Premise parameter estimation and adaptation in fuzzy systems with open-loop clustering methods

Clustering algorithms as unsupervised learning techniques are of fundamental importance in order to group any kind of recorded measurement data (in form of images, signals or physical values from sensors) into separate regions, also called clusters. This grouping is not only applied whenever a classification of feature vectors representing special attributes of the data set is required, but also in the case of approximating arbitrary relationships which possess an intense local (in the case of static processes) or time-variant (in the case of dynamic processes) behavior and therefore cannot be described with one closed analytical formula over the whole domain. In this paper first open-loop clustering methods are described, i.e. clustering methods which are able to adapt former generated clusters pointwise. Afterwards, a new approach for estimating and updating nonlinear parameters in Takagi-Sugeno fuzzy inference systems, i.e. premise parameters in the rules-antecedents, by applying open-loop clustering algorithms is stated together with the impact on the bias error and training time for up to 5-dimensional fuzzy models. Additionally; a detailed analysis of the method is given.