9,149 research outputs found

    Forecasting the geomagnetic activity of the Dst Index using radial basis function networks

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    The Dst index is a key parameter which characterises the disturbance of the geomagnetic field in magnetic storms. Modelling of the Dst index is thus very important for the analysis of the geomagnetic field. A data-based modelling approach, aimed at obtaining efficient models based on limited input-output observational data, provides a powerful tool for analysing and forecasting geomagnetic activities including the prediction of the Dst index. Radial basis function (RBF) networks are an important and popular network model for nonlinear system identification and dynamical modelling. A novel generalised multiscale RBF (MSRBF) network is introduced for Dst index modelling. The proposed MSRBF network can easily be converted into a linear-in-the-parameters form and the training of the linear network model can easily be implemented using an orthogonal least squares (OLS) type algorithm. One advantage of the new MSRBF network, compared with traditional single scale RBF networks, is that the new network is more flexible for describing complex nonlinear dynamical systems

    Representation of Functional Data in Neural Networks

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    Functional Data Analysis (FDA) is an extension of traditional data analysis to functional data, for example spectra, temporal series, spatio-temporal images, gesture recognition data, etc. Functional data are rarely known in practice; usually a regular or irregular sampling is known. For this reason, some processing is needed in order to benefit from the smooth character of functional data in the analysis methods. This paper shows how to extend the Radial-Basis Function Networks (RBFN) and Multi-Layer Perceptron (MLP) models to functional data inputs, in particular when the latter are known through lists of input-output pairs. Various possibilities for functional processing are discussed, including the projection on smooth bases, Functional Principal Component Analysis, functional centering and reduction, and the use of differential operators. It is shown how to incorporate these functional processing into the RBFN and MLP models. The functional approach is illustrated on a benchmark of spectrometric data analysis.Comment: Also available online from: http://www.sciencedirect.com/science/journal/0925231

    A unified wavelet-based modelling framework for non-linear system identification: the WANARX model structure

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    A new unified modelling framework based on the superposition of additive submodels, functional components, and wavelet decompositions is proposed for non-linear system identification. A non-linear model, which is often represented using a multivariate non-linear function, is initially decomposed into a number of functional components via the wellknown analysis of variance (ANOVA) expression, which can be viewed as a special form of the NARX (non-linear autoregressive with exogenous inputs) model for representing dynamic input–output systems. By expanding each functional component using wavelet decompositions including the regular lattice frame decomposition, wavelet series and multiresolution wavelet decompositions, the multivariate non-linear model can then be converted into a linear-in-theparameters problem, which can be solved using least-squares type methods. An efficient model structure determination approach based upon a forward orthogonal least squares (OLS) algorithm, which involves a stepwise orthogonalization of the regressors and a forward selection of the relevant model terms based on the error reduction ratio (ERR), is employed to solve the linear-in-the-parameters problem in the present study. The new modelling structure is referred to as a wavelet-based ANOVA decomposition of the NARX model or simply WANARX model, and can be applied to represent high-order and high dimensional non-linear systems

    WSOM: Building Adaptive Wavelets with Self-organizing Maps

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    The WSOM (Wavelet Self-Organizing Map) model, a neural network for the creation of wavelet bases adapted to the distribution of input data, is introduced. The model provides an efficient on-line way to construct high-dimensional wavelet bases. Simulations of a lD function approximation problem illustrate how WSOM adapts to non-uniformly distributed input data, outperforming the discrete wavelet transform. A speaker-independent vowel recognition benchmark task demonstrates how the model constructs high-dimensional bases using low-dimensional wavelets.National Science Foundation (IIU 91-011659); Office of Naval Research (N00014-95-10409, NOOOH-95-0657

    Sparse model identification using a forward orthogonal regression algorithm aided by mutual information

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    A sparse representation, with satisfactory approximation accuracy, is usually desirable in any nonlinear system identification and signal processing problem. A new forward orthogonal regression algorithm, with mutual information interference, is proposed for sparse model selection and parameter estimation. The new algorithm can be used to construct parsimonious linear-in-the-parameters models

    Entropy of Overcomplete Kernel Dictionaries

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    In signal analysis and synthesis, linear approximation theory considers a linear decomposition of any given signal in a set of atoms, collected into a so-called dictionary. Relevant sparse representations are obtained by relaxing the orthogonality condition of the atoms, yielding overcomplete dictionaries with an extended number of atoms. More generally than the linear decomposition, overcomplete kernel dictionaries provide an elegant nonlinear extension by defining the atoms through a mapping kernel function (e.g., the gaussian kernel). Models based on such kernel dictionaries are used in neural networks, gaussian processes and online learning with kernels. The quality of an overcomplete dictionary is evaluated with a diversity measure the distance, the approximation, the coherence and the Babel measures. In this paper, we develop a framework to examine overcomplete kernel dictionaries with the entropy from information theory. Indeed, a higher value of the entropy is associated to a further uniform spread of the atoms over the space. For each of the aforementioned diversity measures, we derive lower bounds on the entropy. Several definitions of the entropy are examined, with an extensive analysis in both the input space and the mapped feature space.Comment: 10 page

    Theoretical Interpretations and Applications of Radial Basis Function Networks

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    Medical applications usually used Radial Basis Function Networks just as Artificial Neural Networks. However, RBFNs are Knowledge-Based Networks that can be interpreted in several way: Artificial Neural Networks, Regularization Networks, Support Vector Machines, Wavelet Networks, Fuzzy Controllers, Kernel Estimators, Instanced-Based Learners. A survey of their interpretations and of their corresponding learning algorithms is provided as well as a brief survey on dynamic learning algorithms. RBFNs' interpretations can suggest applications that are particularly interesting in medical domains
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