## 4 Results and Discussion
### Working Memory Data
Although the subjects differ in performance, the proposed classification system exhibits accuracies well above what would be expected in a three-class classification task for all of them. The precision, recall and F1 score values indicate that the accuracies obtained by the classifiers for each subject are not the result of class imbalances in the data or biased class selection  
Figure 6: Average classification accuracy for all subjects as a function of the percentage of selected \(\mathrm{TE}_{\mathrm{xx}}^{\theta\theta^{*}}\) features. by the classifiers themselves. Additionally, all subjects, except subject 3, achieve peak performance when the classifier is trained with only 5% of the connectivity features (subject 3 does so when 10% of the features are selected). These results imply that our \(TE_{\text{xx}}^{\phi\phi}\) characterization strategy successfully captures the discriminant directed phase-amplitude interactions elicited during the change-detection task. Moreover, only a small fraction of those interactions are required to discriminate between the task's levels. In fact, employing a higher percentage of features leads to a pronounced decrease in classification performance, as shown in Figure 6. This phenomenon can be explained because all channel connectivity analyses lead to datasets with a large number of features (see Section 3.2.3), which, in turn, leads to a well-known problem in machine learning: the curse of dimensionality. The larger the dimensionality of the data, the higher the chance that most training instances will be far away from each other, and that new instances will also be far away from those used to train the machine learning system. This makes it difficult to make good predictions [51]. In addition, many of the obtained connectivity features will not provide useful information to discriminate between the conditions of the cognitive paradigm of interest [16], and will only add noise and complexity to the classification stage. Adequate feature selection reduces the dimensionality of the data by getting rid of non-relevant features (connectivity values), which can, as in our case, help with classification performance. At this point, it is worth noting that the vector \(\bar{\varrho}\), used to rank the features, is obtained as the average of the relevance vectors stemming from the different folds of an auxiliary cross-validation scheme, outside of the cross-validation process for classification. Therefore, our classification setup suffers from data leakage, and, as a consequence, the above results area is probably higher than that which could be obtained from a classification system suitable for real-world applications. Nonetheless, our results still show that relatively few connectivity values describing directed phase-amplitude interactions can successfully discriminate between the brain activity elicited at different levels of the change-detection task. Furthermore, the vector \(\bar{\varrho}\) provides valuable insights regarding the directed phase-amplitude interactions that arise while the subjects perform the task. It does this by assigning a relevance value \(\varrho_{p}\) to each column, or feature, in the characterizing matrix \(\mathbf{\Phi}\). In the case of our \(TE_{\text{xx}}^{\phi\phi}\) analysis, \(\varrho_{p}\) indicates whether a particular connectivity between two channels, for a specific frequency-band pair (\(\theta-\alpha,\theta-\beta_{l}\), etc), allows for discrimination of the different cognitive loads of the task. A feature's discriminant ability is tantamount to its variation across classes. That is to say, the most relevant connectivities in \(\bar{\varrho}\) are those that change consistently across trials as a function of the cognitive load, which points to the involvement of those directed phase-amplitude interactions in the underlying working memory systems activated during the task. Figure 7: Highest average classification performance for each subject in the WM database.