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A stochastic Model for a Pseudo Affine Projection Algorithm

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2009年第1期57卷 107-118页

作者： de Almeida, Sergio J. M. Bermudez, Jose Carlos M. Bershad, Neil J. Catholic Univ Pelotas RS Brazil Univ Fed Santa Catarina Dept Elect Engn Florianopolis SC Brazil Univ Calif Irvine Dept Elect Engn & Comp Sci Newport Beach CA 92660 USA

This paper presents a statistical analysis of a Pseudo Affine Projection (PAP) algorithm, obtained from the Affine Projection algorithm (AP) for a step size alpha < 1 and a scalar error signal in the weight update. Deterministic recursive equations are derived for the mean weight and for the mean square error (MSE) for a large number of adaptive taps N compared to the order P of the algorithm. Simulations are presented which show good to excellent agreement with the theory in the transient and steady states. The PAP learning behavior is of special interest in applications where tradeoffs are necessary between convergence speed and steady-state misadjustment.

关键词： Adaptive filters affine projection analysis pseudo affine projection stochastic algorithms

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On Error-Saturation Nonlinearities in NLMS Adaptation

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2009年第10期57卷 4105-4111页

作者： Bershad, Neil J. Univ Calif Irvine Henry Samueli Sch Engn Irvine CA 92660 USA

The effect of a saturation-type error nonlinearity in the weight update equation in normalized least mean-square (NLMS) adaptation is investigated for system identification for a white Gaussian data model. Nonlinear recursions are derived for the weight mean error and mean-square deviation (MSD) that include the effect of an error function (erf) saturation-type nonlinearity on the error sequence driving the algorithm. The nonlinear recursion for the MSD is solved numerically and shown in excellent agreement with Monte Carlo simulations, supporting the theoretical model assumptions. The theory is extended to tracking a Markov channel and accurately predicts the tracking behavior as well. The saturation behavior of the algorithm is easily studied by varying a single parameter in the error function, varying from a linear device to a hard limiter. For the white data case, the excess mean square-error (EMSE) is simply related to the MSD. The tradeoff between the extent of error saturation, steady-state EMSE, and algorithm convergence rate is studied using these results.

关键词： Adaptive filters analysis NLMS nonlinear systems stochastic algorithms

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A QUALITATIVE TWO-STEP INVERSION APPROACH FOR THE RECONSTRUCTION OF SUBSURFACE DEFECTS

A QUALITATIVE TWO-STEP INVERSION APPROACH FOR THE RECONSTRUC...

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IEEE International Geoscience and Remote Sensing Symposium

作者： Donellia, Massimo Benedetti, Manuel Lesselier, Dominique Massa, Andrea Univ Trent Dept Informat Engn & Comp Sci ELEDIA Grp Via Sommarive 14 I-38050 Trento Italy UPS11 CNRS SUPELEC Dept Recherche Electromagnetisme Lab Signaux Syst F-91192 Gif Sur Yvette France

ISBN: (纸本)9781424433940

In this work, the problem of the localization and shaping of buried objects or voids is addressed considering an innovative two steps strategy in order to enhance the reconstruction accuracy. In particular, at the first step the approach is aimed at firstly estimating the region-of-interest where the defect is supposed to be located. Then at the second step, the qualitative imaging of the object is improved through a level-set based shaping procedure. In order to assess the effectiveness of the proposed approach, selected numerical results concerned with different scenarios and noisy data are presented and discussed

关键词： NDE/NDT Microwave Imaging stochastic algorithms Level-Set

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An affine combination of two LMS adaptive filters - Transient mean-square analysis

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2008年第5期56卷 1853-1864页

作者： Bershad, Neil J. Bennudez, Jose Carlos M. Toumeret, Jean-Yves Univ Calif Irvine Dept Elect Engn & Comp Sci Newport Beach CA 92660 USA Univ Fed Santa Catarina Dept Elect Engn BR-88040900 Florianopolis SC Brazil ENSEEIHT TESA IRIT Toulouse 7 France

This paper studies the statistical behavior of an affine combination of the outputs of two least mean-square (LMS) adaptive filters that simultaneously adapt using the same white Gaussian inputs. The purpose of the combination is to obtain an LMS adaptive filter with fast convergence and small steady-state mean-square deviation (MSD). The linear combination studied is a generalization of the convex combination, in which the combination factor lambda(n) is restricted to the interval (0,1). The viewpoint is taken that each of the two filters produces dependent estimates of the unknown channel. Thus, there exists a sequence of optimal affine combining coefficients which minimizes the mean-square error (MSE). First, the optimal unrealizable affine combiner is studied and provides the best possible performance for this class. Then two new schemes are proposed for practical applications. The mean-square performances are analyzed and validated by Monte Carlo simulations. With proper design, the two practical schemes yield an overall MSD that is usually less than the MSDs of either filter.

关键词： adaptive filters affine combination analysis convex combination least mean square (LMS) stochastic algorithms

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Runtime analysis of Ant Colony Optimization with best-so-far reinforcement

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METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY 2008年第3期10卷 409-433页

作者： Gutjahr, Walter J. Sebastiani, Giovanni CNR Ist Applicaz Calcolo Mauro Picone I-00161 Rome Italy Univ Roma La Sapienza Dept Math I-00185 Rome Italy Univ Vienna Dept Stat & Decis Support Syst A-1010 Vienna Austria

The paper provides some theoretical results on the analysis of the expected time needed by a class of Ant Colony Optimization algorithms to solve combinatorial optimization problems. A part of the study refers to some general results on the expected runtime of the considered class of algorithms. These results are then specialized to the case of pseudo-Boolean functions. In particular, three well known functions and a combination of two of them are considered: the OneMax, the Needle-in-a-Haystack, the LeadingOnes, and the OneMax-Needle-in-a-Haystack. The results obtained for these functions are also compared to those from the well-investigated (1+1)-Evolutionary Algorithm. The results shed light on a suitable parameter choice for the considered class of algorithms. Furthermore, it turns out that for two of the four studied problems, the expected runtime for the considered class, expressed in terms of the problem size, is of the same order as that for (1+1)-Evolutionary Algorithm. For the other two problems, the results are significantly in favour of the considered class of Ant Colony Optimization algorithms.

关键词： analysis of algorithms combinatorial optimization stochastic algorithms hitting times Markov processes

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On performance bounds for an affine combination of two LMS adaptive filters

On performance bounds for an affine combination of two LMS a...

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33rd IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Bershad, N. J. Bermudez, J. C. M. Tourneret, J. -Y Univ Calif Irvine 1621 Santiago Dr Newport Beach CA 92660 USA Univ Fed Santa Catarina Florianopolis SC Brazil IRIT ENSEEIHT TeSA F-31071 Toulouse France

ISBN: (纸本)9781424414833

This paper studies the statistical behavior of an affine combination of the outputs of two LMS adaptive filters that simultaneously adapt using the same white Gaussian input. The purpose of the combination is to obtain an LMS adaptive filter with fast convergence and small steady-state mean-square error (MSE). The linear combination studied is a generalization of the convex combination, in which the combination factor is restricted to the interval (0, 1). The viewpoint is taken that each of the two filters produces dependent estimates of the unknown channel. Thus, there exists a sequence of optimal affine combining coefficients which minimizes the MSE. The optimal unrealizable affine combiner is studied and provides the best possible performance for this class. Then, a new scheme is proposed for practical applications. It is shown that the practical scheme yields close-to-optimal performance when properly designed (as suggested by the theoretical optimal).

关键词： adaptive filters affine combination convex combination LMS algorithm stochastic algorithms

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Phase stability analysis of liquid-liquid equilibrium with stochastic methods

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BRAZILIAN JOURNAL OF CHEMICAL ENGINEERING 2008年第3期25卷 571-583页

作者： Nagatani, G. Ferrari, J. Cardozo Filho, L. Rossi, C. C. R. S. Guirardello, R. Oliveira, J. Vladimir Corazza, M. L. Univ Reg Integrada Alto Uruguai & Missoes Dept Food Engn BR-99700000 Erechim RS Brazil Univ Estadual Maringa UEM Dept Chem Engn BR-87020900 Maringa Parana Brazil Univ Estadual Campinas DPQ FEQ Coll Chem Engn BR-13081970 Campinas SP Brazil

Minimization of Gibbs free energy Using activity coefficient models and nonlinear equation solution techniques is commonly applied to phase stability problems. However, when conventional techniques, Such as the Newton-Raphson method, are employed, serious convergence problems may arise. Due to the existence Of Multiple solutions, several problem can be found in modeling, liquid-liquid equilibrium of multicomponent systerns, which are highly dependent oil the initial guess. In this Nvork phase stability analysis of liquid-liquid equilibrium is investigated using the NRTL model. For this purpose, two distinct stochastic numerical algorithms are employed to minimize the tangent plane distance of Gibbs free energy: a subdivision algorithm that can find all roots of nonlinear equations for liquid-liquid stability analysis and the Simulated Annealing method. Results obtained in this work for the two stochastic algorithms are compared with those of the Interval Newton method from the literature. Several different binary and multicomponent systerns from the literature were successfully investigated.

关键词： phase stability liquid-liquid equilibrium stochastic algorithms thermodynamic models

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Modelling the dynamics of stochastic local search on k-SAT

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JOURNAL OF HEURISTICS 2007年第6期13卷 587-639页

作者： Fournier, Nicolas G. EPO Munich Germany

A new analytical tool is presented to provide a better understanding of the search space of k-SAT. This tool, termed the local value distribution, describes the probability of finding assignments of any value q' in the neighbourhood of assignments of value q. The local value distribution is then used to define a Markov model to model the dynamics of a corresponding stochastic local search algorithm for k-SAT. The model is evaluated by comparing the predicted algorithm dynamics to experimental results. In most cases the fit of the model to the experimental results is very good, but limitations are also recognised.

关键词： algorithm analysis experimental evaluation stochastic algorithms local search k-SAT

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How to assess and report the performance of a stochastic algorithm on a benchmark problem: mean or best result on a number of runs?

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OPTIMIZATION LETTERS 2007年第3期1卷 309-311页

作者： Birattari, Mauro Dorigo, Marco Univ Libre Bruxelles IRIDIA CoDE Brussels Belgium

Some authors claim that reporting the best result obtained by a stochastic algorithm in a number of runs is more meaningful than reporting some central statistic. In this short note, we analyze and refute the main arg... 详细信息

关键词： Assessment of performance Experimental methodology stochastic algorithms Metaheuristics

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Solving fractional problems with dynamic multistart improving hit-and-run

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ANNALS OF OPERATIONS RESEARCH 2007年第1期156卷 25-44页

作者： Duer, Mirjam Khompatraporn, Charoenchai Zabinsky, Zelda B. Tech Univ Darmstadt Dept Math D-64289 Darmstadt Germany King Mongkuts Univ Technol Thonburi Dept Prod Engn Bangkok 10140 Thailand Univ Washington Seattle WA 98195 USA

Fractional programming has numerous applications in economy and engineering. While some fractional problems are easy in the sense that they are equivalent to an ordinary linear program, other problems like maximizing a sum or product of several ratios are known to be hard, as these functions are highly nonconvex and multimodal. In contrast to the standard Branch-and-Bound type algorithms proposed for specific types of fractional problems, we treat general fractional problems with stochastic algorithms developed for multimodal global optimization. Specifically, we propose Improving Hit-and-Run with restarts, based on a theoretical analysis of Multistart Pure Adaptive Search (cf. the dissertation of Khompatraporn (2004)) which prescribes a way to utilize problem specific information to sample until a certain level alpha of confidence is achieved. For this purpose, we analyze the Lipschitz properties of fractional functions, and then utilize a unified method to solve general fractional problems. The paper ends with a report on numerical experiments.

关键词： fractional programming stochastic algorithms global optimization improving hit-and-run Lipschitz properties multistart pure adaptive search

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