## 3 Results and Discussion
### Data Processing Results Obtained with SSIR
In these cases, only a single node is passed to the SSIR procedure, together with the individual nodes which are not degenerated (all these nodes are called representative nodes or, simply, representatives). Of the previously mentioned 299 non-constant nodes, 237 were selected as representatives. The SSIR procedure detects which representative binary nodes are relevant to classify the samples. At the end of the calculation, the final reported variables are those attached to all the selected nodes and also the represented ones, if any degeneration has occurred. The SSIR algorithm generates rules. A rule is the combination of several levels of distinct nodes. Normally, and for the sake of simplicity, only order 2 and 3 rules are considered when applying SSIR. This is the same as occurs within the design of experiments theory: usually contributions and interactions of two or, at most, three factors are able to explain the relevant variables governing the experiment. Despite finding that order 2 rules were able to detect the relevant variables in this chromatographic problem, surprisingly, the simplest rules of order one performed equally well. This implies that all of the 237 discretized variables were inspected alone, one at a time. A total of 11 representative nodes exhibited a \(p\)-value less than or equal to the threshold value of 0.0005 (see below). As was expected, all intervals centered on half integer values were automatically discarded by the procedure. The total number of represented variables is 13. Table 2 lists the corresponding associated intervals of the selected variables (see supplementary material Algorithm S2 for details of the ranking procedure). For each variable, a reckoning was performed to look for the number of high and low levels found along the two classes of samples. Table 3 presents the relevant data. The values for high and low levels of the same kind of sample (either treated or non-treated) are complementary, with the total sum being the constant of 28 samples. Visually, the asymmetric distribution of values along the columns of high and low variable levels shows classification tendencies. For instance, variables 2 and 7 are found at the high level in all the treated samples, but also in many non-treated ones (5 and 15, respectively). Remarkably, variables 3 and 4 are found at the high level in 23 of the treated samples and in none of \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variable \#** & **Time Interval** & **m/z Interval (amu)** & **1 st PCA Loading** & **2 nd PCA Loading** \\  & **(min)** & **1** & **in Figure 3** & **in Figure 3** \\ \hline
1 & [7.3, 7.7) & 95 & 0.335 & \(-\)0.106 \\
2 & [6.7, 7.0) & 95 & 0.225 & 0.286 \\
3 & [10.3, 10.7) & 110 & 0.341 & 0.194 \\
4 & [10.3, 10.7) & 109 & 0.332 & 0.221 \\
5 & [7.0, 7.3) & 97 & 0.315 & \(-\)0.058 \\
6 & [7.0, 7.3) & 67 & 0.294 & 0.166 \\
7 & [6.7, 7.0) & 96 & 0.249 & 0.198 \\
8 & [7.3, 7.7) & 96 & 0.299 & \(-\)0.243 \\
9 & [10.7, 11.0) & 109 & 0.285 & \(-\)0.217 \\
10 & [10.7, 11.0) & 110 & 0.272 & \(-\)0.286 \\
11 & [7.0, 7.3) & 51 & 0.308 & 0.237 \\
12 & [8.7, 9.0) & 51 & \(-\)0.106 & 0.497 \\
13 & [9.0, 9.3) & 78 & \(-\)0.111 & 0.509 \\ \hline \hline \end{tabular}  
* The interval center is indicated. The interval has a radius of 0.25 amu.  
\end{table} 
Table 2: Selected variables by SSIR after the binary codification of the signals. the non-treated ones. On the other hand, variables 3, 4, 6, 9, 10 and 11 are present at a low level in all the non-treated samples, and the first two of them are present at a low level in only five treated samples. Variable 12 is present in its low level in all the treated samples. Similarly, variable 13 is present at a low level in all of the treated samples but one. Variables 12 and 13 can be associated with the disappearance of a certain compound or compounds. This is also concurrent with the fact that the mean peak areas of these variables among treated samples is less than that of the non-treated ones.