Radial Basis Function Regression Research Articles

An Optimal Experimental Design Perspective on Radial Basis Function Regression

This article provides a new look at radial basis function regression that reveals striking similarities with the traditional optimal experimental design framework. We show theoretically and computationally that the so-called relevant vectors derived through the relevance vector machine (RVM) and corresponding to the centers of the radial basis function network, are very similar and often identical to the support points obtained through various optimal experimental design criteria like D-optimality. This allows us to provide a statistical meaning to the relevant centers in the context of radial basis function regression, but also opens the door to a variety of ways of approach optimal experimental design in multivariate settings.

A logistic radial basis function regression method for discrimination of cover crops in olive orchards

Olive ( Olea europaea L.) is the main perennial Spanish crop. Soil management in olive orchards is mainly based on intensive and tillage operations, which have a great relevancy in terms of negative environmental impacts. Due to this reason, the European Union (EU) only subsidizes cropping systems which require the implementation of conservation agro-environmental techniques such as cover crops between the rows. Remotely sensed data could offer the possibility of a precise follow-up of presence of cover crops to control these agrarian policy actions, but firstly, it is crucial to explore the potential for classifying variations in spectral signatures of olive trees, bare soil and cover crops using field spectroscopy. In this paper, we used hyperspectral signatures of bare soil, olive trees, and sown and dead cover crops taken in spring and summer in two locations to evaluate the potential of two methods (MultiLogistic regression with Initial and Radial Basis Function covariates, MLIRBF; and SimpleLogistic regression with Initial and Radial Basis Function covariates, SLIRBF) for classifying them in the 400–900 nm spectrum. These methods are based on a MultiLogistic regression model formed by a combination of linear and radial basis function neural network models. The estimation of the coefficients of the model is carried out basically in two phases. First, the number of radial basis functions and the radii and centres’ vector are determined by means of an evolutionary neural network algorithm. A maximum likelihood optimization method determines the rest of the coefficients of a MultiLogistic regression with a set of covariates that include the initial variables and the radial basis functions previously estimated. Finally, we apply forward stepwise techniques of structural simplification. We compare the performance of these methods with robust classification methods: Logistic Regression without covariate selection, MLogistic; Logistic Regression with covariate selection, SLogistic; Logistic Model Trees algorithm (LMT); the C4.5 induction tree; Naïve Bayesian tree algorithm (NBTree); and boosted C4.5 trees using AdaBoost.M1 with 10 and 100 boosting iterations. MLIRBF and SLIRBF models were the best discriminant functions in classifying sown or dead cover crops from olive trees and bare soil in both locations and seasons by using a seven-dimensional vector with green (575 nm), red (600, 625, 650 and 675 nm), and near-infrared (700 and 725 nm) wavelengths as input variables. These models showed a correct classification rate between 95.56% and 100% in both locations and seasons. These results suggest that mapping covers crops in olive trees could be feasible by the analysis of high resolution airborne imagery acquired in spring or summer for monitoring the presence or absence of cover crops by the EU or local administrations in order to make the decision on conceding or not the subsidy.