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Estimating the Basin of Attraction for the Power Flow Equations in Power Distribution Networks

IEEE TRANSACTIONS ON POWER SYSTEMS 2024年第6期39卷 7457-7460页

作者： Garces-Ruiz, Alejandro Univ Tecnol Pereira Dept Elect Power Engn Pereira 660003 Colombia

This letter presents an inner and outer estimation for the basin of attraction of the power flow in power distribution networks. The proposed methodology can be used to define the convergence region of the power flow algorithm and to estimate the minimum and maximum voltage of the grid without explicitly solving the power flow equations. Numerical experiments in the three-phase unbalanced IEEE 906 nodes test system show the use of the proposed methodology. Results include convergence analysis as well as a quasi-dynamic simulation considering 1440 different scenarios of load and renewable power generation.

关键词： fixed-point algorithm power flow fixed-point algorithm three-phase unbalanced power distribution networks three-phase unbalanced power distribution networks quasi- dynamic power flow three-phase unbalanced power distribution networks

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Fast high-order matched filter for hyperspectral image target detection

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INFRARED PHYSICS & TECHNOLOGY 2018年 94卷 151-155页

作者： Yang, Shuo Song, Ziyang Yuan, Hongyi Zou, Zhengxia Shi, Zhenwei Beijing Electromech Engn Inst Beijing 100074 Peoples R China China Aerosp Sci & Ind Corp Ltd Acad 3 Satellite Operat Div HiWing Beijing 100070 Peoples R China Beihang Univ Sch Astronaut Image Proc Ctr Beijing 100191 Peoples R China

Hyperspectral image target detection is an important application for both of its civil and military uses. Traditional hyperspectral image target detection algorithms are usually designed based on the second-order statistics of the data where it is assumed that the target follows a Gaussian distribution. However, due to the low spatial resolution of the hyperspectral sensor, sometimes the targets of interest only occupy a few pixels. In this case, targets are more suitable to be described by high-order statistics. In this paper, we propose a fast high-order matched filter (FHMF) algorithm which describes the essence of the data more properly and then formulate the detection problem as an optimization problem. To solve the optimization problem efficiently, a fixed-point algorithm is proposed inspired by the FastICA algorithm of the signal processing field. The experiments are conducted with a synthetic hyperspectral image and a real hyperspectral image. The experiment results show that FHMF has better detection performance than other classical detection algorithms. In addition, the fast convergence speed also demonstrates the effectiveness of the proposed fixed-point algorithm.

关键词： Hyperspectral image Target detection Fast high-order matched filter (FHMF) fixed-point algorithm

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Maximum correntropy Kalman filter

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AUTOMATICA 2017年 76卷 70-77页

作者： Chen, Badong Liu, Xi Zhao, Haiquan Principe, Jose C. Xi An Jiao Tong Univ Sch Elect & Informat Engn Xian Peoples R China Southwest Jiaotong Univ Sch Elect Engn Chengdu Peoples R China Univ Florida Dept Elect & Comp Engn Gainesville FL 32611 USA

Traditional Kalman filter (KF) is derived under the well-known minimum mean square error (MMSE) criterion, which is optimal under Gaussian assumption. However, when the signals are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises, the performance of KF will deteriorate seriously. To improve the robustness of KF against impulsive noises, we propose in this work a new Kalman filter, called the maximum correntropy Kalman filter (MCKF), which adopts the robust maximum correntropy criterion (MCC) as the optimality criterion, instead of using the MMSE. Similar to the traditional KF, the state mean vector and covariance matrix propagation equations are used to give prior estimations of the state and covariance matrix in MCKF. A novel fixed-point algorithm is then used to update the posterior estimations. A sufficient condition that guarantees the convergence of the fixed-point algorithm is also given. Illustration examples are presented to demonstrate the effectiveness and robustness of the new algorithm. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Kalman filter Maximum correntropy criterion (MCC) fixed-point algorithm

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Complex correntropy function: Properties, and application to a channel equalization problem

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EXPERT SYSTEMS WITH APPLICATIONS 2018年 107卷 173-181页

作者： Guimaraes, Joao P. F. Fontes, Aluisio I. R. Rego, Joilson B. A. Martins, Allan de M. Principe, Jose C. Fed Inst Rio Grande Norte BR-59015300 Natal RN Brazil Univ Fed Rio Grande do Norte Dept Comp Engn & Automat BR-59078900 Natal RN Brazil Univ Florida Dept Elect & Comp Engn Gainesville FL 32611 USA

The use of correntropy as a similarity measure has been increasing in different scenarios due to the well-known ability to extract high-order statistic information from data. Recently, a new similarity measure between complex random variables was defined and called complex correntropy. Based on a Gaussian kernel, it extends the benefits of correntropy to complex-valued data. However, its properties have not yet been formalized. This paper studies the properties of this new similarity measure and extends this definition to positive-definite kernels. Complex correntropy is applied to a channel equalization problem as good results are achieved when compared with other algorithms such as the complex least mean square (CLMS), complex recursive least squares (CRLS), and least absolute deviation (LAD). (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Channel equalization Complex-valued data Correntropy fixed-point algorithm Maximum complex correntropy criterion Properties

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CONVERGENCE RATE ANALYSIS OF PRIMAL-DUAL SPLITTING SCHEMES

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SIAM JOURNAL ON OPTIMIZATION 2015年第3期25卷 1912-1943页

作者： Davis, Damek Univ Calif Los Angeles Dept Math Los Angeles CA 90025 USA Cornell Univ Sch Operat Res & Informat Engn Ithaca NY 14850 USA

Primal-dual splitting schemes are a class of powerful algorithms that solve complicated monotone inclusions and convex optimization problems that are built from many simpler pieces. They decompose problems that are built from sums, linear compositions, and infimal convolutions of simple functions so that each simple term is processed individually via proximal mappings, gradient mappings, and multiplications by the linear maps. This leads to easily implementable and highly parallelizable or distributed algorithms, which often obtain nearly state-of-the-art performance. In this paper, we analyze a monotone inclusion problem that captures a large class of primal-dual splittings as a special case. We introduce a unifying scheme and use some abstract analysis of the algorithm to prove convergence rates of the proximal point algorithm, forward-backward splitting, Peaceman-Rachford splitting, and forward-backward-forward splitting applied to the model problem. Our ergodic convergence rates are deduced under variable metrics, stepsizes, and relaxation parameters. Our nonergodic convergence rates are the first shown in the literature. Finally, we apply our results to a large class of primal-dual algorithms that are a special case of our scheme and deduce their convergence rates.

关键词： primal-dual algorithms convergence rates proximal point algorithm forward-backward splitting forward-backward-forward splitting nonexpansive operator Douglas-Rachford splitting Peaceman-Rachford splitting averaged operator fixed-point algorithm

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Structured Sparsity Optimization With Non-Convex Surrogates of l2,0-Norm: A Unified algorithmic Framework

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2023年第5期45卷 6386-6402页

作者： Zhang, Xiaoqin Zheng, Jingjing Wang, Di Tang, Guiying Zhou, Zhengyuan Lin, Zhouchen Wenzhou Univ Coll Comp Sci & Artificial Intelligence Wenzhou 325035 Zhejiang Peoples R China Xi An Jiao Tong Univ Ctr Intelligent Decis Making & Machine Learning Sch Management Xian 710049 Shaanxi Peoples R China Stanford Univ Dept Elect Engn Stanford CA 94305 USA Peking Univ Sch Intelligence Sci & Technol Key Lab Machine Percept MOE Beijing 100871 Peoples R China

this article, we present a general optimization framework that leverages structured sparsity to achieve superior recovery results. The traditional method for solving the structured sparse objectives based on L-2,L-0-norm is to use the L-2,L-1-norm as a convex surrogate. However, such an approximation often yields a large performance gap. To tackle this issue, we first provide a framework that allows for a wide range of surrogate functions (including non-convex surrogates), which exhibits better performance in harnessing structured sparsity. Moreover, we develop a fixed point algorithm that solves a key underlying non-convex structured sparse recovery optimization problem to global optimality with a guaranteed super-linear convergence rate. Building on this, we consider three specific applications, i.e., outlier pursuit, supervised feature selection, and structured dictionary learning, which can benefit from the proposed structured sparsity optimization framework. In each application, how the optimization problem can be formulated and thus be relaxed under a generic surrogate function is explained in detail. We conduct extensive experiments on both synthetic and real-world data and demonstrate the effectiveness and efficiency of the proposed framework.

关键词： Optimization Convergence Sparse matrices Machine learning Minimization Mathematical models Iterative algorithms Structured sparsity non-convex surrogate fixed-point algorithm

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Maximization by parts in likelihood inference

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2005年第472期100卷 1145-1158页

作者： Song, PXK Fan, YQ Kalbfleisch, JD Univ Waterloo Dept Stat & Actuarial Sci Waterloo ON N2L 3G1 Canada Vanderbilt Univ Dept Econ Nashville TN 37235 USA Univ Michigan Sch Publ Hlth Dept Biostat Ann Arbor MI 48109 USA

This article presents and examines a new algorithm for solving a score equation for the maximum likelihood estimate in certain problems of practical interest. The method circumvents the need to compute second-order derivatives of the full likelihood function. It exploits the structure of certain models that yield a natural decomposition of a very complicated likelihood function. In this decomposition, the first part is a log-likelihood from a simply analyzed model, and the second part is used to update estimates from the first part. Convergence properties of this iterative (fixed-point) algorithm are examined, and asymptotics are derived for estimators obtained using only a finite number of iterations. Illustrative examples considered in the article include multivariate Gaussian copula models, nonnormal random-effects models, generalized linear mixed models, and state-space models. Properties of the algorithm and of estimators are evaluated in simulation studies on a bivariate copula model and a nonnormal linear random-effects model.

关键词： copula model fixed-point algorithm generalized linear mixed model information dominance iterative algorithm nonnormal random effects score equation state-space model

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Implementation of new navigation algorithm based on cross-correntropy for precise positioning in low latitude regions of South India

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INTERNATIONAL JOURNAL OF SPEECH TECHNOLOGY 2020年第4期23卷 747-756页

作者： Sirish Kumar, P. Srilatha Indira Dutt, V. B. S. Ganesh, L. Aditya Inst Technol & Management Tekkali 532201 India GITAM Univ Visakhapatnam 530045 Andhra Pradesh India GVP Coll Engn Women Visakhapatnam 530048 Andhra Pradesh India

The objective of this article is to develop a new positioning algorithm to estimate the position accurately in low latitude region and assess the algorithm's performance in terms of accuracy and precision. The Kalman Filter (KF) has been widely recognized as one of the most powerful state estimation techniques in estimating system state variables and suppressing measurement noise. The Kalman Filter is desirable because the uncertainty in the Minimum Mean Square Error (MMSE) estimation can be minimized. In this article, we implemented a new algorithm called as Cross-Correntropy Kalman Filter (CCKF) to enhance the position accuracy and performance of the GPS receiver. Primarily the improvement depends on the Cross-Correntropy criterion which is a measure of local similarity, and a novel fixed-point algorithm for updating subsequent estimates. In this work, we present a thorough derivation of the method suggested, how to accurately measure the estimate of the GPS receiver position. Furthermore, in tabular forms, we provide a comparison of receiver position error (X, Y, Z coordinates) and performance metrics (2-D & 3-D) together with graphical representations for both algorithms (KF & CCKF).

关键词： Cross-correntropy Kalman filter Cross-correntropy Kalman filter fixed-point algorithm GPS

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New algorithms for M-estimation of multivariate scatter and location

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JOURNAL OF MULTIVARIATE ANALYSIS 2016年 144卷 200-217页

作者： Duembgen, Lutz Nordhausen, Klaus Schuhmacher, Heike Univ Bern CH-3012 Bern Switzerland Univ Turku SF-20500 Turku Finland

We present new algorithms for M-estimators of multivariate scatter and location and for symmetrized M-estimators of multivariate scatter. The new algorithms are considerably faster than currently used fixed-point and other algorithms. The main idea is to utilize a Taylor expansion of second order of the target functional and devise a partial Newton-Raphson procedure. In connection with symmetrized M-estimators we work with incomplete U-statistics to accelerate our procedures initially. (C) 2015 Elsevier Inc. All rights reserved.

关键词： fixed-point algorithm Matrix exponential function Newton-Raphson algorithm Taylor expansion

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Spatial independent component analysis of functional MRI time-series: To what extent do results depend on the algorithm used?

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HUMAN BRAIN MAPPING 2002年第3期16卷 146-157页

作者： Esposito, F Formisano, E Seifritz, E Goebel, R Morrone, R Tedeschi, G Di Salle, F Univ Naples Federico II Nuovo Policlin 2 Div Neuroradiol Dept Neurol Sci I-80127 Naples Italy Univ Naples 2 Inst Neurol Sci Naples Italy Maastricht Univ Dept Cognit Neurosci Maastricht Netherlands Univ Basel Dept Psychiat CH-4003 Basel Switzerland Morrone Diagnost Ctr Caserta Italy

Independent component analysis (ICA) has been successfully employed to decompose functional MRI (fMRI) time-series into sets of activation maps and associated time-courses. Several ICA algorithms have been proposed in the neural network literature. Applied to fMRI, these algorithms might lead to different spatial or temporal readouts of brain activation. We compared the two ICA algorithms that have been used so far for spatial ICA (sICA) of fMRI time-series: the Infomax (Bell and Sejnowski [1995]: Neural Comput 7:1004-1034) and the fixed-point (Hyvarinen [1999]: Adv Neural Inf Proc Syst 10:273-279) algorithms. We evaluated the Infomax- and fixed point-based sICA decompositions of simulated motor, and real motor and visual activation fMRI time-series using an ensemble of measures. Log-likelihood (McKeown et al. [1998]: Hum Brain Mapp 6:160-188) was used as a measure of how significantly the estimated independent sources fit the statistical structure of the data;receiver operating characteristics (ROC) and linear correlation analyses were used to evaluate the algorithms' accuracy of estimating the spatial layout and the temporal dynamics of simulated and real activations;cluster sizing calculations and an estimation of a residual gaussian noise term within the components were used to examine the anatomic structure of ICA components and for the assessment of noise reduction capabilities. Whereas both algorithms produced highly accurate results, the fixed-point outperformed the Infomax in terms of spatial and temporal accuracy as long as inferential statistics were employed as benchmarks. Conversely, the Infomax sICA was superior in terms of global estimation of the ICA model and noise reduction capabilities. Because of its adaptive nature, the Infomax approach appears to be better suited to investigate activation phenomena that are not predictable or adequately modelled by inferential techniques. (C) 2002 Wiley-Liss, Inc.

关键词： functional magnetic resonance imaging exploratory data-driven analysis independent component analysis fixed-point algorithm adaptive algorithm information maximization receiver operating characteristics Infomax algorithm

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