## 4 Results  
PLS stands out when it comes to model data that have high collinearity because it uses latent variables. To evaluate the collinearity of the data, principal component analysis (PCA) was carried out with \(\mathbf{X}_{TR}\) and \(\mathbf{Y}_{TR}\) of \(PLS_{OP}\). The result of this analysis shows that 4860 dimensions of \(\mathbf{X}_{TR}\) can be represented with 5 to 8 components, explaining 88.2% to 93.3% of the variance, respectively. Similar results were obtained when analyzing \(\mathbf{Y}_{TR}\), where the number of principal components is 7, much smaller than the original dimension, 35, and explaining all the variance. In addition, in this case, 15.2% of the pairwise correlation coefficients between \(\mathbf{Y}_{TR}\) columns are, in absolute value, greater than 0.5. These results, specific to our problem, indicates the need to use a regression on latent variables, such as PLS. Optimization of the PLS model, Section 3.8, generates 280 ECOC matrices; therefore, 280 matrices \(\mathbf{Y}_{TR}\) result in 280 PLS models. Each of these iterations may have a different \(c\), codeword length, of the ECOC matrix and a different DMCEN index. The optimization looks to minimize the DMCEN index in the training subset, \(\mathbf{X}_{TR}\), obtaining a \(PLS_{OP}\) optimum model with seven latent variables. DMCEN \(=0.031\), and codeword length \(c=35\). All codeword lengths and DMCEN values obtained are depicted in Figure 4. Codeword length varies from 30 to 39, greater than the expected 30 (Section 3.3), with a median value of 36. DMCEN varies from 0.031 to 0.217 with a median and mean value of 0.12 with a very symmetric distribution. Figure 4: Some characteristics of the 280 repetitions made in the optimisation step. (**a**) Codeword length of ECOC matrices. (**b**) DMCEN values for PLS models built with these ECOC matrices. Sensitivity and specificity in the training matrix \(\mathbf{S}_{TR}\) are shown in Table 1. The meaning of this matrix was thoroughly discussed at the beginning of Section 2. There are two elements in Table 1 that differ from one (the best possible result); both cases will be commented. First, the element marked with (*), 0.86, means that one \(\mathrm{C}_{3}\) sample was wrongly assigned to the \(C_{1}\) class, so the \(C_{1}\) class model is not completely specific against \(C_{3}\). Second, the element marked with (*), 0.71, means that two \(\mathrm{C}_{6}\) samples were assigned to \(C_{5}\), so the \(C_{5}\) class model is not completely specific against \(\mathrm{C}_{6}\). From this analysis, we can say that the \(C_{1}\) and \(C_{5}\) class models are unable to fully reject signals from \(C_{3}\) and \(\mathrm{C}_{6}\), respectively. Applying the \(PLS_{OP}\) model to the test matrix \(\mathbf{X}_{TS}\), the sensitivity and specificity matrix \(\mathbf{S}_{TS}\) is obtained, Table 2, and DMCEN associated with \(\mathbf{X}_{TS}\) is 0.209. Again, we are going to comment on the three elements of \(\mathbf{S}_{TS}\) that differ from the one in Table 2. First, the element marked with (*), 0.67, means that one out of the three signals from the \(C_{3}\) class was wrongly rejected from the \(C_{3}\) class model. Therefore, the class \(C_{3}\) model sensitivity lowered to 0.67. The \(C_{3}\) class model also wrongly accepted two signals belonging to \(C_{8}\), thus reducing its specificity against \(C_{8}\) to 0.33, marked as (**). Lastly, the element marked as (***), 0.33, means that the \(C_{5}\) class model failed to reject two signals from the \(C_{6}\) class, so its specificity against \(C_{6}\) reduced to 0.33. From these results, we can say the \(C_{3}\) class model is having problems to model the \(C_{3}\) signals like its own and is failing to completely reject all signals from \(C_{8}\). The \(C_{5}\) class model is presenting the same flaw as in the training set wrongly assigning \(C_{6}\) signals to itself.