Neural network with radial basis functions

The term radial distribution functions shouM not be confused with radial basis functions (RBF), a term introduced by Broomhead and Lowe in 1988 and which represents a type of function used for neural networks employing a hidden layer of radial units [37]. 

Li, Q., Chen, X. and Hu, Z. (2004) Quantitative structure-property relationship studies for estimating boiling points of alcohols using calculated molecular descriptors with radial basis function neural networks. Chemom. Intell. Lab. Syst., 72, 93-100. 

Girosi, F., and Anzellotti, G., Rales of convergence for radial basis functions and neural networks. Artificial Neural Networks with Applications in Speech and Vision, (R. J. Matttmone, ed.), p. 97. Chapman Hall, London, 1993. 

Despite the fact that the neural network literature increasingly contains examples of radial basis function network applications, their use in genome informatics has rarely been -reported—not because the potential for applications is not there, but more likely due to a lag time between development of the technology and applications to a given field. Casidio et al. (1995) used a radial basis function network to optimally predict the free energy contributions due to hydrogen bonds, hydrophobic interactions and the unfolded state, with simple input measures. 

One other network that has been used with supervised learning is the radial basis function (RBF) network.f Radial functions are relatively simple in form, and by definition must increase (or decrease) monotonically with the distance from a certain reference point. Gaussian functions are one example of radial functions. In a RBF network, the inputs are fed to a layer of RBFs, which in turn are weighted to produce an output from the network. If the RBFs are allowed to move or to change size, or if there is more than one hidden layer, then the RBF network is non-linear. An RBF network is shown schematically for the case of n inputs and m basis functions in Fig. 3. The generalized regression neural network, a special case of the RBF network, has been used infrequently especially in understanding in vitro-in vivo correlations. 

Various density-functional theory based descriptors were probed with success by Arulmozhiraja and Morita [155]. In 2005, Hirokawa and coworkers employed Hartree-Fock theory, which identifies the polarization as a key parameter for QSAR on AhR binding [156]. Wang et al. extended their work to include polybrominated compounds and reached a cross-validated r2 of 0.580 and 0.680 using CoMFA and CoMSIA, respectively [157], Zheng and coworkers [158] employed radial basis function neural networks and obtained... 

Harding, Popelier, and co-workers [285,286] have employed a variety of quantum chemical approaches in their estimation of the pK s ol oxyacids. In a study of 228 carboxylic acids they used what they call quantum chemical topology to find pK estimates. They tested several different methods, including partial least squares (PLS), support vector machines (SVMs), and radial basis function neural networks (RBFNNs) with Hartree-Fock and density functional calculations, concluding that the SVM models with HF/6-31G calculations were most efficient [285]. Foi a data set of 171 phenols they found that the C-0 bond length provided an effective descriptor for pK estimation [286]. 

The ANNs were developed in an attempt to imitate, mathematically, the characteristics of the biological neurons. They are composed by intercoimected artificial neurons responsible for the processing of input-output relationships, these relationships are learned by training the ANN with a set of irqmt-output patterns. The ANNs can be used for different proposes approximation of functions and classification are examples of such applications. The most common types of ANNs used for classification are the feedforward neural networks (FNNs) and the radial basis function (RBF) networks. Probabilistic neural networks (PNNs) are a kind of RBFs that uses a Bayesian decision strategy (Dehghani et al., 2006). 

Tetteh and co-workers described the application of radial basis function (RBF) neural network models for property prediction and screening (114). They employed a network optimization strategy based on biharmonic spline interpolation for the selection of an optimum number of RBF neurons in the hidden layer and their associated spread parameter. Comparisons with the performance of a PLS regression model showed the superior predictive ability of the RBF neural model. 

Selection of the supervised classification technique or the combination of techniques suitable for accomplishing the classification task. Popular supervised classifiers are Multi-Layer Perceptron Artificial Neural Networks (MLP-ANN), Support Vector Machines (SVM), k-Nearest Neighbours (k-NN), combinations of genetic algorithms (GA) for feature selection with Linear Discriminant Analysis (LDA), Decision Trees and Radial Basis Function (RBF) classifiers. 

---