We introduce Enhanced Kernel-based Relevance Analysis (EKRA) that aims to support the automatic identification of brain activity patterns using electroencephalographic recordings. EKRA is a data-driven strategy that incorporates two kernel functions to take advantage of the available joint information, associating neural responses to a given stimulus condition. Regarding this, a Centered Kernel Alignment functional is adjusted to learning the linear projection that best discriminates the input feature set, optimizing the required free parameters automatically. Our approach is carried out in two scenarios: (i) feature selection by computing a relevance vector from extracted neural features to facilitating the physiological interpretation of a given brain activity task, and (ii) enhanced feature selection to perform an additional transformation of relevant features aiming to improve the overall identification accuracy. Accordingly, we provide an alternative feature relevance analysis strategy that allows improving the system performance while favoring the data interpretability. For the validation purpose, EKRA is tested in two well-known tasks of brain activity: motor imagery discrimination and epileptic seizure detection. The obtained results show that the EKRA approach estimates a relevant representation space extracted from the provided supervised information, emphasizing the salient input features. As a result, our proposal outperforms the state-of-the-art methods regarding brain activity discrimination accuracy with the benefit of enhanced physiological interpretation about the task at hand.