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Partial Least-Squares (PLS) Regression is a widely used tool in chemometricsfor performing multivariate regression. PLS is a bi-linear method that has alimited capacity of modelling non-linear relations between the predictorvariables and the response. Kernel PLS (K-PLS) has been introduced formodelling non-linear predictor-response relations. In K-PLS, the input data ismapped via a kernel function to a Reproducing Kernel Hilbert space (RKH), wherethe dependencies between the response and the input matrix are assumed to belinear. K-PLS is performed in the RKH space between the kernel matrix and thedependent variable. Most available studies use fixed kernel parameters. Only afew studies have been conducted on optimizing the kernel parameters for K-PLS.In this article, we propose a methodology for the kernel function optimizationbased on Kernel Flows (KF), a technique developed for Gaussian processregression (GPR). The results are illustrated with four case studies. The casestudies represent both numerical examples and real data used in classificationand regression tasks. K-PLS optimized with KF, called KF-PLS in this study, isshown to yield good results in all illustrated scenarios. The paper presentscross-validation studies and hyperparameter analysis of the KF methodology whenapplied to K-PLS.

KF-PLS: Optimizing Kernel Partial Least-Squares (K-PLS) with Kernel Flows