Kernel partial robust M-regression as a flexible robust nonlinear modeling technique

Kernel partial least squares (KPLS) is potentially very efficient for tackling nonlinear systems by mapping an original input space into a high-dimensional feature space. Unlike other nonlinear modeling technique, KPLS does not involve any nonlinear optimization procedure and possesses low computational complexity similar to that of linear partial least squares (PLS). But when there are some outliers in the training data set, KPLS regression will have poor properties due to the sensitiveness of PLS to outliers. Under this circumstance, a more robust regression method such as partial robust M-regression (PRM) can be used instead of PLS in the nonlinear kernel-based algorithm. In this paper, a kernel partial robust M-regression (KPRM) is presented. Nonlinear structure in the original input space is transformed into linear one in the high-dimensional feature space; and through choosing appropriately weighting strategy, the proposed method becomes entirely robust to two types of outliers. The prediction performance of KPRM is compared to those of PLS, PRM, and KPLS using three examples; KPRM yields much lower prediction errors for these three data sets, and the loss in efficiency to be paid for is very small.