Global sparse partial least squares

The partial least squares (PLS) is designed for prediction problems when the number of predictors is larger than the number of training samples. PLS is based on latent components that are linear combinations of all of the original predictors, it automatically employs all predictors regardless of their relevance. This will degrade its performance and make it difficult to interpret the result. In this paper, global sparse PLS (GSPLS) is proposed to allow common variable selection in each deflation process as well as dimension reduction. We introduce the ℓ_{2, 1} norm to direction matrix and develop an algorithm for GSPLS via employing the Bregmen Iteration algorithm, illustrate the performance of proposed method with an analysis to red wine dataset. Numerical studies demonstrate the superiority of proposed GSPLS compared with standard PLS and other existing methods for variable selection and prediction in most of the cases.