Identification of Hinging Hyperplane Models by Fuzzy c-Regression Clustering

This article deals with the identification of the so called 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 that is based on a fuzzy clustering technique called Fuzzy c-Regression Clustering. This clustering technique applies linear models as prototypes and the model parameters and fuzzy membership degrees are identified simultaneously. 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 identifies a hinging hyperplane model first that contains two linear submodels, and after that the two halves of the model (the two linear hyperplanes) are treated separately: two other hinging hyperplane models are identified on the basis of the operating regions of the first two linear submodels. Following these steps, a tree structured piecewise linear model is identified, where the branches correspond to linear division of the operating regime, and the leaves correspond to linear models. In this way a piecewise linear model is constructed.