4.2.2. Working Memory Results

Figure 10 presents the average classification accuracy for all subjects in the WM database as a function of the number of selected features, for TE*κα* and TE*<sup>θ</sup> κα*. The results show that the classifier trained from phase TE features markedly outperforms the one trained using real-valued TE estimates, as long as the appropriate percentage of features is selected. This difference might be attributed to the hypothesized phase-based nature of directed interactions during WM tasks [35,50], which would be better captured by phase TE. Furthermore, both accuracy curves highlight the importance of feature selection, since they show a steep performance degradation as more features are used to train the classifiers. In this case, the CKA-based relevance analysis not only allows reducing the number of features needed to successfully classify the three cognitive load levels present in the WM data but also prevents the classifiers from being confounded by connections that do not hold relevant information to discriminate between the target conditions.

**Figure 10.** Average classification accuracies, and their standard deviations, for all subjects in the WM database as a function of the number features selected to train the classifiers.

Figure 11 depicts the highest average classification accuracy per subject for TE*<sup>θ</sup> κα*, GC*<sup>θ</sup>* and PSI. The subjects are ordered from highest to lowest performance. Unlike the results obtained for the MI database, we do not observe an underperforming group of subjects, especially after considering the fact that for the WM database the classifiers must discriminate among three classes instead of two. On the other hand, in this case, the TE*<sup>θ</sup> κα*-based classifier largely outperforms those based on alternative connectivity estimation strategies in most subjects. Here, we must point out that the auxiliary cross-validation step introduced for feature selection, aiming to obtain stable CKA results for the reduced number of available trials, leads to data leakage. This is because, ultimately, it requires all the available data to estimate **¯**, which renders it a nonviable approach for practical BCI implementations and can inflate performance evaluations, such as the accuracy results previously discussed. However, since the same strategy was implemented for all classification systems and connectivity measures considered for the WM database, comparisons among them remain valid, and the relative differences in performance are still informative.

**Figure 11.** Highest average classification accuracy for each subject in the WM database. The subjects are ordered from highest to lowest performance according to the accuracies obtained for the TE*<sup>θ</sup> κα*-based classifier.

In order to elucidate the pairwise connectivities, and their corresponding frequency bands, that allow the TE*<sup>θ</sup> κα*-based classification system to successfully discriminate among different memory loads, we proceeded as described in Section 4.2.1 and from **¯** obtained a node relevance vector ¯*<sup>n</sup>* <sup>∈</sup> <sup>R</sup>3*C*. Then, we applied t-SNE on ¯*n*. Figure 12A shows the obtained two-dimensional representation of the relevance vectors for each subject in the WM database. Unlike the results observed before for the MI database, there is not a clear association between the subject distribution on the plot and their classification accuracies. Nonetheless, Figure 12A shows the presence of well-defined groups sharing similar relevance patterns. As before, we grouped the subjects into clusters using the k-means algorithm. The number of clusters was selected as three by visual inspection of the t-SNE results. Figure 12B displays the three groups, termed G. I, G. II, and G. III. The TE*<sup>θ</sup> κα*-based classifier has average accuracies of 0.94 ± 0.04, 0.92 ± 0.08, and 0.93 ± 0.08 for the subjects in G. I, G. II, and G. III, respectively.

Lastly, Figure 13 shows the average nodal relevance, as defined by *n*, and the most relevant connectivities for each group, discriminated by frequency band. For G. I we observe widespread high node relevance in both the *α* and *β<sup>l</sup>* bands and low node relevance in the *θ* band. Most relevant connections are present in the *β<sup>l</sup>* band with many connections originating in the parieto-occipital region and targeting frontal and centro-frontal areas. For G. II and G. III node relevance is more evenly distributed across the three frequency bands considered. Spatially, it is more prominent around some pre-frontal, frontal, centroparietal, and parietal nodes. In terms of the most relevant connections, we observe longrange contralateral interactions involving mostly the regions previously listed, as well as some connections to and from temporal areas. Therefore, we argue that the information flow between frontal, parietal, and temporal regions, coded in the phases of oscillatory

activity in the *θ*, *α*, and *β<sup>l</sup>* bands, is what allowed us to discriminate among different memory loads from TE*<sup>θ</sup> κα* features. These results agree with several studies that identify fronto-parietal and fronto-temporal neural circuits operating in frequency ranges spanning from *θ* to *β* as key during the activation of working memory [35,50,51].

**Figure 12.** (**A**) Two-dimensional representation of the relevance vectors for each subject in the WM database obtained after applying t-SNE on *n*. (**B**) Groups identified by k-means. For the TE*<sup>θ</sup> κα*-based classifier the subjects grouped in G. I, have an average accuracy of 0.94 ± 0.04, while those in G. II and G.III have average accuracies of 0.92 ± 0.08 and 0.93 ± 0.08, respectively.

**Figure 13.** Topoplots of the average node (channel) relevance for each group of clustered subjects and frequency band of interest in the WM database (see Figure 12). The arrows represent the most relevant connectivities for each group. For visualization purposes, only the 1% of the connections, those with the highest average relevance values per group, are depicted.
