# Multiblock Analysis Applied to TD-NMR of Butters and Related Products  
[PERSON]  
1 INRAE, ITAP, Montpellier SupAgro, University of Montpellier, F-34096 Montpellier, France;  
[EMAIL_ADDRESS]  
2 ChemHouse Research Group, F-34096 Montpellier, France  
3 INRAE, UR OPAALE, 17 Avenue de Cucille, CS 64427, F-35044 Rennes, France;  
[EMAIL_ADDRESS] (M.C. ); [EMAIL_ADDRESS] (C.R.-M.)  
[PERSON]  
this process, a decaying signal called the Free Induction Decay (FID) is obtained. Other dedicated sequences yield the acquisition of the two intrinsic parameters in NMR, namely longitudinal relaxation time (T\({}_{1}\)) and transverse relaxation time (T\({}_{2}\)). T\({}_{2}\) is widely used to measure solid fat content and the water and oil amounts of foodstuffs, based on well-known international standard methods (AOCS Cd 16b-93, AOCS Cd 16-81, ISO 8292, IUPAC 2.150). However, these NMR standard methods are often non-applicable to non-anhydrous products 1. Moreover, there is little application of these methods in complex food systems characterized by a phase-compositional diversity of molecules, such as butters and related products. In these systems, the interpretation of the signal can be very tedious since chemical and diffusional proton exchanges modulate the signal intensities. In terms of signal analysis, chemometrics offers efficient solutions to process TD-NMR data. In the 1990s, [PERSON] et al. [5; 6] showed that chemometrics offers fast and efficient methods, such as partial least-squares regression (PLS) [7], for determining the information content of the signals. Demonstrations on margarine and butters for determining their water content, or the water mobility in starchy-lignin samples were rather convincing. Since then, PLS were mainly used on TD-NMR data for the rapid evaluation of oil or water content in food samples [8; 9; 10; 11; 12; 13]. Although PLS is still the most popular chemometric tool, other methods can be useful to assist in the processing of TD-NMR data. Thus, chemometrics offers methods for merging several measurements performed on the same samples, referred to as multiblock analysis methods. [14]. Various multiblock PLS methods have been developed following similar rationales [15]. More recently the Sequential and Orthogonalized PLS (SO-PLS) was proposed [16]. This method uses a successive decomposition of the blocks in order to take advantage of the full predictive potential of the data. Chemometrics also provides methods for variable selection. The purpose of variable selection is twofold: First, identify the parts of the signal that are most important for characterizing a product. This type of selection can be performed by examining the loadings of factorial methods, such as PLS or Principal Component Analysis (PCA), by using iterative methods such as iPLS [17], or by using criteria such as Variable Importance in Projection (VIP) [18]. The second objective of variable selection is to identify a small number of variables on which a calibration model can be built. This could be of great interest in NMR to reduce analysis time. The most commonly used methods in chemometrics with this purpose are the sparse methods [19], or variance based methods such as SPA [20] or CovSel [21]. The variable selection in a multiblock calibration framework has been little investigated. The VIP concept has been adapted to SO-PLS [22], which allows for detecting important areas in the signals as in classical PLS. The combination of SO-PLS and CovSel recently led to SO-CovSel [23], which allows for selecting a very small number of variables from multiblock data, most related to a predicted response. In this work, we proposed to apply the multiblock analysis methods on NMR measurements in complex foodstuffs. As mentioned before, most of the standard NMR methods use transverse T\({}_{2}\) relaxation time measurements or combination of both T\({}_{1}\) and T\({}_{2}\) measurements for water and/or fat quantification [2].