SOMPLS: A supervised self-organising map--partial least squares algorithm for multivariate regression problems

Recently we introduced the XY-fused (XYF) and the Bi-Directional Kohonen (BDK) networks for solving classification problems. It was observed that XYF and BDK are not suited to tackle regression problems due to the limited number of output values stored in the output map weights and the fact that these networks can not interpolate between the learned output values.We combine in this paper the mapping strength of BDK with the modelling power of partial least squares (PLS). In a supervised way a BDK input and output map, which captures, in a global sense, the multivariate structure and the input–output relationship present in the data, is built. Based on the weights of the input map a kernel matrix, which serves as starting point for the PLS algorithm, is computed. This kernel approach guarantees that linear, as well as non-linear, regression problems can be handled.It is shown that the cascade of the supervised BDK Self-Organising Maps and PLS (referred to as SOMPLS) yields a transparent and powerful regression model: the BDK maps and the PLS loadings and regression coefficients will be exploited to visualise various model properties. Moreover, the SOMPLS algorithm guarantees a stable and fast solution for various complex regression problems.For a number of real-world data sets and one simulated data set the performance of SOMPLS is compared to PLS, Kernel Function PLS (KPLS) and Support Vector Machines (SVMs).We demonstrate that SOMPLS allows an in-depth analysis of all aspects of the regression model and is much faster than KPLS and SVMs, especially if large data sets are examined, while yielding the same or even a better performance.