New possibilistic method for discovering linear local behavior using hyper-Gaussian distributed membership function

Abstract

This paper presents a method to find a model of a system based on the integration of a set of local models. Mainly, properties are sought for the local models: independence of clusters and interpretability of their validity. This has been achieved through the introduction of a possibilistic clustering for the first property and a pre-fixed shape of the membership functions for the second one. A new cost index for the clustering optimization problem has been defined consisting of two terms: one for global error and another for local errors. By giving higher importance to the local errors term, local models valid regionally can be found. To avoid local optima and numerical issues, the parameters of the models are found using global optimization. This new method has been applied to several data sets, and results show how the desired characteristics can be achieved in the resulting models.