BCI-competition 2003 - the Graz data set
Model Description
Christin Schaefer
Fraunhofer FIRST Institut,
Kekulestr.7, 12489 Berlin, Germany
christin.schaefer@first.fraunhofer.de
Steven Lemm
Universitaetsklinikum Benjamin Franklin,
Hindenburgdamm 30, 12200 Berlin, Germany
steven.lemm@first.fraunhofer.de
Preprocessing
From the neurophysiological perspective imaginary hand movement leads
to a suppression of the mu-rhythm, Event Related Desynchronization
(ERD) at 10Hz and 20Hz over the motor-cortex (C3 and C4).
Consequently, we focus only on the channels C3 and C4. (Cz is
excluded.) The data are narrow bandpass filtered using Morlet-Wavelets
at the lower and higher frequency mu-rhythm, in that specific case
centered at 10Hz and 22Hz, respectively. To match the requirements of
processing the data online, all filter were chosen to be causal.
Model
From the preprocessed training data we estimate for every time
instance t_i, i = 1, ..., 1152, a multivariate normal distribution
for each class (left/right) in a robust manner. Further more for every
time instance, we obtain an upper bound for the Bayes error of the two
probability models. Using this, we calculate a weight function by
w(t) = 0.5 - Bayes error(t).
For online classification at time instance T the decision is based on
all previous time instances t <= T using the expectation of the
weighted probabilities:
p_t(left|x) = P_t(x_t|left) / P_t(x_t|left) + P_t(x_t|right) ,
D_T(left|x_1, ..., x_T) = (sum_{t<=T} w(t) p_t(left|x_t)) / (sum_{t<=T} w(t)) .
To match the convention that negative (positive) values indicate left
(right) trials, we transform the result:
D'_T = 0.5 - D_T,
where the magnitude reflects the confidence we can assign to the actual
decision.