Weighted Clusterwise Linear Regression based on adaptive quadratic form distance. (15th December 2021) - da Silva, Ricardo A.M.; de Carvalho, Francisco de A.T.
Abstract: The standard approach to Clusterwise Regression is the Clusterwise Linear Regression method. This approach can lead to data over-fitting, and it is not able to distinguish linear relationships in groups of observations well separated in the space of explanatory variables. This paper presents a Weighted Clusterwise Linear Regression method to obtain homogeneous clusters of observations while maintaining a proper fitting for the response variable, by the minimization of an optimization criterion that combines a k-means-like criterion (based on an adaptive quadratic form dissimilarity) in x-space and the criterion of minimum squared residuals of Regression Analysis. The adaptive metric allows automatic weighing or take into account the correlation between explanatory variables under multiple constraints types. We explore six constraints types. Experiments with synthetic and benchmark datasets corroborate the usefulness of the proposed method. Highlights: A Weighted Clusterwise Regression to obtain homogeneous clusters. Objective function combining a kmeans-like and a minimum SSQ criteria. Based on adaptive quadratic form dissimilarity, in x-space. Automatic weighing of explanatory variables under six constraints types. Synthetic and real datasets corroborate the usefulness of the method.