Abstract
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.
Highlights
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
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
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)
Summary
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 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. Multi-way analysis allows simplifying the interpretation of the results and providing more adequate and robust models using relatively few parameters [5,6]. While this is true in general, it is worth noticing that when dealing with real-time monitoring, e.g. in batch process monitoring, N-way models may not represent a real advantage with respect to adopting a proper unfolding/refolding procedure as by using Multiway-PCA [7].
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