10,288 research outputs found
Theoretical Interpretations and Applications of Radial Basis Function Networks
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
Local Regularization Assisted Orthogonal Least Squares Regression
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 (OLS) 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. This LROLS algorithm has computational advantages over the recently introduced relevance vector machine (RVM) method
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Improved streamflow forecasting using self-organizing radial basis function artificial neural networks
Streamflow forecasting has always been a challenging task for water resources engineers and managers and a major component of water resources system control. In this study, we explore the applicability of a Self Organizing Radial Basis (SORB) function to one-step ahead forecasting of daily streamflow. SORB uses a Gaussian Radial Basis Function architecture in conjunction with the Self-Organizing Feature Map (SOFM) used in data classification. SORB outperforms the two other ANN algorithms, the well known Multi-layer Feedforward Network (MFN) and Self-Organizing Linear Output map (SOLO) neural network for simulation of daily streamflow in the semi-arid Salt River basin. The applicability of the linear regression model was also investigated and concluded that the regression model is not reliable for this study. To generalize the model and derive a robust parameter set, cross-validation is applied and its outcome is compared with the split sample test. Cross-validation justifies the validity of the nonlinear relationship set up between input and output data. © 2004 Elsevier B.V. All rights reserved
Bayesian interpolation
Although Bayesian analysis has been in use since Laplace, the Bayesian method of model-comparison has only recently been developed in depth. In this paper, the Bayesian approach to regularization and model-comparison is demonstrated by studying the inference problem of interpolating noisy data. The concepts and methods described are quite general and can be applied to many other data modeling problems. Regularizing constants are set by examining their posterior probability distribution. Alternative regularizers (priors) and alternative basis sets are objectively compared by evaluating the evidence for them. “Occam's razor” is automatically embodied by this process. The way in which Bayes infers the values of regularizing constants and noise levels has an elegant interpretation in terms of the effective number of parameters determined by the data set. This framework is due to Gull and Skilling
Representation of Functional Data in Neural Networks
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
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