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fixed-point blind source separation algorithm based on ICA

Frontiers of Electrical and Electronic Engineering in China 2008年第3期3卷 343-346页

作者： Hongyan LI Jianfen MA Deng’ao LI Huakui WANG College of Information Engineering Taiyuan University of TechnologyTaiyuan 030024China

This paper introduces the fixed-point learning algorithm based on independent component analysis(ICA);the model and process of this algorithm and simulation results are *** was adopted as the estimation rule of *** results of the experiment show that compared with the traditional ICA algorithm based on random grads,this algorithm has advantages such as fast convergence and no necessity for any dynamic parameter,*** algorithm is a highly efficient and reliable method in blind signal separation.

关键词： independent component analysis(ICA) blind source separation fixed-point algorithm

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fixed-point Minimum Error Entropy With Fiducial points

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2020年 68卷 3824-3833页

作者： Xie, Yuqing Li, Yingsong Gu, Yuantao Cao, Jiuwen Chen, Badong Xi An Jiao Tong Univ Inst Artificial Intelligence & Robot Xian 710049 Peoples R China Harbin Engn Univ Coll Informat & Commun Engn Harbin 150001 Peoples R China Tsinghua Univ Beijing Natl Res Ctr Informat Sci & Technol Dept Elect Engn Beijing 100084 Peoples R China Hangzhou Dianzi Univ Key Lab IOT & Informat Fus Technol Zhejiang Hangzhou 310018 Peoples R China

Compared with traditional learning criteria, such as minimum mean square error (MMSE), the minimum error entropy (MEE) criterion has received increasing attention in the domains of nonlinear and non-Gaussian signal processing and machine learning. Since the MEE criterion is shift-invariant, one has to add a bias to achieve zero-mean error over training datasets. Thus, a modification of the MEE called minimization of error entropy with fiducial points (MEEF) was proposed, which controls the bias for MEE in a more elegant and efficient way. In the present paper, we propose a fixed-point minimization of error entropy with fiducial points (MEEF-FP) as an alternative to the gradient based MEEF for training a linear-in-parameters (LIP) model because of its fast convergence speed, robustness and step-size free. Also, we provide a sufficient condition that guarantees the convergence of the MEEF-FP algorithm. Moreover, we develop a recursive MEEF-FP (RMEEF-FP) for online adaptive learning with low-complexity. Finally, illustrative examples are presented to show the excellent performance of the new methods.

关键词： Entropy Convergence Lips Training Kernel Adaptation models Signal processing algorithms Minimum error entropy (MEE) correntropy fixed-point algorithm linear-in-parameters model convergence analysis

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fixed-point CONTINUATION APPLIED TO COMPRESSED SENSING:IMPLEMENTATION AND NUMERICAL EXPERIMENTS

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Journal of Computational Mathematics 2010年第2期28卷 170-194页

作者： Elaine T.Hale Department of Computational and Applied Mathematics Rice University

fixed-point continuation （FPC） is an approach, based on operator-splitting and continuation, for solving minimization problems with l1-regularization：min ｜｜x｜｜1＋uf（x）.We investigate the application of this algorithm to compressed sensing signal recovery, in which f（x） = 1/2｜｜Ax-b｜｜2M,A∈m×n and m≤n. In particular, we extend the original algorithm to obtain better practical results, derive appropriate choices for M and u under a given measurement model, and present numerical results for a variety of compressed sensing problems. The numerical results show that the performance of our algorithm compares favorably with that of several recently proposed algorithms.

关键词： l1 regularization fixed-point algorithm Continuation Compressed sensing,Numerical experiments.

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fixed-point accelerated iterative method to solve nonlinear matrix equation X - Σi=1^mAi*X^-1Ai = Q

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COMPUTATIONAL & APPLIED MATHEMATICS 2022年第8期41卷 1-13页

作者： Li, Tong Peng, Jingjing Peng, Zhenyun Tang, Zengao Zhang, Yongshen Guilin Univ Elect Technol Coll Math & Computat Sci Guilin 541004 Peoples R China

Nonlinear matrix equation X - Sigma(m)(i=1) A(i)*X(-1)A(i) = Q has wide applications in control theory, dynamic planning, interpolation theory and random filtering. In this paper, a fixed-point accelerated iteration method is proposed, and based on the basic characteristics of the Thompson distance, the convergence and error estimation of the proposed algorithm are proved. Numerical comparison experiments show that the proposed algorithm is feasible and effective.

关键词： Nonlinear matrix equation fixed-point algorithm Anderson acceleration algorithm Thompson distance

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fixed-point CONTINUATION FOR l₁-MINIMIZATION: METHODOLOGY AND CONVERGENCE

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SIAM JOURNAL ON OPTIMIZATION 2008年第3期19卷 1107-1130页

作者： Hale, Elaine T. Yin, Wotao Zhang, Yin Rice Univ Dept Computat & Appl Math Houston TX 77005 USA

We present a framework for solving the large-scale l(1)-regularized convex minimization problem: min parallel to x parallel to(1) + mu f(x). Our approach is based on two powerful algorithmic ideas: operator-splitting and continuation. Operator-splitting results in a fixed-point algorithm for any given scalar mu;continuation refers to approximately following the path traced by the optimal value of x as mu increases. In this paper, we study the structure of optimal solution sets, prove finite convergence for important quantities, and establish q-linear convergence rates for the fixed-point algorithm applied to problems with f(x) convex, but not necessarily strictly convex. The continuation framework, motivated by our convergence results, is demonstrated to facilitate the construction of practical algorithms.

关键词： l(1) regularization fixed-point algorithm q-linear convergence continuation compressed sensing

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fixed-point generalized maximum correntropy: Convergence analysis and convex combination algorithms

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SIGNAL PROCESSING 2019年 154卷 64-73页

作者： Zhao, Ji Zhang, Hongbin Wang, Gang Univ Elect Sci & Technol China Sch Elect Engn Chengdu 611731 Sichuan Peoples R China

Compared with the MSE criterion, the generalized maximum correntropy (GMC) criterion shows a better robustness against impulsive noise. Some gradient based GMC adaptive algorithms have been derived and available for practice. But, the fixed-point algorithm on GMC has not yet been well studied in the literature. In this paper, we study a fixed-point GMC (FP-GMC) algorithm for linear regression, and derive a sufficient condition to guarantee the convergence of the FP-GMC. Also, we apply sliding-window and recursive methods to the FP-GMC to derive online algorithms for practice, these two called sliding-window GMC (SW-GMC) and recursive GMC (RGMC) algorithms, respectively. Since the solution of RGMC is not analyzable, we derive some approximations that fundamentally result in the poor convergence rate of the RGMC in non-stationary situations. To overcome this issue, we propose a novel robust filtering algorithm (termed adaptive convex combination of RGMC algorithms (AC-RGMC)), which relies on the convex combination of two RGMC algorithms with different memories. Moreover, by an efficient weight control method, the tracking performance of the AC-RGMC is further improved, and this new one is called AC-RGMC-C algorithm. The good performance of proposed algorithms are tested in plant identification scenarios with abrupt change under impulsive noise environment. (C) 2018 Published by Elsevier B.V.

关键词： Convergence fixed-point algorithm Convex combination Adaptive filter Non-Gaussian noise Generalized maximum correntropy (GMC) criterion

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A fixed-point method for a class of super-large scale nonlinear complementarity problems

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2014年第5期67卷 999-1015页

作者： Zhao, Jian Xun Tianjin Univ Sch Sci Dept Math Tianjin 300072 Peoples R China

We consider a class of complementarity problems involving functions which are nonlinear. In this paper we reformulate this nonlinear complementarity problem as a system of absolute value equations (which is nonsmooth). Then we propose a fixed-point method to solve this nonsmooth system. We prove that the proposed method is globally linearly convergent under a mild condition. The proposed method is greatly effective not only for small and medium size problems, but also for large and super-large scale problems. Especially, our method can efficiently solve super-large scale problems, with a million variables, in a few tens of minutes on a PC. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： fixed-point algorithm Absolute value equations Smoothing function Global convergence Q-linear convergence

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STOCHASTIC QUASI-FEJER BLOCK-COORDINATE fixed point ITERATIONS WITH RANDOM SWEEPING

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SIAM JOURNAL ON OPTIMIZATION 2015年第2期25卷 1221-1248页

作者： Combettes, Patrick L. Pesquet, Jean-Christophe Univ Paris 06 Sorbonne Univ UMR 7598 Lab Jacques Louis Lions F-75005 Paris France Univ Paris Est CNRS UMR 8049 Lab Informat Gaspard Monge F-77454 Marne La Vallee 2 France

This work proposes block-coordinate fixed point algorithms with applications to nonlinear analysis and optimization in Hilbert spaces. The asymptotic analysis relies on a notion of stochastic quasi-Fejer monotonicity, which is thoroughly investigated. The iterative methods under consideration feature random sweeping rules to select arbitrarily the blocks of variables that are activated over the course of the iterations and they allow for stochastic errors in the evaluation of the operators. algorithms using quasi-nonexpansive operators or compositions of averaged nonexpansive operators are constructed, and weak and strong convergence results are established for the sequences they generate. As a by-product, novel block-coordinate operator splitting methods are obtained for solving structured monotone inclusion and convex minimization problems. In particular, the proposed framework leads to random block-coordinate versions of the Douglas-Rachford and forward-backward algorithms and of some of their variants. In the standard case of m = 1 block, our results remain new as they incorporate stochastic perturbations.

关键词： arbitrary sampling block-coordinate algorithm fixed-point algorithm monotone operator splitting primal-dual algorithm stochastic quasi-Fejer sequence stochastic algorithm structured convex minimization problem

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Stochastic quasi-Fejer block-coordinate fixed point iterations with random sweeping II: mean-square and linear convergence

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MATHEMATICAL PROGRAMMING 2019年第1-2期174卷 433-451页

作者： Combettes, Patrick L. Pesquet, Jean-Christophe North Carolina State Univ Dept Math Raleigh NC 27695 USA Univ Paris Saclay CentraleSupelec Ctr Visual Comp F-92295 Chatenay Malabry France

Combettes and Pesquet (SIAM J Optim 25:1221-1248,2015) investigated the almost sure weak convergence of block-coordinate fixed point algorithms and discussed their applications to nonlinear analysis and optimization. This algorithmic framework features random sweeping rules to select arbitrarily the blocks of variables that are activated over the course of the iterations and it allows for stochastic errors in the evaluation of the operators. The present paper establishes results on the mean-square and linear convergence of the iterates. Applications to monotone operator splitting and proximal optimization algorithms are presented.

关键词： Block-coordinate algorithm fixed-point algorithm Mean-square convergence Monotone operator splitting Linear convergence Stochastic algorithm

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fixed-point Minimum Error Entropy With Sparsity Penalty Constraints

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2021年第8期68卷 2997-3001页

作者： Li, Jianxing Xie, Yuqing Dang, Lujuan Song, Chengtian Chen, Badong Xi An Jiao Tong Univ Sch Elect & Informat Engn Xian 710049 Peoples R China Beijing Inst Technol Sch Mech Engn Beijing 100081 Peoples R China

In recent years, the sparse system identification (SSI) has received increasing attention, and various sparsity-aware adaptive algorithms based on the minimum mean square error (MMSE) criterion have been developed, which are optimal under the assumption of Gaussian distributions. However, the Gaussian assumption does not always hold in real-world environments. The maximum correntropy criterion (MCC) is used to replace the MMSE criterion to suppress the heavy-tailed non-Gaussian noises. For some more complex non-Gaussian noises such as those from multimodal distributions, the minimum error entropy (MEE) criterion can outperform MCC although it is computationally somewhat more expensive. To improve the performance of SSI in non-Gaussian noises, in this brief we develop a class of sparsity-aware MEE algorithms with the fixed point iteration (MEE-FP) by incorporating the zero-attracting (l(1)-norm), reweighted zero-attracting (reweighted l(1)-norm) and correntropy induced metric (CIM) penalty terms into the cost function. The corresponding algorithms are termed as ZA-MEE-FP, RZA-MEE-FP, and CIM-MEE-FP, which can achieve better performance than the original MEE-FP algorithm and the MCC based sparsity-aware algorithms. Simulation results confirm the excellent performance of the new algorithms.

关键词： Sparse system identification minimum error entropy criterion fixed-point algorithm sparsity constraint non-Gaussian noises

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