  Auditory attention decoding (AAD) algorithms decode the auditory attention
from electroencephalography (EEG) signals that capture the listener's neural
activity. Such AAD methods are believed to be an important ingredient towards
so-called neuro-steered assistive hearing devices. For example, traditional AAD
decoders allow detecting to which of multiple speakers a listener is attending
to by reconstructing the amplitude envelope of the attended speech signal from
the EEG signals. Recently, an alternative paradigm to this stimulus
reconstruction approach was proposed, in which the directional focus of
auditory attention is determined instead, solely based on the EEG, using common
spatial pattern filters (CSP). Here, we propose Riemannian geometry-based
classification (RGC) as an alternative for this CSP approach, in which the
covariance matrix of a new EEG segment is directly classified while taking its
Riemannian structure into account. While the proposed RGC method performs
similarly to the CSP method for short decision lengths (i.e., the amount of EEG
samples used to make a decision), we show that it significantly outperforms it
for longer decision window lengths.
