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A FAST projection algorithm FOR ADAPTIVE FILTERING

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 1995年第10期E78A卷 1355-1361页

作者： TANAKA, M KANEDA, Y MAKINO, S KOJIMA, J NTT Human Interface Lab Musashino-shi Japan

This paper proposes a new algorithm called the fast projection algorithm, which reduces the computational complexity of the projection algorithm from (p+1)L+O(p(3)) to 2L+20p (where L is the length of the estimation filter and p is the projection order.) This algorithm has properties that lie between those of NLMS and RLS, i.e. less computational complexity than RLS but much faster convergence than NLMS for input signals like speech. The reduction of computation consists of two parts. One concerns calculating the pre-filtering vector which originally took O(p(3)) operations. Our new algorithm computes the pre-filtering vector recursively with about 15p operations. The other reduction is accomplished by introducing an approximation vector of the estimation filter. Experimental results for speech input show that the convergence speed of the projection algorithm approaches that of RLS as the projection order increases with only a slight extra calculation complexity beyond that of NLMS, which indicates the efficiency of the proposed fast projection algorithm.

关键词： ADAPTIVE FILTERING projection algorithm COMPLEXITY REDUCTION

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COMBINING projection algorithm AND SCENARIO APPROACH FOR VIRTUAL REFERENCE FEEDBACK TUNING CONTROL

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INTERNATIONAL JOURNAL OF INNOVATIVE COMPUTING INFORMATION AND CONTROL 2019年第4期15卷 1337-1350页

作者： Jiang, Hong Wang, Jianhong Jingdezhen Ceram Inst Sch Mech & Elect Engn 86 Taoyang Rd Jingdezhen 333403 Peoples R China

The problem of designing two feedback controllers for an unknown plant based on measured data is discussed here in a linear setting. Virtual reference feedback tuning control is a direct method that aims at minimizing a cost function of the 2-norm type by using a set of data. When constructing the cost function, we consider two model-matching problems between closed loop transfer function and sensitivity function simultaneously. In these model-matching procedures, we analyze how to design the reference input signal and disturb signal respectively. After transforming the problem of identifying unknown parameter vectors in virtual reference feedback tuning control into two linear regression models, the projection algorithm is introduced to achieve our first on-line parameter estimation scheme. And we also see that the projection algorithm is equivalent to one optimization problem. Further in this paper, scenario optimization is used to determine the number of scenarios that determine the solution. The maximum number of data points that determine the so-called support points equals the number of optimization variables.

关键词： Virtual reference feedback tuning control Scenario program Parameter identification projection algorithm

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Discovering themes in biomedical literature using a projection-based algorithm

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BMC BIOINFORMATICS 2018年第1期19卷 1-12页

作者： Yeganova, Lana Kim, Sun Balasanov, Grigory Wilbur, W. John NIH Natl Ctr Biotechnol Informat Natl Lib Med Bldg 10 Bethesda MD 20892 USA

Background: The need to organize any large document collection in a manner that facilitates human comprehension has become crucial with the increasing volume of information available. Two common approaches to provide a broad overview of the information space are document clustering and topic modeling. Clustering aims to group documents or terms into meaningful clusters. Topic modeling, on the other hand, focuses on finding coherent keywords for describing topics appearing in a set of documents. In addition, there have been efforts for clustering documents and finding keywords simultaneously. Results: We present an algorithm to analyze document collections that is based on a notion of a theme, defined as a dual representation based on a set of documents and key terms. In this work, a novel vector space mechanism is proposed for computing themes. Starting with a single document, the theme algorithm treats terms and documents as explicit components, and iteratively uses each representation to refine the other until the theme is detected. The method heavily relies on an optimization routine that we refer to as the projection algorithm which, under specific conditions, is guaranteed to converge to the first singular vector of a data matrix. We apply our algorithm to a collection of about sixty thousand PubMed (R) documents examining the subject of Single Nucleotide Polymorphism, evaluate the results and show the effectiveness and scalability of the proposed method. Conclusions: This study presents a contribution on theoretical and algorithmic levels, as well as demonstrates the feasibility of the method for large scale applications. The evaluation of our system on benchmark datasets demonstrates that our method compares favorably with the current state-of-the-art methods in computing clusters of documents with coherent topic terms.

关键词： Theme discovery First singular vector projection algorithm

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A double-projection-based algorithm for large-scale nonlinear systems of monotone equations

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NUMERICAL algorithmS 2015年第2期68卷 213-228页

作者： Amini, Keyvan Kamandi, Ahmad Bahrami, Somayeh Razi Univ Dept Math Fac Sci Kermanshah Iran

In this paper, we propose a derivative free algorithm for solving large-scale nonlinear systems of monotone equations which combines a new idea of projection methodology with a line search strategy, while an improvement in the projection step is exerted. At each iteration, the algorithm constructs two appropriate hyperplanes which strictly separate the current approximation from the solution set of the problem. Then the new approximation is determined by projecting the current point onto the intersection of two halfspaces that are constructed by these hyperplanes and contain the solution set of the problem. Under some mild conditions, the global convergence of the algorithm is established. Preliminary numerical results indicate that the proposed algorithm is promising.

关键词： Nonlinear equations Monotone equations Derivative free methods projection algorithm

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An infeasible projection type algorithm for nonmonotone variational inequalities

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NUMERICAL algorithmS 2022年第4期89卷 1723-1742页

作者： Ye, Minglu China West Normal Univ Sch Math & Informat Nanchong Sichuan Peoples R China

It is well known that the monotonicity of the underlying mapping of variational inequalities plays a central role in the convergence analysis. In this paper, we propose an infeasible projection algorithm (IPA for short) for nonmonotone variational inequalities. The next iteration point of IPA is generated by projecting a vector onto a half-space. Hence, the computational cost of computing the next iteration point of IPA is much less than the algorithm of Ye and He (Comput. Optim. Appl. 60, 141-150, 2015) (YH for short). Moreover, if the underlying mapping is Lipschitz continuous with its modulus is known, by taking suitable parameters, IPA requires only one projection onto the feasible set per iteration. The global convergence of IPA is obtained when the solution set of its dual variational inequalities is nonempty. Moreover, if in addition error bound holds, the convergence rate of IPA is Q-linear. IPA can be used for a class of quasimonotone variational inequality problems and a class of quasiconvex minimization problems. Comparing with YH and algorithm 2 in Deng, Hu and Fang (Numer. Algor. 86, 191-221, 2021) (DHF for short) by solving high-dimensional nonmonotone variational inequalities, numerical experiments show that IPA is much more efficient than YH and DHF from CPU time point of view. Moreover, IPA is less dependent on the initial value than YH and DHF.

关键词： Variational inequalities projection algorithm Infeasible Quasimonotone Nonmonotone

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Electronic image stabilization method based on projection algorithm

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Guangzi Xuebao/Acta Photonica Sinica 2005年第8期34卷 1266-1269页

作者： Zhu, Juanjuan Guo, Baolong Feng, Zongzhe School of Electromechanical Engineering ICIE Institute Xidian Univ. Xi'an 710071 China

An analysis of the causes of image motion is made and a research on the characteristics of the unwanted camera motion and the intentional camera movement is carried out. And then an EIS method based on projection algorithm PMCA is presented. Original estimated motion vectors are smoothed through a moving average filter. An error propagation control method is used to prevent boundary error. Experimental results show that this algorithm can effectively smooth out the unwanted camera motion and follow the intentional camera movement.

关键词： Electronic image stabilization Motion compensation Motion correction Motion estimation projection algorithm

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Servo turntable adaptive step size momentum projection identification algorithm based on ARX model

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JOURNAL OF THE FRANKLIN INSTITUTE 2024年第5期361卷

作者： Liu, Zhiwen Cheng, Tianji Liu, Enhai Wang, Ranjun Chinese Acad Sci Natl Key Lab Opt Field Manipulat Sci & Technol Chengdu 610209 Peoples R China Chinese Acad Sci Inst Opt & Elect Chengdu 610209 Peoples R China Chinese Acad Sci Key Lab Sci & Technol Space Optoelect Precis Measu Chengdu 610209 Peoples R China Univ Chinese Acad Sci Beijing 100149 Peoples R China

In this paper, two improved projection algorithms are proposed for a servo turntable system based on the autoregressive exogenous (ARX) model. The improvement pertains to the complexity, convergence speed and estimation accuracy of the algorithm. First, the ARX model structure to be identified is obtained from the open -loop velocity model of the servo turntable. To solve the problems of imprecise step size calculation and slow convergence, the adaptive step size momentum projection (AMP) algorithm is proposed, in which segmented adaptive step sizes are adopted and momentum factors are introduced. On this basis, the latest estimation -based hierarchical adaptive step size momentum projection (LE -AMP) algorithm, which has faster convergence, is proposed as a combination of the hierarchical strategy and the latest estimation approach. Second, the complexity and convergence performance of the proposed algorithms are compared and analyzed. Finally, the effectiveness of the algorithms is verified using two examples. Theoretical analysis and simulation experiments show that the AMP algorithm has excellent parameter estimation accuracy, and its convergence speed is further improved through the addition of the momentum factor and the latest estimation, and these improved strategies do not cause any significant increase in complexity.

关键词： Parameter estimation projection algorithm Momentum factor Hierarchical identification principle

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Approximate subgradient projection algorithm for convex feasibility problem

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Chinese Journal of Systems Engineering and Electronics 2010年第3期000卷

作者： Li Li Yan Gao Business School University of Shanghai for Science and TechnologyShanghai 200093P.R.China

An ε-subgradient projection algorithm for solving a convex feasibility problem is *** on the iterative projection methods and the notion of ε-subgradient,a series of special projection hyperplanes is ***,compared with the existing projection hyperplanes methods with subgradient,the proposed hyperplanes are interactive with ε,and their ranges are more *** convergence of the proposed algorithm is given under some mild conditions,and the validity of the algorithm is proved by the numerical test.

关键词： ε-subgradient projection algorithm convex feasibility problem

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Generalized projection Identification algorithm

Generalized Projection Identification Algorithm

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International Conference on Signal Processing(ICSP’90)

作者： Helmut Hoyer Guanhua Wen Chair of Process Control FernUniversitat Hagen P.O.Box 940 D-5800 HagenWest Germany

Because of its simplicity,Kaczmarz algorithm and the projection algorithm are widely used for identification of dynamic *** there are some problems with its *** this paper a new method,Generalized projection Identification algorithm GPIA,is proposed. The theorem 1 gives out a strict proof of convergence of the GPIA,where the convergence rate is also discussed. Furthermore an usable adaptive estimator is *** is shown by computer simulations that" "the new algorithm is much suitable for time-invariant as well as for time-varying systems,More than that,it is suitable not only for systems with slow varying parameters,but also for systems with fast varying parameters,which makes it possible that GPIA can be used to robots and other complicated systems.

关键词： projection algorithm Lyapunov function convergence rate stability normalization

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projection algorithms for solving nonmonotone equilibrium problems in Hilbert space

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2016年 302卷 106-117页

作者： Bui Van Dinh Kim, Do Sang Le Quy Don Tech Univ Fac Informat Technol Hanoi Vietnam Pukyong Natl Univ Dept Appl Math Busan South Korea

We propose two projection algorithms for solving an equilibrium problem where the bifunction is not required to be satisfied any monotone property. Under assumptions on the continuity, convexity of the bifunction and the nonemptyness of the solution set of the Minty equilibrium problem, we show that the sequences generated by the proposed algorithms converge weakly and strongly to a solution of the primal equilibrium problem respectively. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Non-monotonicity Equilibria Extragradient method projection algorithm Armijo linesearch

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