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

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

Neural networks in geophysical applications

Neural networks are increasingly popular in geophysics. Because they are universal approximators, these tools can approximate any continuous function with an arbitrary precision. Hence, they may yield important contributions to finding solutions to a variety of geophysical applications. However, knowledge of many methods and techniques recently developed to increase the performance and to facilitate the use of neural networks does not seem to be widespread in the geophysical community. Therefore, the power of these tools has not yet been explored to their full extent. In this paper, techniques are described for faster training, better overall performance, i.e., generalization,and the automatic estimation of network size and architecture

OCReP: An Optimally Conditioned Regularization for Pseudoinversion Based Neural Training

In this paper we consider the training of single hidden layer neural networks by pseudoinversion, which, in spite of its popularity, is sometimes affected by numerical instability issues. Regularization is known to be effective in such cases, so that we introduce, in the framework of Tikhonov regularization, a matricial reformulation of the problem which allows us to use the condition number as a diagnostic tool for identification of instability. By imposing well-conditioning requirements on the relevant matrices, our theoretical analysis allows the identification of an optimal value for the regularization parameter from the standpoint of stability. We compare with the value derived by cross-validation for overfitting control and optimisation of the generalization performance. We test our method for both regression and classification tasks. The proposed method is quite effective in terms of predictivity, often with some improvement on performance with respect to the reference cases considered. This approach, due to analytical determination of the regularization parameter, dramatically reduces the computational load required by many other techniques.Comment: Published on Neural Network

Incremental Sparse Bayesian Ordinal Regression

Ordinal Regression (OR) aims to model the ordering information between different data categories, which is a crucial topic in multi-label learning. An important class of approaches to OR models the problem as a linear combination of basis functions that map features to a high dimensional non-linear space. However, most of the basis function-based algorithms are time consuming. We propose an incremental sparse Bayesian approach to OR tasks and introduce an algorithm to sequentially learn the relevant basis functions in the ordinal scenario. Our method, called Incremental Sparse Bayesian Ordinal Regression (ISBOR), automatically optimizes the hyper-parameters via the type-II maximum likelihood method. By exploiting fast marginal likelihood optimization, ISBOR can avoid big matrix inverses, which is the main bottleneck in applying basis function-based algorithms to OR tasks on large-scale datasets. We show that ISBOR can make accurate predictions with parsimonious basis functions while offering automatic estimates of the prediction uncertainty. Extensive experiments on synthetic and real word datasets demonstrate the efficiency and effectiveness of ISBOR compared to other basis function-based OR approaches