  Many brain-computer interfaces make use of brain signals that are elicited in
response to a visual, auditory or tactile stimulus, so-called event-related
potentials (ERPs). In visual ERP speller applications, sets of letters shown on
a screen are flashed randomly, and the participant attends to the target letter
they want to spell. When this letter flashes, the resulting ERP is different
compared to when any other non-target letter flashes. We propose a new
unsupervised approach to detect this attended letter. In each trial, for every
available letter our approach makes the hypothesis that it is in fact the
attended letter, and calculates the ERPs based on each of these hypotheses. We
leverage the fact that only the true hypothesis produces the largest difference
between the class means. Note that this unsupervised method does not require
any changes to the underlying experimental paradigm and therefore can be
employed in almost any ERP-based setup. To deal with limited data, we use a
block-Toeplitz regularized covariance matrix that models the background
activity. We implemented the proposed novel unsupervised mean-difference
maximization (UMM) method and evaluated it in offline replays of brain-computer
interface visual speller datasets. For a dataset that used 16 flashes per
symbol per trial, UMM correctly classifies 3651 out of 3654 letters
($99.92\,\%$) across 25 participants. In another dataset with fewer and shorter
trials, 7344 out of 7383 letters ($99.47\,\%$) are classified correctly across
54 participants with two sessions each. Even in more challenging datasets
obtained from patients with amyotrophic lateral sclerosis ($77.86\,\%$) or when
using auditory ERPs ($82.52\,\%$), the obtained classification rates obtained
by UMM are competitive. In addition, UMM provides stable confidence measures
which can be used to monitor convergence.
