A major challenge in single-trial electroencephalography (EEG) analysis and Brain Computer Interfacing (BCI) is the so called, inter-subject/inter-session variability: (i.e large variability in measurements obtained during different recording sessions). This variability restricts the number of samples available for single-trial analysis to a limited number that can be obtained during a single session. Here we propose a novel method that distinguishes between subject-invariant features and subject-specific features, based on a bilinear formulation. The method allows for one to combine multiple recording of EEG to estimate the subject-invariant parameters, hence addressing the issue of inter-subject variability, while reducing the complexity of estimation for the subject-specific parameters. The method is demonstrated on 34 datasets from two different experimental paradigms: Perception categorization task and Rapid Serial Visual Presentation (RSVP) task. We show significant improvements in classification performance over state-of-the-art methods. Further, our method extracts neurological components never before reported on the RSVP thus demonstrating the ability of our method to extract novel neural signatures from the data.