This work presents a novel approach for automatic epilepsy seizure detection based on EEG analysis that exploits the underlying non-linear nature of EEG data. In this paper, two main contributions are presented and validated: the use of non-linear classifiers through the so-called kernel trick and the proposal of a Bag-of-Words model for extracting a non-linear feature representation of the input data in an unsupervised manner. The performance of the resulting system is validated with public datasets, previously processed to remove artifacts or external disturbances, but also with private datasets recorded under realistic and non-ideal operating conditions. The use of public datasets caters for comparison purposes whereas the private one shows the performance of the system under realistic circumstances of noise, artifacts, and signals of different amplitudes. Moreover, the proposed solution has been compared to state-of-the-art works not only for pre-processed and public datasets but also with the private datasets. The mean F1-measure shows a 10% improvement over the second-best ranked method including cross-dataset experiments. The obtained results prove the robustness of the proposed solution to more realistic and variable conditions.