Scatter-partitioning Radial Basis Function (RBF) networks increase their number of degrees of freedom with the complexity of an input-output mapping to be estimated on the basis of a supervised training data set. Due to its superior expressive power a scatter-partitioning Gaussian RBF (GRBF) model, termed Supervised Growing Neural Gas (SGNG), is selected from the literature. SGNG employs a one-...

Some response surface functions in complex engineering systems are usually highly nonlinear, unformed, and expensive to evaluate. To tackle this challenge, Bayesian optimization (BO), which conducts sequential design via a posterior distribution over the objective function, is critical method used find global optimum of black-box functions. Kernel play an important role shaping estimated functi...

In this addition to the regular paper, we derive the required derivatives required to implement the informative prior from a simulator in PILCO [1]. First, for completeness, we repeat the derivation of the mean, covariance, and input-output covariance of the predictive mean of a Gaussian process (GP) when the prior mean is a radial basis function network (RBF). Then, we detail the partial deriv...

The paper outlines a mixture distribution of Gaussian method for estimation the probability density function. A RBF neural network architecture for realising such estimation is proposed. Moreover, the learning algorithm is derived. The practical use of the method is illustrated by a small example of an recognition application. The aim of which is to recognise vehicles based on the acoustical si...

This paper shows how scale-based clustering can be done using the radial basis function network (RBFN), with the RBF width as the scale parameter and a dummy target as the desired output. The technique suggests the "right" scale at which the given data set should be clustered, thereby providing a solution to the problem of determining the number of RBF units and the widths required to get a goo...

Extracting rules from RBFs is not a trivial task because of nonlinear functions or high input dimensionality. In such cases, some of the hidden units of the RBF network have a tendency to be “shared” across several output classes or even may not contribute to any output class. To address this we have developed an algorithm called LREX (for Local Rule EXtraction) which tackles these issues by ex...

The purpose of this study is to investigate the accuracy of predictions of aniline removal efficiency in a moving bed biofilm reactor (MBBR) by various methods, namely by RBF, ANFIS, and fuzzy regression analysis. The reactor was operated in an aerobic batch and was filled by light expanded clay aggregate (LECA) as a carrier for the treatment of Aniline synthetic wastewater. Exploratory data an...

We describe a Fourier Volume Rendering (FVR) algorithm for datasets that are irregularly sampled and require anisotropic (e.g., elliptical) kernels for reconstruction. We sample the continuous frequency spectrum of such datasets by computing the continuous Fourier transform of the spatial interpolation kernel which is a radially symmetric Gaussian basis function (RBF) that may be anisotropicall...

We prove a new oracle inequality for support vector machines with Gaussian RBF kernels solving the regularized least squares regression problem. To this end, we apply the modulus of smoothness. With the help of the new oracle inequality we then derive learning rates that can also be achieved by a simple data-dependent parameter selection method. Finally, it turns out that our learning rates are...