Radial Basis Functions for Data Mining

This chapter deals with the design and applications of the radial basis function (RBF) radial basis function (RBF) model. It is organized into three parts. The first part, consisting of Sect. 35.1, describes the two data mining activities addressed here: classification and regression. Next, we discuss the important issue of bias-variance tradeoff and its relationship to model complexity. The second part consists of Sects. 35.2 to 35.4. Section 35.2 describes the RBF model architecture and its parameters. In Sect. 35.3.1 we briefly describe the four common algorithms used for its design: clustering, orthogonal least squares, regularization, and gradient descent. In Sect. 35.3.2 we discuss an algebraic algorithm, the SG algorithm, which provides a step-by-step approach to RBF design. Section 35.4 presents a detailed example to illustrate the use of the SG algorithm on a small data set. The third part consists of Sects. 35.5 and 35.6. In Sect. 35.5 we describe the development of RBF classifiers for a well-known benchmark problem to determine whether Pima Indians have diabetes. We describe the need for and importance of partitioning the data into training, validation, and test sets. The training set is employed to develop candidate models, the validation set is used to select a model, and the generalization performance of the selected model is assessed using the test set. Section 35.6 describes a recent data mining application in bioinformatics, where the objective is to analyze the gene expression profiles of Leukemia data from patients whose classes are known to predict the target cancer class. Finally, Sect. 35.7 provides concluding remarks and directs the reader to related literature. Although the material in this chapter is applicable to other types of basis funktions, we have used only the Gaussian function for illustrations and case studies because of its popularity and good mathematical properties.