Regional models: A new approach for nonlinear system identification via clustering of the self-organizing map

Global modelling consists in fitting a single regression model to the available data, using the whole set of input and output observations. On the other side of the spectrum stands the local modelling approach, in which the input space is segmented into several small partitions and a specialized regression model is fit to each partition. In this paper, we propose a novel approach, called Regional Models (RM), that stands in between the global and local modelling ones. The proposal extends the two-level clustering approach by Vesanto and Alhoniemi (2000 [1]) to regression problems, more specifically, to system identification. In this regard, we first partition the input space using the Self-Organizing Map (SOM), and then perform clustering over the prototypes of the trained SOM. Finally, regional regression models are built over the clusters (i.e. over the regions) of SOM prototypes, not over each SOM prototype as in local modelling. Under the proposed framework, we build regional linear and nonlinear regression models. For the linear case, we use autoregressive models with eXogenous (ARX) whose parameters are estimated using the ordinary least-squares (OLS) method. Regional nonlinear ARX (NARX) models are built using the Extreme Learning Machine network. Additionally, we develop robust variants of the proposed regional models through the use of M-estimation, a statistical framework for handling outliers, since the OLS is highly sensitive to them. Comprehensive performance evaluation of the proposed models on synthetic and real-world datasets is carried out and the results compared to those achieved by standard global and local models.