lines precisely. No matter how much the average degree is,whether sparse or not, random graphs can be quickly formed to satisfy the requirements. An approach is developed to generate random graphs with prescribed numbers of connected components, in order to simulate the power grid topology under fault conditions. Our experimental study on several realistic power grid topologies proves that the proposed algorithm can quickly generate a large number of random graphs with the topology characteristics of real-world power grid.

关键词： Power gird topology Dual-stage constructed random graph(DSCRG)algorithm Random graph generation Connectivity Average degree Connected component

Applications of gauge duality in robust principal component analysis and semidefinite programming

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Science China mathematics 2016年第8期59卷 1579-1592页

作者： ma shiqian YANG JunFeng Department of Systems Engineering and Engineering management The Chinese University of Hong Kong Department of mathematics Nanjing University

Gauge duality theory was originated by Freund(1987), and was recently further investigated by Friedlander et al.(2014). When solving some matrix optimization problems via gauge dual, one is usually able to avoid full matrix decompositions such as singular value and/or eigenvalue decompositions. In such an approach,a gauge dual problem is solved in the first stage, and then an optimal solution to the primal problem can be recovered from the dual optimal solution obtained in the first stage. Recently, this theory has been applied to a class of semidefinite programming(SDP) problems with promising numerical results by Friedlander and mac?edo(2016). We establish some theoretical results on applying the gauge duality theory to robust principal component analysis(PCA) and general SDP. For each problem, we present its gauge dual problem, characterize the optimality conditions for the primal-dual gauge pair, and validate a way to recover a primal optimal solution from a dual one. These results are extensions of Friedlander and mac?edo(2016) from nuclear norm regularization to robust PCA and from a special class of SDP which requires the coefficient matrix in the linear objective to be positive definite to SDP problems without this restriction. Our results provide further understanding in the potential advantages and disadvantages of the gauge duality theory.

关键词：主成分分析半定规划应用稳健对偶理论范性矩阵分解特征值分解

1-Neighbour knapsack problem and prospective greedy algorithm of intentional islanding in active distribution network

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Science China(Technological Sciences) 2014年第3期57卷 568-577页

作者： YU YiXin ma shiqian Key Laboratory of Smart Grid of Ministry of Education Tianjin University

A connected and undirected graph model of active distribution networks with considering the function of interconnecting switches is constructed in this paper.Based on this model,the island partition problem of active distribution networks can be described as a 1-neighbour knapsack problem.An effective heuristic algorithm named prospective greedy algorithm is then proposed to solve this problem.Case studies on PG&E 69-bus network show the validity of the proposed model and algorithm.

关键词：背包问题配电网贪婪算法孤岛故意启发式算法分销网络划分问题

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机器学习中的双层优化算法简介

计算数学 2024年第2期46卷 129-143页

作者：马士谦莱斯大学计算应用数学与运筹学系休斯顿TX77005美国

双层优化是近年来的一个热门研究方向.这主要归功于机器学习的兴起和双层优化在机器学习中的许多重要应用.本文对双层优化的算法、理论及应用最近几年的发展做一个简要的介绍内容主要包括双层优化的历史,双层优化在电力系统,超参优化,... 详细信息

双层优化是近年来的一个热门研究方向.这主要归功于机器学习的兴起和双层优化在机器学习中的许多重要应用.本文对双层优化的算法、理论及应用最近几年的发展做一个简要的介绍内容主要包括双层优化的历史,双层优化在电力系统,超参优化,元学习等领域的应用,以及双层优化的算法设计和理论保证。算法方面我们主要分两种情况:下层问题是强凸问题和下层问题是一般凸问题,这里我们会讨论梯度法和基于下层最优函数的方法.我们也会重点讨论分布式网络中的双层优化,包括去中心化的双层优化和联邦双层优化的算法和理论分析.

关键词：双层优化一阶算法超参优化元学习去中心化计算联邦学习

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带先验约束的地表参数提取的有效反演方法

中国科学（D辑） 2009年第3期39卷 360-369页

作者：王彦飞 Shiqian ma 杨华王锦地李小文中国科学院地质与地球物理研究所油气综合地球物理重点实验室北京100029 北京师范大学遥感与GIS中心北京100875 北京师范大学与中国科学院遥感应用研究所联合遥感科学国家重点实验室北京100875 Department of Industrial Engineering and Operations Research Columbia University New York NY 10027-6902 USA

地球表面的各向异性特性可以用地表二向反射函数(BRDF)恰当地描述.BRDF的核心是利用线性核驱动模型,数学上表述为各向同性核、体散射核和几何光学核的线性组合.随着多角度遥感领域的发展,BRDF模型越来越被看作是可以反演重要的有关地表... 详细信息

地球表面的各向异性特性可以用地表二向反射函数(BRDF)恰当地描述.BRDF的核心是利用线性核驱动模型,数学上表述为各向同性核、体散射核和几何光学核的线性组合.随着多角度遥感领域的发展,BRDF模型越来越被看作是可以反演重要的有关地表生物的或气候的参数,比如说叶面积指数和地表反照率.一个线性逼近的核驱动BRDF模型通常可以写成下述形式(Roujean等,1992):fiso+kvol(ti,tv,φ)fvol+kgeo(ti,tv,φ)fgeo=r(ti,tv,φ),其中r表示地表的二向反射;kvol和kgeo为通常所说的核函数,即为已知的入射和观测几何特性的函数,分别描述了体散射和几何散射(包括折射和反射);ti是太阳方向天顶角,tv是观测方向天顶角;φ表示太阳-观测方向的相对方位角;fiso,fvol和fgeo为未知的待反演参数,可以用来拟合观测.计算过程的稳定性是由核矩阵的代数算子特征谱和观测噪音/误差来刻画的.因此为了计算地表反照率,成功反演模型参数是至关重要的环节.我们首先考虑了为计算BRDF模型反演的光滑解方法.业已知道,这是一个不适定的反问题.不适定性是由线性核驱动BRDF模型的欠定性表征的,比如说观测严重不足或观测方向范围有限,或者是观测数据高度线性相关以及噪音的污染等.例如,一次单角度观测可以导致一个欠定的系统(核算子的零空间含有非零向量)或者系统无解(系数矩阵的秩不等于增广矩阵的秩).因此,光滑性或正则化技巧应当加以利用来压制不适定性.Li等(2001)应用先验知识把原始模型转换为一个超定的模型并求得最小二乘解.Pokrovsky等(2002)应用QR分解反演BRDF模型.Wang等(2007)考虑到了反演的正则化策略并提出了不适定地表参数反演的一个完整的正则化理论.在文中,强调从不同的空间添加先验信息于反演模型中.首先从数学物理的观点,第一次提出了一个用于反演的施加先验约束的一般的正则化模型,接着阐述了两种正则化策略.第一个是正则化的奇异值分解方法(Wang等,2007),接着提出了一个基于l1空间的反演方法.我们证明了新提出的方法对于有效观测数据不足情况下反演地表参数是可行的,并通过数值试验验证了新提出方法的反演有效性.

关键词：不适定问题地表参数提取最优化正则化