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A fast multi-output RBF neural network construction method

NEUROCOMPUTING 2010年第10-12期73卷 2196-2202页

作者： Du, Dajun Li, Kang Fei, Minrui Shanghai Univ Sch Mechatron Engn & Automat Shanghai Key Lab Power Stn Automat Technol Shanghai 200072 Peoples R China Queens Univ Belfast Sch Elect Elect Engn & Comp Sci Belfast BT9 5AH Antrim North Ireland

This paper investigates the center selection of multi-output radial basis function (RBF) networks, and a multi-output fast recursive algorithm (MFRA) is proposed. This method can not only reveal the significance of each candidate center based on the reduction in the trace of the error covariance matrix, but also can estimate the network weights simultaneously using a back substitution approach. The main contribution is that the center selection procedure and the weight estimation are performed within a well-defined regression context, leading to a significantly reduced computational complexity. The efficiency of the algorithm is confirmed by a computational complexity analysis, and simulation results demonstrate its effectiveness. (C) 2010 Elsevier B.V. All rights reserved.

关键词： linear-in-the-parameters model Multi-output radial basis function (RBF) neural network Center selection Computational complexity analysis Multi-output fast recursive algorithm (MFRA)

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Neural input selection - A fast model-based approach

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NEUROCOMPUTING 2007年第4-6期70卷 762-769页

作者： Li, Kang Peng, Jian-Xun Queens Univ Belfast Sch Elect & Elect Engn Belfast BT9 5AH Antrim North Ireland

Neural input selection is an important stage in neural network configuration. For neural modeling and control of nonlinear dynamic systems, the inputs to the neural networks may include any system variable of interest with various time lags. To choose a set of significant inputs is a combinational problem, and the selection procedure can be very time consuming. In this paper, a model-based neural input selection method is proposed. Essentially, the neural input selection is transformed into the problem of identifying the significant terms for a linear-in-the-parameters model. A fast method is then proposed to identify significant nonlinear terms or functions, from which the neural inputs are grouped and selected. Both theoretic analysis and simulation examples demonstrate the effectiveness and efficiency of the proposed model-based approach. (c) 2006 Elsevier B.V. All rights reserved.

关键词： neural input selection model-based approach nonlinear systems modeling and control linear-in-the-parameters model

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Elastic net orthogonal forward regression

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NEUROCOMPUTING 2015年 148卷 551-560页

作者： Hong, Xia Chen, Sheng Univ Reading Sch Syst Engn Reading RG6 2AH Berks England Univ Southampton Sch Elect & Comp Sci Southampton SO17 1BJ Hants England King Abdulaziz Univ Fac Engn Jeddah 21589 Saudi Arabia

An efficient two-level model identification method aiming at maximising a model's generalisation capability is proposed for a large class of linear-in-the-parameters models from the observational data. A new elastic net orthogonal forward regression (ENOFR) algorithm is employed at the lower level to carry out simultaneous model selection and elastic net parameter estimation. The two regularisation parameters in the elastic net are optimised using a particle swarm optimisation (PSO) algorithm at the upper level by minimising the leave one out (LOO) mean square error (LOOMSE). There are two elements of original contributions. Firstly an elastic net cost function is defined and applied based on orthogonal decomposition, which facilitates the automatic model structure selection process with no need of using a predetermined error tolerance to terminate the forward selection process. Secondly it is shown that the LOOMSE based on the resultant ENOFR models can be analytically computed without actually splitting the data set, and the associate computation cost is small due to the ENOFR procedure. Consequently a fully automated procedure is achieved without resort to any other validation data set for iterative model evaluation. Illustrative examples are included to demonstrate the effectiveness of the new approaches. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Elastic net Forward regression linear-in-the-parameters model Regularisation Leave one out errors Cross validation

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Two-Stage Orthogonal Least Squares Methods for Neural Network Construction

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2015年第8期26卷 1608-1621页

作者： Zhang, Long Li, Kang Bai, Er-Wei Irwin, George W. Queens Univ Belfast Sch Elect Elect Engn & Comp Sci Belfast BT7 1NN Antrim North Ireland Univ Iowa Dept Elect & Comp Engn Iowa City IA 52242 USA Queens Univ Belfast Sch Elect Elect Engn & Comp Sci Belfast BT9 5AH Antrim North Ireland

A number of neural networks can be formulated as the linear-in-the-parameters models. Training such networks can be transformed to a model selection problem where a compact model is selected from all the candidates using subset selection algorithms. Forward selection methods are popular fast subset selection approaches. However, they may only produce suboptimal models and can be trapped into a local minimum. More recently, a two-stage fast recursive algorithm (TSFRA) combining forward selection and backward model refinement has been proposed to improve the compactness and generalization performance of the model. This paper proposes unified two-stage orthogonal least squares methods instead of the fast recursive-based methods. In contrast to the TSFRA, this paper derives a new simplified relationship between the forward and the backward stages to avoid repetitive computations using the inherent orthogonal properties of the least squares methods. Furthermore, a new term exchanging scheme for backward model refinement is introduced to reduce computational demand. Finally, given the error reduction ratio criterion, effective and efficient forward and backward subset selection procedures are proposed. Extensive examples are presented to demonstrate the improved model compactness constructed by the proposed technique in comparison with some popular methods.

关键词： Backward model refinement computational complexity forward selection linear-in-the-parameters model orthogonal least square (OLS)

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A novel locally regularized automatic construction method for RBF neural models

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NEUROCOMPUTING 2012年 98卷 4-11页

作者： Du, Dajun Li, Xue Fei, Minrui Irwin, George W. Shanghai Univ Sch Mechatron Engn & Automat Shanghai Key Lab Power Stn Automat Technol Shanghai 200072 Peoples R China Queens Univ Belfast Sch Elect Elect Engn & Comp Sci Belfast BT9 5AH Antrim North Ireland

This paper investigates automatic construction of radial basis function (RBF) neural models for nonlinear dynamic systems. The main objective is to automatically and effectively produce a parsimonious RBF neural model that generalizes well. This is achieved by proposing a locally regularized automatic construction (LRAC) method which combines a recently proposed fast recursive algorithm (FRA) with the leave-one-out (LOU) cross-validation criterion. The new method offers distinctive advantages over existing approaches. Firstly, it uses an error criterion where the original model parameters are regularized, in contrast to orthogonal least square (OLS) based approaches where transformed model parameters are regularized. This enables the determination of the significance of each original candidate center and produces a compact neural model. Further, it can automatically determine the network size by the iteratively minimizing a LOU mean-square-error (MSE) without the need to specify any additional termination criterion. Finally, by defining a proper regression context, the whole network construction process can be concisely formulated and easily implemented with significantly reduced computation. An analysis of computational complexity confirms the efficiency of the proposed method, and simulation results reveal its effectiveness in comparison with alternative approaches for producing sparse RBF neural models. (c) 2012 Elsevier B.V. All rights reserved.

关键词： Center selection Leave-one-out (LOO) cross-validation linear-in-the-parameters model Radial basis function (RBF) neural networks Regularization

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A two-stage algorithm for identification of nonlinear dynamic systems

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AUTOMATICA 2006年第7期42卷 1189-1197页

作者： Li, Kang Peng, Jian-Xun Bai, Er-Wei Queens Univ Belfast Sch Elect Elect Engn & Comp Sci Belfast BT9 5AH Antrim North Ireland Univ Iowa Dept Elect & Comp Engn Iowa City IA 52242 USA

This paper investigates the two-stage stepwise identification for a class of nonlinear dynamic systems that can be described by linear-in-theparameters models, and the model has to be built from a very large pool of basis functions or model terms. The main objective is to improve the compactness of the model that is obtained by the forward stepwise methods, while retaining the computational efficiency. The proposed algorithm first generates an initial model using a forward stepwise procedure. The significance of each selected term is then reviewed at the second stage and all insignificant ones are replaced, resulting in an optimised compact model with significantly improved performance. The main contribution of this paper is that these two stages are performed within a well-defined regression context, leading to significantly reduced computational complexity. The efficiency of the algorithm is confirmed by the computational complexity analysis, and its effectiveness is demonstrated by the simulation results. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： system identification nonlinear system linear-in-the-parameters model model structure selection forward model selection model refinement computational complexity model compactness

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A novel automatic two-stage locally regularized classifier construction method using the extreme learning machine

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NEUROCOMPUTING 2013年 102卷 10-22页

作者： Du, Dajun Li, Kang Irwin, George W. Deng, Jing Shanghai Univ Sch Mechatron Engn & Automat Shanghai Key Lab Power Stn Automat Technol Shanghai 200072 Peoples R China Queens Univ Belfast Sch Elect Elect Engn & Comp Sci Belfast BT9 5AH Antrim North Ireland

This paper investigates the design of a linear-in-the-parameters (LITP) regression classifier for two-class problems. Most existing algorithms generally learn a classifier (model) from the available training data based on some stopping criterions, such as the Akaike's final prediction error (FPE). The drawback here is that the classifier obtained is then not directly obtained based on its generalization capability. The main objective of this paper is to improve the sparsity and generalization capability of a classifier, while reducing the computational expense in producing it. This is achieved by proposing an automatic two-stage locally regularized classifier construction (TSLRCC) method using the extreme learning machine (ELM). In this new algorithm, the nonlinear parameters in each term, such as the width of the Gaussian function and the power of a polynomial term, are firstly determined by the ELM. An initial classifier is then generated by the direct evaluation of these candidates models according to the leave-one-out (LOO) misclassification rate in the first stage. The significance of each selected regressor term is also checked and insignificant ones are replaced in the second stage. To reduce the computational complexity, a proper regression context is defined which allows fast implementation of the proposed method. Simulation results confirm the effectiveness of the proposed technique. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Classification Extreme learning machine Leave-one-out (LOO) misclassification rate linear-in-the-parameters model Regularization Two-stage stepwise selection

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Sparse model Construction using Coordinate Descent Optimization

Sparse Model Construction using Coordinate Descent Optimizat...

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18th International Conference on Digital Signal Processing (DSP)

作者： Hong, Xia Guo, Yi Chen, Sheng Gao, Junbin Univ Reading Sch Syst Engn Reading RG6 2AH Berks England CSIRO N Ryde NSW 1670 Australia Univ Southampton ECS Southampton Hants England Charles Sturt Univ Bathurst NSW 2795 Australia

ISBN: (纸本)9781467358057

We propose a new sparse model construction method aimed at maximizing a model's generalisation capability for a large class of linear-in-the-parameters models. The coordinate descent optimization algorithm is employed with a modified l(1)-penalized least squares cost function in order to estimate a single parameter and its regularization parameter simultaneously based on the leave one out mean square error (LOOMSE). Our original contribution is to derive a closed form of optimal LOOMSE regularization parameter for a single term model, for which we show that the LOOMSE can be analytically computed without actually splitting the data set leading to a very simple parameter estimation method. We then integrate the new results within the coordinate descent optimization algorithm to update model parameters one at the time for linear-in-the-parameters models. Consequently a fully automated procedure is achieved without resort to any other validation data set for iterative model evaluation. Illustrative examples are included to demonstrate the effectiveness of the new approaches.

关键词： lasso linear-in-the-parameters model regularization leave one out errors cross validation

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A TWO-STAGE ALGORITHM FOR IDENTIFICATION OF NONlinear DYNAMIC SYSTEMS

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IFAC Proceedings Volumes 2006年第1期39卷 570-575页

作者： Jian-Xun Peng Kang Li Er-Wei Bai School of Electrical and Electronic Engineering Queen's University Belfast Belfast BT9 5AH UK Department of Electrical and Computer Engineering University of Iowa Iowa City IA 52242 USA

A two-stage algorithm is proposed for fast identification of optimal linear-in-the-parameters models for nonlinear dynamic systems. In the first stage, an initial model is selected from a significant number of candidates, using a stepwise forward procedure. The significance of each selected model term is reviewed iteratively at the second stage using a fast review procedure and insignificant terms are then replaced, resulting in a locally optimised compact model. The contribution is that both the forward and backward model selection is performed within a well-defined regression context, leading to significantly reduced computational complexity. The computational complexity analysis confirms the arithmetic efficiency and the simulation results demonstrate the effectiveness.

关键词： System identification nonlinear system linear-in-the-parameters model model structure selection computational complexity

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