Kernel partial diagnostic robust potential to handle high-dimensional and irregular data space on near infrared spectral data

Abstract

In practice, the collected spectra are very often composes of complex overtone and many overlapping peaks which may lead to misinterpretation because of its significant nonlinear characteristics. Using linear solution might not be appropriate. In addition, with a high-dimension of dataset due to large number of observations and data points the classical multiple regressions will neglect to fit. These complexities commonly will impact to multicollinearity problem, furthermore the risk of contamination of multiple outliers and high leverage points also increases. To address these problems, a new method called Kernel Partial Diagnostic Robust Potential (KPDRGP) is introduced. The method allows the nonlinear solution which maps nonlinearly the original input $X$ matrix into higher dimensional feature mapping with corresponds to the Reproducing Kernel Hilbert Spaces (RKHS). In dimensional reduction, the method replaces the dot products calculation of elements in the mapped data to a nonlinear function in the original input space. To prevent the contamination of the multiple outlier and high leverage points the robust procedure using Diagnostic Robust Generalized Potentials (DRGP) algorithm was used. The results verified that using the simulation and real data, the proposed KPDRGP method was superior to the methods in the class of non-kernel and some other robust methods with kernel solution.

Keywords: Analytical chemistry; Diagnostic robust generalized potential; Hilbert-space; Kernel; Near infrared; Nonlinear; Partial least squares; Spectral data.