Enhanced weighted kernel regression with prior knowledge in solving small sample problems

Abstract

Previously, weighted kernel regression (WKR) for solving small samples problem has been reported. In general, WKR has proven to be effective when learning from small samples as compared to artificial neural network with back-propagation (ANNBP) and some other techniques. In order to extend the capability of the technique, we introduce a new approach to improve the WKR by incorporating the prior knowledge. In practice, different forms of prior knowledge may be available and it might avoid the weakness of the training samples limitation. In this study, the incorporation of the prior knowledge will produce a set of solutions by considering the available training samples and prior knowledge in modeling. The process involved in obtaining a set of solutions can be regarded as a bi-objective optimization problem. The proposed technique is derived based on the pareto optimality concept (POC) by using multi-objective optimization technique (MOPT). We only focus the study on the challenges of formulating the two objective functions. We demonstrate the capability of the proposed technique to robot manipulator problem. It is shown that the incorporation of the prior knowledge based on POC can be implemented and relatively improved the regression performance. Some related issues of the proposed technique are also discussed.