KF-PLS: Optimizing Kernel Partial Least-Squares (K-PLS) with Kernel
  Flows
Zina-Sabrina Duma Jouni Susiluoto Otto Lamminpää Tuomas Sihvonen Satu-Pia Reinikainen Heikki Haario
Partial Least-Squares (PLS) Regression is a widely used tool in chemometrics
for performing multivariate regression. PLS is a bi-linear method that has a
limited capacity of modelling non-linear relations between the predictor
variables and the response. Kernel PLS (K-PLS) has been introduced for
modelling non-linear predictor-response relations. In K-PLS, the input data is
mapped via a kernel function to a Reproducing Kernel Hilbert space (RKH), where
the dependencies between the response and the input matrix are assumed to be
linear. K-PLS is performed in the RKH space between the kernel matrix and the
dependent variable. Most available studies use fixed kernel parameters. Only a
few studies have been conducted on optimizing the kernel parameters for K-PLS.
In this article, we propose a methodology for the kernel function optimization
based on Kernel Flows (KF), a technique developed for Gaussian process
regression (GPR). The results are illustrated with four case studies. The case
studies represent both numerical examples and real data used in classification
and regression tasks. K-PLS optimized with KF, called KF-PLS in this study, is
shown to yield good results in all illustrated scenarios. The paper presents
cross-validation studies and hyperparameter analysis of the KF methodology when
applied to K-PLS.