There has been a growing interest in studying electroencephalography signals (EEG) as a possible biometric. The brain signals captured by EEG are rich and carry information related to the individual, tasks being performed, mental state, and other channel/measurement noise due to session variability and artifacts. To effectively extract person-specific signatures present in EEG, it is necessary to define a subspace that enhances the biometric information and suppresses other nuisance factors. i-vector and x-vector are state-of-art subspace techniques used in speaker recognition. In this paper, novel modifications are proposed for both frameworks to project person-specific signatures from multi-channel EEG into a subspace. The modified i-vector and x-vector systems outperform baseline i-vector and x-vector systems with an absolute improvement of 10.5% and 15.9%, respectively.