An Optimization Perspective on Kernel Partial Least Squares Regression

This work provides a novel derivation based on optimization for the partial least squares (PLS) algorithm for linear regression and the kernel partial least squares (K-PLS) algorithm for nonlinear regression. This derivation makes the PLS algorithm, popularly and successfully used for chemometrics applications, more accessible to machine learning researchers. The work introduces Direct K-PLS, a novel way to kernelize PLS based on direct factorization of the kernel matrix. Computational results and discussion illustrate the relative merits of K-PLS and Direct K-PLS versus closely related kernel methods such as support vector machines and kernel ridge regression. ∗This work was supported by NSF grant number IIS-9979860. Many thanks to Roman Rosipal, Nello Cristianini, and Johan Suykens for many helpful discussions on PLS and kernel methods, Sean Ekans from Concurrent Pharmaceutical for providing molecule descriptions for the Albumin data set, Curt Breneman and N. Sukumar for generating descriptors for the Albumin data, and Tony Van Gestel for an efficient Gaussian kernel implementation algorithm. This work appears in J.A.K. Suykens, G. Horvath, S. Basu, C. Micchelli, J. Vandewalle (Eds.) Advances in Learning Theory: Methods, Models and Applications, NATO Science Series III: Computer & Systems Sciences, Volume 190, IOS Press Amsterdam, 2003,p. 227-250. 2 K.P. Bennett, M.J. Embrechts