Orthogonal least squares methods and their application to non-linear system identification
TLDR
Identification algorithms based on the well-known linear least squares methods of gaussian elimination, Cholesky decomposition, classical Gram-Schmidt, modified Gram- Schmidt, Householder transformation, Givens method, and singular value decomposition are reviewed.Abstract:
Identification algorithms based on the well-known linear least squares methods of gaussian elimination, Cholesky decomposition, classical Gram-Schmidt, modified Gram-Schmidt, Householder transformation, Givens method, and singular value decomposition are reviewed. The classical Gram-Schmidt, modified Gram-Schmidt, and Householder transformation algorithms are then extended to combine structure determination, or which terms to include in the model, and parameter estimation in a very simple and efficient manner for a class of multivariate discrete-time non-linear stochastic systems which are linear in the parameters.read more
Citations
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Radial Basis Function Network Configuration Using Mutual Information and the Orthogonal Least Squares Algorithm
TL;DR: The mutual information between the input variables and the output of the network is used to select a suboptimal set of input variables for the network and variables which have a higher mutual information with the output and lower dependence on other selected variables are used as network inputs.
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A Novel Continuous Forward Algorithm for RBF Neural Modelling
TL;DR: A continuous forward algorithm is proposed for nonlinear modelling and identification using radial basis function (RBF) neural networks, and offers two important advantages: first, the model performance can be significantly improved through continuous parameter optimization, and second, the neural representation can be built without generating and storing all candidate regressors, leading to significantly reduced memory usage and computational complexity.
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Parameter estimation of photovoltaic cells using improved Lozi map based chaotic optimization Algorithm
TL;DR: This study proposes an Improved Lozi Map based Chaotic Optimization Algorithm (ILCOA) algorithm to estimate the unknown parameters of the solar cells, with remarkable local and global searching abilities that give it a distinct edge over other optimization methods.
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Wavelet–Volterra coupled model for monthly stream flow forecasting
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TL;DR: This paper describes a methodology that yields a 1 month ahead forecast of stream flow using wavelets based multiscale nonlinear models and indicates presence of discernable nonlinear characteristics in the stream flow data.
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Particle Swarm Optimization Aided Orthogonal Forward Regression for Unified Data Modeling
Sheng Chen,Xia Hong,Chris Harris +2 more
TL;DR: A particle swarm optimization (PSO) aided orthogonal forward regression (OFR) algorithm based on leave-one-out (LOO) criteria is developed to construct parsimonious radial basis function (RBF) networks with tunable nodes.
References
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Book
Applied Regression Analysis
Norman R. Draper,Harry Smith +1 more
TL;DR: In this article, the Straight Line Case is used to fit a straight line by least squares, and the Durbin-Watson Test is used for checking the straight line fit.
Journal ArticleDOI
Singular value decomposition and least squares solutions
Gene H. Golub,C. Reinsch +1 more
TL;DR: The decomposition of A is called the singular value decomposition (SVD) and the diagonal elements of ∑ are the non-negative square roots of the eigenvalues of A T A; they are called singular values.
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Linear regression analysis
TL;DR: In this paper, the authors take into serious consideration the further development of regression computer programs that are efficient, accurate, and considered an important part of statistical research, and provide up-to-date accounts of computational methods and algorithms currently in use without getting entrenched in minor computing details.
Journal ArticleDOI
Input-output parametric models for non-linear systems Part II: stochastic non-linear systems
TL;DR: Recursive input-output models for non-linear multivariate discrete-time systems are derived, and sufficient conditions for their existence are defined.