Fuzzy Clustering for the Identification of Hinging Hyperplanes Based Regression Trees

Abstract

This article deals with the identification of hinging hyperplane models. This type of non-linear black-box models is relatively new, and its identification is not thoroughly examined and discussed so far. They can be an alternative to artificial neural nets but there is a clear need for an effective identification method. This paper presents a new identification technique for that purpose based on a fuzzy clustering technique called Fuzzy c-Regression Clustering. To use this clustering procedure for the identification of hinging hyperplanes there is a need to handle restrictions about the relative location of the hyperplanes: they should intersect each other in the operating regime covered by the data points. The proposed method recursively identifies a hinging hyperplane model that contains two linear submodels by partitioning of the operating region of one local linear model resuling in a binary regression tree. Hence, this paper proposes a new algorithm for the identification of tree structured piecewise linear models, where the branches correspond to linear division of the operating regime based on the intersection of two local linear models. The effectiveness of the proposed model is demonstrated by a dynamic model identification example.