Monitoring and prediction of changes in the human cognitive states, such as alertness and drowsiness, using physiological signals are very important for drivers safety. Typically, physiological studies on real-time detection of drowsiness usually use the same model for all subjects. However, the relatively large individual variability in EEG dynamics relating to loss of alertness implies that for many subjects, group statistics may not be useful to accurately predict changes in cognitive states. Researchers have attempted to build subject-dependent models based on his/her pilot data to account for individual variability. Such approaches cannot account for the cross-session variability in EEG dynamics, which may cause problems due to various reasons including electrode displacements, environmental noises, and skin-electrode impedance. Hence, we propose an unsupervised subject- and session-independent approach for detection departure from alertness in this study. Experimental results showed that the EEG power in the alpha-band (as well as in the theta-band) is highly correlated with changes in the subjects cognitive state with respect to drowsiness as reflected through his driving performance. This approach being an unsupervised and session-independent one could be used to develop a useful system for noninvasive monitoring of the cognitive state of human operators in attention-critical settings.