  Based on the cumulated experience over the past 25 years in the field of
Brain-Computer Interface (BCI) we can now envision a new generation of BCI.
Such BCIs will not require training; instead they will be smartly initialized
using remote massive databases and will adapt to the user fast and effectively
in the first minute of use. They will be reliable, robust and will maintain
good performances within and across sessions. A general classification
framework based on recent advances in Riemannian geometry and possessing these
characteristics is presented. It applies equally well to BCI based on
event-related potentials (ERP), sensorimotor (mu) rhythms and steady-state
evoked potential (SSEP). The framework is very simple, both algorithmically and
computationally. Due to its simplicity, its ability to learn rapidly (with
little training data) and its good across-subject and across-session
generalization, this strategy a very good candidate for building a new
generation of BCIs, thus we hereby propose it as a benchmark method for the
field.
