Robust generalized fuzzy systems training from high-dimensional time-series data using local structure preserving PLS

• Edwin Lughofer
• Ramin Nikzad-Langerodi

Establishing fuzzy models from time-series data with predictive capabilities for numerical targets typically requires dimension reduction techniques to overcome red the severe curse of dimensionality effects. Linear projection methods are promising candidates in this context as they — unlike non-linear dimension reduction techniques — preserve interpretability of the resulting models. However, linear projections do not reveal the inherent (non-linear, local) cluster structure of the data and are thus not ideally suited for the identification of fuzzy rule bases. To overcome this limitation, we here present a new fuzzy modeling approach that combines generalized fuzzy systems modeling with a local structure preserving variant of partial least squares (PLS). In contrast to ordinary PLS, our approach maps a weighted (adjacency) graph on the directions associated with high co-variance with the response in order to emphasizes local data structures when constructing the latent variable (LV) space. This operates into the direction from which the (training of the) fuzzy model benefits, as therein local regions are represented by sub-models in form of generalized TS fuzzy rules. The local structure preserving LV space is obtained by solving a new penalized objective function, which assures global optimality of the solutions by virtue of the specific properties of the Laplacian matrix. Local regions are characterized in two ways, i.) through nearest neighbor points (assuming fixed local region sizes) and ii.) through density regions identified by clustering (achieving variable local region sizes). To establish a robust time-series based forecast model, the training of a generalized TS fuzzy model is conducted in the LV space with reduced dimensionality. It is realized by an iterative robust version of Gen-Smart-EFS , allowing multiple passes over the complete data sets until convergence of the antecedent space. Consequent parameters are estimated by ...