## 4 Discussion and Concluding Remarks  
Brain information processing is a complex task that is not yet entirely mapped and understood. Despite the previous knowledge about brain regions interactions in motor or emotional means, works that allow improving the interpretability of results in different BEA scenarios would lead to the development of more precise frameworks for analysis, diagnosis, and treatment of mental pathologies, among other tasks. In this work, we proposed a framework for discriminate BEA using raw data with the support of a spectral kernel that identifies relationships between channels on behalf of a probabilistic methodology of multi-output Gaussian process. One of the essential remarks of this framework is the capability of learning EEG connectivity patterns by estimating raw data spectral components without a feature extraction stage. Further, this proposal of generative models working directly with EEG data has the advantage of adjusting the model relying on the optimization of kernel hyperparameters just from the channels information in a data-driven framework. The results presented in Section 3 evidenced that introducing the MOSM kernel to MOGPs becomes a reliable tool for BEA modeling, due to the spectral designing properties. It is well known that EEG channels share complex frequency relationships that can be exploited using the design of a covariance function in that particular domain. Regarding this property, the posterior distribution over the data measured by the MAE in Figure 3 shows an adequate adjustment of the model on the original data. It also allows us to conclude that the inclusion of more spectral components into the covariance function benefits the model adjusting to the data. Moreover, the identification of the spectral relationships between channels, performed by the MOSM kernel, allows gaining a better understanding of the latent functional connectivity between brain regions. As Figure 6 evidenced, the MOSM-GP identifies representative frequency bands for the cognitive process. The positive linear relationships are grouped among channels from the same hemisphere, with strong specific dependencies between channels, like \(P3-P7\), and \(Fc6-Af4\). The negative relationships are explained by lower PSD amplitudes at \(Cz\), \(C2\), and \(CP6\) for the left-hand MI task, and \(C6,CP1,CP6\) for the right-hand MI task. All these interactions quantified by the MOSM kernel in terms of higher or lower values of the PSD can be directly related with the activations of neural cells in different regions of the brain related with emotions (amygdala, hippocampus, and frontal cortex) or related with motor activities (primary motor cortex and posterior parietal cortex). Nevertheless, further studies must be completed from the evidence of these relationships to an accurate source reconstruction before determining the specific brain region of the acquired neural activity. Finally, the discriminative results regarding the emotional and motor imagery conditions conclude that probabilistic models can be efficiently employed as a classification tool for EEG data. In this case, the probability distribution of tested data against the trained models directly becomes a classification algorithm by following a direct comparison of the mean likelihood value between the models from two classes. Despite lacking a feature extraction stage, the proposed DMOSM-GP produces discriminative information from the data. Moreover, the total accuracy of the subject-dependent and condition-dependent tests is comparable with state-of-art works, as Tables 5 and 6 illustrate. One of the drawbacks of this framework is the computational complexity of training a considerable number of MOSM-GP models. In addition, increasing the number of MOSM kernel mixtures and the size of BEA data will derive into an exponential growth of the training time.