Identification of Optimal Subspace from PLS Regression

Partial least-squares regression, a novel approach for multivariate analysis, is widely used for modeling a multi-collinear variable data set, with improved model accuracy and reliability based on building a subspace with most explanatory ability to the data set. In this paper the factor analysis method is presented to transform orthogonally the optimal subspace, which is obtained from partial least-squares regression. The transformation can identify each factor in a meaningful way but does not change the results of partial least-squares regression model. Therefore, the physical meaning of the optimal subspace of partial least-squares regression can be illustrated. A case study demonstrates that the original variable set is divided into several variable groups after the orthogonal transform, each of which is corresponding to a new factor in the subspace such that its explanatory ability is improved.