Collaborative Learning-Based Clustered Support Vector Machine for Modeling of Nonlinear Processes Subject to Noise

The least squares support vector machine (LS-SVM) is often employed to model data with a nonlinear distribution using a divide-and-conquer strategy. However, when nonlinear data are contaminated by either noise or outliers, LS-SVM is often an ineffective approach due to a lack of robustness. In this paper, a collaborative learning-based clustered LS-SVM method is proposed for modeling of nonlinear processes that are subject to noise or outliers. First, a large-scale dataset is divided into several subsets and the data distribution of each subset is estimated. A robust LS-SVM is then developed to represent each subset using this distributional information. A global model is further constructed through integration of all submodels, whose continuity and smoothness are ensured by the development of the collaborative learning technique. As a result, the proposed method considers both the nonlinear distribution of data and the robustness of each submodel, and ensures the continuity and smoothness of the global model. Thus, it can effectively model nonlinear data that is subject to either noise or outliers. As further validation of this approach, both artificial and real cases demonstrated its effectiveness.