Kernel Partial Least Square Regression with High Resistance to Multiple Outliers and Bad Leverage Points on Near-Infrared Spectral Data Analysis

Abstract

Multivariate statistical analysis such as partial least square regression (PLSR) is the common data processing technique used to handle high-dimensional data space on near-infrared (NIR) spectral datasets. The PLSR is useful to tackle the multicollinearity and heteroscedasticity problem that can be commonly found in such data space. With the problem of the nonlinear structure in the original input space, the use of the classical PLSR model might not be appropriate. In addition, the contamination of multiple outliers and high leverage points (HLPs) in the dataset could further damage the model. Generally, HLPs contain both good leverage points (GLPs) and bad leverage points (BLPs); therefore, in this case, removing the BLPs seems relevant since it has a significant impact on the parameter estimates and can slow down the convergence process. On the other hand, the GLPs provide a good efficiency in the model calibration process; thus, they should not be eliminated. In this study, robust alternatives to the existing kernel partial least square (KPLS) regression, which are called the kernel partial robust GM6-estimator (KPRGM6) regression and the kernel partial robust modified GM6-estimator (KPRMGM6) regression are introduced. The nonlinear solution on PLSR was handled through kernel-based learning by nonlinearly projecting the original input data matrix into a high-dimensional feature mapping that corresponded to the reproducing kernel Hilbert spaces (RKHS). To increase the robustness, the improvements on GM6 estimators are presented with the nonlinear PLSR. Based on the investigation using several artificial dataset scenarios from Monte Carlo simulations and two sets from the near-infrared (NIR) spectral dataset, the proposed robust KPRMGM6 is found to be superior to the robust KPRGM6 and non-robust KPLS.