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GOLS - Genetic orthogonal least squares algorithm for training RBF networks

NEUROCOMPUTING 2006年第16-18期69卷 2041-2064页

作者： Barreto, A. M. S. Barbosa, H. J. C. Ebecken, N. F. F. Univ Fed Rio de Janeiro COPPE Programa Engn Civil Cidade UnivCtr Technol BR-21945970 Rio de Janeiro RJ Brazil Lab Nacl Comp Cient BR-25651070 Petropolis RJ Brazil

This work presents the genetic orthogonal least squares approach, a hybrid algorithm blending orthogonal least squares method with a genetic algorithm at the same hierarchical level. The resulting method assimilates the advantages of both original approaches, generating solutions substantially better than those produced by the orthogonal least squares algorithm, without incurring in the computational cost of the standard genetic algorithm. To support this statement, the new approach is submitted to several computational experiments with artificial and real-world data. (c) 2006 Elsevier B.V. All rights reserved.

关键词： radial basis function networks orthogonal least squares algorithm genetic algorithms

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Nonlinear Fisher discriminant analysis using a minimum squared error cost function and the orthogonal least squares algorithm

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NEURAL NETWORKS 2002年第2期15卷 263-270页

作者： Billings, SA Lee, KL Univ Sheffield Dept Automat Control & Syst Engn Sheffield S1 3JD S Yorkshire England

The nonlinear discriminant function obtained using a minimum squared error cost function can be shown to be directly related to the nonlinear Fisher discriminant (NFD). With the squared error cost function, the orthogonal least squares (OLS) algorithm can be used to find a parsimonious description of the nonlinear discriminant function. Two simple classification techniques will be introduced and tested on a number of real and artificial data sets. The results show that the new classification technique can often perform favourably compared with other state of the art classification techniques. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： pattern classification Fisher discriminant orthogonal least squares algorithm squared error cost function nonlinear kernel functions parsimonious Kernel Fisher Discriminant

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Locally regularised orthogonal least squares algorithm for the construction of sparse kernel regression models

Locally regularised orthogonal least squares algorithm for t...

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6th International Conference on Signal Processing

作者： Sheng, C Univ Southampton Dept Elect & Comp Sci Southampton SO17 1BJ Hants England

ISBN: (纸本)0780374886

The paper proposes to combine an orthogonal least squares (OLS) model selection with local regularisation for efficient sparse kernel data modelling. By assigning each orthogonal weight in the regression model with an individual regularisation parameter, the ability for the OLS model selection to produce a very parsimonious model with excellent generalisation performance is greatly enhanced.

关键词： least squares approximations statistical analysis data models Hessian matrices orthogonal least squares algorithm sparse kernel regression models local regularisation data modelling learning procedure Hessian matrix

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Combined genetic algorithm optimization and regularized orthogonal least squares learning for radial basis function networks

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IEEE TRANSACTIONS ON NEURAL NETWORKS 1999年第5期10卷 1239-1243页

作者： Chen, S Wu, Y Luk, BL Univ Southampton Dept Elect & Comp Sci Southampton SO17 1BJ Hants England William Beaumont Hosp Dept Radiat Oncol Royal Oak MI 48073 USA Univ Portsmouth Dept Elect & Elect Engn Portsmouth PO1 3DJ Hants England

The paper presents a two-level learning method for radial basis function (RBF) networks. A regularized orthogonal least squares (ROLS) algorithm is employed at the lower level to construct RBF networks while the two key learning parameters, the regularization parameter and the RBF width, are optimized using a genetic algorithm (GA) at the upper level. Nonlinear time series modeling and prediction is used as an example to demonstrate the effectiveness of this hierarchical learning approach.

关键词： genetic algorithms orthogonal least squares algorithm radial basis function networks regularization

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Local regularization assisted orthogonal least squares regression

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NEUROCOMPUTING 2006年第4-6期69卷 559-585页

作者： Chen, S Univ Southampton Sch Elect & Comp Sci Southampton SO17 1BJ Hants England

A locally regularized orthogonal least squares (LROLS) algorithm is proposed for constructing parsimonious or sparse regression models that generalize well. By associating each orthogonal weight in the regression model with an individual regularization parameter, the ability for the orthogonal least squares model selection to produce a very sparse model with good generalization performance is greatly enhanced. Furthermore, with the assistance of local regularization, when to terminate the model selection procedure becomes much clearer. A comparison with a state-of-the-art method for constructing sparse regression models, known as the relevance vector machine, is given. The proposed LROLS algorithm is shown to possess considerable computational advantages, including well conditioned solution and faster convergence speed. (c) 2005 Elsevier B.V. All rights reserved.

关键词： orthogonal least squares algorithm regularization regression Bayesian learning relevance vector machines evidence procedure

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Fully complex-valued radial basis function networks: orthogonal least squares regression and classification

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NEUROCOMPUTING 2008年第16-18期71卷 3421-3433页

作者： Chen, S. Hong, X. Harris, C. J. Hanzo, L. Univ Southampton Sch Elect & Comp Sci Southampton SO17 1BJ Hants England Univ Reading Sch Syst Engn Reading RG6 6AY Berks England

We consider a fully complex-valued radial basis function (RBF) network for regression and classification applications. For regression problems, the locally regularised orthogonal least squares (LROLS) algorithm aided with the D-optimality experimental design, originally derived for constructing parsimonious real-valued RBF models, is extended to the fully complex-valued RBF (CVRBF) network. Like its real-valued counterpart, the proposed algorithm aims to achieve maximised model robustness and sparsity by combining two effective and complementary approaches. The LROLS algorithm alone is capable of producing a very parsimonious model with excellent generalisation performance while the D-optimality design criterion further enhances the model efficiency and robustness. By specifying an appropriate weighting for the D-optimality cost in the combined model selecting criterion, the entire model construction procedure becomes automatic. An example of identifying a complex-valued nonlinear channel is used to illustrate the regression application of the proposed fully CVRBF network. The proposed fully CVRBF network is also applied to four-class classification problems that are typically encountered in communication systems. A complex-valued orthogonal forward selection algorithm based on the multi-class Fisher ratio of class separability measure is derived for constructing sparse CVRBF classifiers that generalise well. The effectiveness of the proposed algorithm is demonstrated using the example of nonlinear beamforming for multiple-antenna aided communication systems that employ complex-valued quadrature phase shift keying modulation scheme. (C) 2007 Elsevier B.V. All rights reserved.

关键词： Complex-valued radial basis function network Regression Classification orthogonal least squares algorithm D-optimality experimental design Fisher ratio of class separability measure

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orthogonal least squares for radial basis function network in reproducing Kernel Hilbert space

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IFAC Proceedings Volumes 2004年第12期37卷 847-852页

作者： Chooleewan Dachapak Shunshoku Kanae Zi-Jiang Yang Kiyoshi Wada Department of Electrical and Electronic System Engineering Kyushu University Fukuoka 812-8581 JAPAN

The present study employs an idea of mapping data into a high dimensional feature space which is known as Reproducing Kernel Hilbert Space (RKHS), then performs Radial Basis Function (RBF) network in the feature space and finally, orthogonal least squares (OLS) method is employed to select a suitable set of centers (regressors) from a large set of candidates in order to obtain a sparse regression model in the feature space.

关键词： Reproducing kernel Hilbert space orthogonal least squares algorithm Radial basis function Neural networks

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Non-linear system identification using particle swarm optimisation tuned radial basis function models

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INTERNATIONAL JOURNAL OF BIO-INSPIRED COMPUTATION 2009年第4期1卷 246-258页

作者： Chen, Sheng Hong, Xia Luk, Bing L. Harris, Chris J. Univ Southampton Sch Elect & Comp Sci Southampton SO17 1BJ Hants England Univ Reading Sch Syst Engn Reading RG6 6AY Berks England City Univ Hong Kong Dept Mfg Engn & Engn Management Hong Kong Hong Kong Peoples R China

A novel particle swarm optimisation (PSO) tuned radial basis function (RBF) network. model is proposed for identification of non-linear systems. At each stage of orthogonal forward regression (OFR) model construction process, PSO is adopted to tune one RBF unit's centre vector and diagonal covariance matrix by minimising the leave-one-out (LOO) mean square error (MSE). This PSO aided OFR automatically determines how many tunable RBF nodes are sufficient for modelling. Compared with the-state-of-the-art local regularisation assisted orthogonal least squares algorithm based on the LOO MSE criterion for constructing fixed-node RBF network models, the PSO tuned RBF model construction produces more parsimonious RBF models with better generalisation performance and is often more efficient in model construction. The effectiveness of the proposed PSO aided OFR algorithm for constructing tunable node RBF models is demonstrated using three real data sets.

关键词： non-linear system orthogonal least squares algorithm OLS algorithm leave-one-out cross validation tunable radial basis function network tunable RBF network particle swarm optimisation PSO

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COMPLEX-VALUED RADIAL BASIS FUNCTION NETWORK .1. NETWORK ARCHITECTURE AND LEARNING algorithmS

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SIGNAL PROCESSING 1994年第1期35卷 19-31页

作者： CHEN, S MCLAUGHLIN, S MULGREW, B Department of Electrical Engineering University of Edinburgh King's Buildings Edinburgh EH9 3JL Scotland UK

The paper proposes a complex radial basis function network. The network has complex centres and connection weights, but the nonlinearity of its hidden nodes remains a real-valued function. This kind of network is able to generate complicated nonlinear decision surfaced or to approximate an arbitrary nonlinear function in complex multi-dimensional space, and it provides a powerful tool for nonlinear signal processing involving complex signals. The paper is divided into two parts. The first part introduces the network architecture and derives both block-data and recursive learning algorithms for this complex radial basis function network. The complex orthogonal least squares algorithm is a batch learning algorithm capable of constructing an adequate network structure, while a complex version of the hybrid clustering and least squares algorithm offers real-time adaptation capability. The identification of a nonlinear communications channel model is used to illustrate these two learning algorithms. In the second part of the paper, a practical application of this complex radial basis function network is demonstrated using digital communications channel equalisation.

关键词： COMPLEX-VALUED SIGNAL RADIAL BASIS FUNCTION NETWORK orthogonal least squares algorithm UNSUPERVISED CLUSTERING

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Identification of multiscale spatio-temporal dynamical systems using a wavelet multiresolution analysis

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2009年第11期40卷 1115-1126页

作者： Guo, L. Z. Billings, S. A. Coca, D. Univ Sheffield Dept Automat Control & Syst Engn Sheffield S1 3JD S Yorkshire England

In this article, a new algorithm for the multiscale identification of spatio-temporal dynamical systems is derived. It is shown that the input and output observations can be represented in a multiscale manner based on a wavelet multiresolution analysis. The system dynamics at some specific scale of interest can then be identified using an orthogonal forward least-squares algorithm. This model can then be converted between different scales to produce predictions of the system outputs at different scales. The method can be applied to both multiscale and conventional spatio-temporal dynamical systems. For multiscale systems, the method can generate a parsimonious and effective model at a coarser scale while considering the effects from finer scales. Additionally, the proposed method can be used to improve the performance of the identification when the measurements are noisy. Numerical examples are provided to demonstrate the application of the proposed new approach.

关键词： multiscale identification spatio-temporal system orthogonal least squares algorithm multiresolution analysis

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