Conventional biometrics have been employed in high security user authentication systems for over 20 years now. However, some of these modalities face low security issues in common practice. Brain wave based user authentication has emerged as a promising alternative method, as it overcomes some of these drawbacks and allows for continuous user authentication. In the present study we address the problem of individual user variability, by proposing a data-driven Electroencephalography (EEG) based authentication method. We introduce machine learning techniques, in order to reveal the optimal classification algorithm that best fits the data of each individual user, in a fast and efficient manner. A set of 15 power spectral features (delta, theta, lower alpha, higher alpha, and alpha) is extracted from the three EEG channels. The results show that our approach can reliably grant or deny access to the user (mean accuracy 95,6%), while at the same time poses as a viable option for real time applications, as the total time of the training procedure was kept under one minute.