## 2 Materials and Methods
### Samples
#### 2.1.2 MIR Measurements  
MIR spectra of both pure and adulterated bell pepper samples were collected using a PerkinElmer Spectrum Two(tm) (PerkinElmer, Waltham, MA, USA) FT-IR spectrometer, equipped with a PerkinElmer Universal Attenuated Total Reflectance (uATR) device (with single bounce diamond crystal) and a deuterated triglycine sulfate (DTGS) detector. The inspected spectral range was between 4000 cm\({}^{-1}\) and 400 cm\({}^{-1}\) (1 cm\({}^{-1}\) nominal resolution). The background was collected with the crystal exposed to the air and updated (approximately) every hour. Any possible sample leftover on the attenuated total reflectance (ATR) crystal was removed using soft tissues and methanol. The cleaning procedure was carried out prior to every measurement and the crystal was air-dried before collecting a new spectrum. IR signals were recorded by pressing the ATR device on the ground samples. The pressure applied was optimized for each sample, by means of a monitoring system implemented in the software of the instrument. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Sample \#**} & **Adulterant** & \multirow{2}{*}{**Sample \#**} & **Adulterant** & \multirow{2}{*}{**Sample \#**} & **Adulterant** & \multirow{2}{*}{**Sample \#**} & **Adulterant** \\  & **(\%)** & & **(\%)** & & **(\%)** & & **(\%)** \\ \hline
1 & 2 & 11 & 6 & 21 & 10.5 & 31 & 29 \\
2 & 2.5 & 12 & 6.5 & 22 & 11 & 32 & 31 \\
3 & 2.8 & 13 & 7 & 23 & 13 & 33 & 33 \\
4 & 3 & 14 & 7.5 & 24 & 15 & 34 & 35 \\
5 & 3.5 & 15 & 8 & 25 & 17 & 35 & 37 \\
6 & 4 & 16 & 8.5 & 26 & 19 & 36 & 39 \\
7 & 4.5 & 17 & 9 & 27 & 20 & 37 & 43 \\
8 & 5 & 18 & 9.5 & 28 & 23 & 38 & 46 \\
9 & 5.5 & 19 & 9.7 & 29 & 25 & 39 & 48 \\
10 & 5.7 & 20 & 10 & 30 & 27 & 40 & 50 \\ \hline \end{tabular}
\end{table} 
Table 1: Adulterated samples, percentage of the adulterant (paprika). Data Fusion Approaches: Sequential and Orthogonalized Partial Least Squares-Linear Discriminant Analysis (SO-PLS-LDA) and Sequential and Orthogonalized Covariance Selection-Linear Discriminant Analysis (SO-CovSel-LDA)  
Sequential and orthogonalized partial least squares (SO-PLS) [15; 22] is a multi-block method conceived for solving regression problems which has been extended to deal with classification problems by combination with linear discriminant analysis (LDA) [23; 24]. SO-PLS allows a sequential extraction of non-redundant information from different data blocks and it is particularly suitable to handle highly correlated data sets. Considering the case where two sets of measurements (\(X_{1}\) and \(X_{2}\)), e.g., data collected by different analytical platforms, are used to estimate a response \(Y\), the SO-PLS algorithm can be briefly summarized as follows:  
1. \(Y\) is fitted to \(X_{1}\) by PLS regression: \(\hat{Y}=X_{1}B_{1}\). 2. \(X_{2}\) is orthogonalized with respect to the \(X_{1}\)-scores estimated in (a), obtaining \(X_{2,Orth}\). 3. \(X_{2,Orth}\) is fitted to the residuals from step (a) by partial least squares (PLS) regression. 4. The overall regression model is obtained by combining the outcomes of (a) and (c), and can be expressed as: \(\hat{Y}=\hat{Y}_{1}+\hat{Y}_{2,orth}=X_{1}B_{1}+X_{2,\ orth}B_{2,orth}\), where the hat (\(\cdot\)) indicates model predictions and \(B_{1}\) and \(B_{2,orth}\) are the regression coefficient matrices. In order to use SO-PLS to deal with classification problems, i.e., in SO-PLS-LDA, at first, information about class belonging has to be encoded in a dummy response matrix, as it is customarily performed in partial least squares-discriminant analysis (PLS-DA). Then, a SO-PLS regression model is calculated between the independent blocks of data and the dummy \(Y\) and eventually, once the SO-PLS model is built, LDA can be applied either to the concatenated scores of scores of \(X_{1}\) and \(X_{2,Orth}\) or to the predicted responses [15; 24]. SO-CovSel is a multi-block regression method derived from SO-PLS [25].