## 4 Results and Discussion
### EEG Data Results
#### 4.2.1 Motor Imagery Results
In order to gain insight into the observed performance differences, in the case of \(\text{TE}^{\theta}_{\text{ex}}\), we exploited the second advantage provided by the CKA-based relevance analysis. The relevance vector index \(\varphi\) not only allows us to perform feature selection but also provides a one-to-one relevance mapping to each connectivity feature. That is to say, we can reconstruct normalized relevance connectivity matrices by properly reshaping \(\varphi\), so as to visualize the connectivity pairs and frequency ranges that are discriminant for the task of interest. In that line, we followed the approach proposed in [23] to interpret the relevance information by clustering the subjects according to common relevance patterns. First, for each subject and frequency band of interest, we obtained a relevance vector \(\varphi_{n,\Delta f}\in\mathbb{R}^{C}\) whose elements were associated with each node (EEG channel) in the data by computing the relevance of the total information flow of every node. Such magnitude was defined as the sum of the relevance values \(\varphi\), obtained from all data in the training dataset, corresponding to all directed interactions targeting and originating from a particular node. Then, we concatenated the vectors \(\varphi_{n,\Delta f}\in\mathbb{R}^{C}\) for all frequency bands to obtain a single relevance vector \(\varphi_{n}\in\mathbb{R}^{2C}\). Next, we reduced the dimension of the relevance vectors \(\varphi_{n}\) of each subject through t-Distributed Stochastic Neighbor Embedding (t-SNE), which preserves the spatial relationships existing in the initial higher-dimensional space [63]. Figure 8A shows the obtained two-dimensional representation of the relevance vectors for each subject in the MI database, colored according to their respective classification accuracy. Figure 7: (**A**) Highest average classification accuracy for each subject in the MI database during the training-validation stage. (**B**) Accuracies obtained for each subject during the testing stage. The subjects are ordered from highest to lowest performance according to the accuracies obtained for the \(\text{TE}^{\theta}_{\text{ex}}\)-based classifier in the training-validation stage. Note that the distribution of the subjects in the plot is related to their classification accuracies. This indicates that shared relevance patterns are related to the obtained classification results, meaning that subjects with similar \(\mathbf{q}_{n}\) had close performances. Then, we grouped the subjects into two clusters using the k-means algorithm. The number of clusters was selected by visual inspection of the t-SNE results. Figure 8B displays the two groups, termed G. I and G. II. The TE\({}_{\text{xx}}^{\theta}\)-based classifier has average accuracies of \(0.59\pm 0.05\) and \(0.80\pm 0.09\) for the subjects in G. I and G. II, respectively. Finally, Figure 9 shows the average nodal relevance, as defined by \(\mathbf{q}_{n}\), and the most relevant connectivities for each group, discriminated by frequency band. For G. I we observe high node relevance mostly in the \(\alpha\) band in right fronto-central, left-central, and centro-parietal regions. The most relevant connections in the \(\alpha\) band tend to originate or target fronto-central nodes, while the ones in the \(\beta_{l}\) band favor parietal and centro-parietal areas. For G. II, the node relevance is concentrated around the right centro-parietal region, particularly channel CP4, for both frequency bands. The most relevant connections in the \(\alpha\) band involve short-range interactions mainly between centro-parietal and central regions. The most relevant connections in the \(\beta_{l}\) band, which display higher values than those of \(\alpha\), originate from CP3 and CP4 and target central and fronto-central nodes.