Assessing feature relevance in NPLS models by VIP

• Variable Importance in Projection (VIP) extended to multi-way data, i.e. NPLS models.
• VIPs are defined for each mode, for each single y-response and for all Y altogether.
• VIPs are discussed comparatively to NPLS weights and regression coefficients.

Multilinear PLS (NPLS) and its discriminant version (NPLS-DA) are very diffuse tools to model multi-way data arrays. Analysis of NPLS weights and NPLS regression coefficients allows data patterns, feature correlation and covariance structure to be depicted. In this study we propose an extension of the Variable Importance in Projection (VIP) parameter to multi-way arrays in order to highlight the most relevant features to predict the studied dependent properties either for interpretative purposes or to operate feature selection. The VIPs are implemented for each mode of the data array and in the case of multivariate dependent responses considering both the cases of expressing VIP with respect to each single y-variable and of taking into account all y-variables altogether.Three different applications to real data are presented: i) NPLS has been used to model the properties of bread loaves from near infrared spectra of dough, acquired at different leavening times, and corresponding to different flour formulations. VIP values were used to assess the spectral regions mainly involved in determining flour performance; ii) assessing the authenticity of extra virgin olive oils by NPLS-DA elaboration of gas chromatography/mass spectrometry data (GC–MS). VIP values were used to assess both GC and MS discriminant features; iii) NPLS analysis of a fMRI-BOLD experiment based on a pain paradigm of acute prolonged pain in healthy volunteers, in order to reproduce efficiently the corresponding psychophysical pain profiles. VIP values were used to identify the brain regions mainly involved in determining the pain intensity profile.