A clusterwise nonlinear regression algorithm for interval-valued data

Abstract

Interval-valued variables are required in data analysis since this type of data represents either the uncertainty existing in an error measurement or the natural variability of the data. Currently, methods and algorithms which aim to manage interval-valued data are very much required. Hence, this paper presents a center and range clusterwise nonlinear regression algorithm for interval-valued data. The proposed algorithm combines a k-means type algorithm with the center and range linear and nonlinear regression methods for interval-valued data, with the aim to identify both the partition of the data and the relevant regression models fitted on the center and range of the intervals simultaneously, one for each cluster. The proposed method is able to automatically select the best pair of center and range (linear and/or nonlinear) functions according to optimization criteria. A simulation study with synthetic data sets with the purpose of assessing the parameter estimation and the prediction performance of the proposed algorithm was undertaken. Finally, applications on real data sets were performed and the prediction accuracy of the proposed method was compared to the linear case. The results obtained showed that the proposed method performed well on both synthetic and real data sets.