Smooth PLS Regression for Spectral Data

Abstract

Partial least squares (PLS) regression reduces the regression problem from a large-p number of interrelated predictors to a small-m number of extracted factors. These use information for predicting the response making PLS regression models extremely good for prediction purposes. The PLS regression coefficient vector is determined by the PLS factor loadings which drive the dimension reduction process; it should therefore be smooth, especially when the factor subspace dimension is small. We explore smooth alternatives for PLS regression revisiting a topic that triggered the research interest over the last two decades. We use for this the discrete wavelet transform focusing on PLS regression applications in near infra-red spectroscopy.