Feature selection using distributions of orthogonal PLS regression vectors in spectral data

Feature selection, which is important for successful analysis of chemometric data, aims to produce parsimonious and predictive models. Partial least squares (PLS) regression is one of the main methods in chemometrics for analyzing multivariate data with input X and response Y by modeling the covariance structure in the X and Y spaces. Recently, orthogonal projections to latent structures (OPLS) has been widely used in processing multivariate data because OPLS improves the interpretability of PLS models by removing systematic variation in the X space not correlated to Y. The purpose of this paper is to present a feature selection method of multivariate data through orthogonal PLS regression (OPLSR), which combines orthogonal signal correction with PLS. The presented method generates empirical distributions of features effects upon Y in OPLSR vectors via permutation tests and examines the significance of the effects of the input features on Y. We show the performance of the proposed method using a simulation study in which a three-layer network structure exists in compared with the false discovery rate method. To demonstrate this method, we apply it to both real-life NIR spectra data and mass spectrometry data.