O2‐PLS, a two‐block (X–Y) latent variable regression (LVR) method with an integral OSC filter

Abstract

The O2-PLS method is derived from the basic partial least squares projections to latent structures (PLS) prediction approach. The importance of the covariation matrix (Y T X) is pointed out in relation to both the prediction model and the structured noise in both X and Y. Structured noise in X (or Y) is defined as the systematic variation of X (or Y) not linearly correlated with Y (or X). Examples in spectroscopy include baseline, drift and scatter effects. If structured noise is present in X, the existing latent variable regression (LVR) methods, e.g. PLS, will have weakened score±loading correspondence beyond the first component. This negatively affects the interpretation of model parameters such as scores and loadings. The O2-PLS method models and predicts both X and Y and has an integral orthogonal signal correction (OSC) filter that separates the structured noise in X and Y from their joint X±Y covariation used in the prediction model. This leads to a minimal number of predictive components with full score±loading correspondence and also an opportunity to interpret the structured noise. In both a real and a simulated example, O2-PLS and PLS gave very similar predictions of Y. However, the interpretation of the prediction models was clearly improved with O2-PLS, because structured noise was present. In the NIR example, O2-PLS revealed a strong water peak and baseline offset in the structured noise components. In the simulated example the O2-PLS plot of observed versus predicted Y-scores (u vs u hat ) showed good predictions. The corresponding loading vectors provided good interpretation of the covarying analytes in X and Y.

Subtle metabolic and liver gene transcriptional changes underlie diet-induced fatty liver susceptibility in insulin-resistant mice

“…The method was also applied to determine global metabolic changes derived from plasma 1 H NMR data in response to short-term and prolonged fat feeding in 129S6 mice. Further details of standard O-PLS implementation in metabonomics have been given previously [17,20].…”

Gut bacteria–host metabolic interplay during conventionalisation of the mouse germfree colon

“…All data were first visualised by Principal Component Analysis in order to identify potential outliers. Orthogonal partial least-square discriminant analysis (OPLS-DA) models (Trygg, Svante 2003) were then fitted between successive time-points in order to highlight discriminant metabolites. Principal Component Analysis, O-PLS, O-PLS-DA and Statistical Total Correlation Spectroscopy were performed using an in-house routines (Cloarec et al, 2005).…”

“…To test this notion, statistical modelling (using O2-PLS methods) was employed to detect significant correlations between microbial groups and the mucosal transcriptome, the mucosal and urine metabolic profiles. O2-PLS regression-models (Trygg, Svante 2003) between 1 H NMR urine spectra and level-2 (genera-like) MITChip absolute abundance scores were performed to search for statistically and biologically meaningful correlations between microbial taxa in the colon, colon transcriptome and concentrations of specific metabolites. The MITChip probe intensities that were best predicted by the variation in the 1 H NMR data were assigned to level-2 groups within the phylum Bacteroidetes.…”

A Sparse PLS for Variable Selection when Integrating Omics Data

“…In the context of feature selection from both data sets, one closely related work proved to bring biologically meaningful results is the O2PLS model (Trygg and Wold, 2003), associated to variable selection in Bylesjö et al (2007) for combining and selecting transcript and metabolite data in Arabidopsis Thaliana in a regression framework. O2PLS decomposes each data set in three structures (predictive, unique and residual).…”