IEEE Computational Intelligence Magazine - May 2018 - 71

based on the idea that the unlabeled data
points derived during the online use of a
BCI can be subdivided into groups, where
every group displays a different ratio of
target to non-target data points. To enable
this approach for a visual matrix speller, a
modification of the spelling paradigm is
necessary. Hübner et al. [26] proposed to
modify the spelling interface with the following three adjustments: (a) The spelling
matrix is extended by 10 additional #symbols which serve as visual blanks and
should never be attended by the user-as
such they are non-targets by construction. (b) Instead of using a row-column
highlighting scheme, the flexible highlighting scheme by Verhoeven et al. [69]
is used. (c) Each trial (i.e., spelling one
character) is composed of two interleaved highlighting sequences, where
sequence 1 only highlights normal character (it does not highlight #-symbols)
and sequence 2 highlights normal characters as well as #-symbols. These modifications lead to two subgroups of EEG
data, namely the epochs measured during
sequence 1 and epochs from sequence 2.
The groups show different but known
target- to non-target ratios, which are
stored in a mixing matrix P and are
known from constructing the sequences.
The mean ERP responses of sequence 1
and 2 (n 1, n 2) are then given by a linear
combination of the target and non-target
class means n T , n N as
; E = P;
n1
n2

E, where P: = ;

2
rT

rT rN
2

An online study with 13 healthy
subjects showed that LLP could reliably
learn the classifier weights from scratch
[26]. Simulated online experiments
revealed, that this unsupervised learning
approach initially outperforms the EMapproach, but falls behind when more
and more data is available from extended
online use.
4) mixture method
The mixture method (MIX) by Verhoeven et al. [27] describes an analytical
combination of the EM and LLP method. It is built on the observation that the
previously explained two methods, EM
and LLP, have complementary strengths
and weaknesses. It uses a reformulation
of the EM algorithm which is explicitly
estimating the class means instead of the
projection only. In the MIX method,
the estimation of the class-wise means is
proposed as a linear combination of the
mean estimations found with the EM
(n EM ) and those estimated by the LLP
method (n LLP ),
t MIX (c)
n

(3)

where c ! [0, 1] denotes the mixing
coefficient. The coefficient c is found by
minimizing the expected mean squared
error between the estimated value nt MIX
and the unknown true parameter value
n. Verhoeven and colleagues showed,
that this approach leads to an analytical
formulation for the optimal mixture
coefficient c * [27]:

(2)
c

By inverting P and computing the
sample means of the two sequences
t 1, nt 2, unsupervised estimates for the
n
class means are obtained. Importantly,
the LLP approach comes with the theoretical guarantee of converging to the
right class means given independent and
identically distributed data points [26].
As a final step in the approach of Hübner et al., a modification of the linear
discriminant analysis-using the global
covariance instead of the shared covariance matrix similar to the case in Section II-A2-is used to compute the
desired projection vector w .

= (1 - c) nt EM + cnt LLP

= 1+
2
/ d Var6nt EM,d@ - / d Var6nt LLP,d@
.
2
2 nt EM - nt LLP
(4)

Here, d denotes the feature dimensionality, and Var [nt ($),d] denotes the variance
(over different realizations of the data)
of the estimator for the dth entry of the
estimated mean nt ($). This variance is a
measure of the uncertainty of the estimated value. The higher the uncertainty
on the output of the LLP method, the
higher the weight given to the output
of the EM method and vice versa. To

estimate the variance in LLP, one can
derive a closed-form solution which
only depends on the mixing matrix and
data variance. For the EM, no closedform solution exists. Additionally, only
one realization of the data is observable
in practical applications, and simulating
other realizations is time-consuming
and inaccurate. Hence, the authors used
the approximation that the EM-estimator converges asymptotically to a Gaussian distribution where the variance can
be computed based on the data [27].
Verhoeven et al. [27] compared LLP,
EM and MIX in offline simulations on
data of 13 subjects which is openly available at the Zenodo database1. It was found
that the MIX method does not only combine the strengths of EM and LLP but that
it actually transcends the two single performances for almost any amount of data
on the group grand average. Interestingly,
the simulations also showed that the MIX
performance can compete with a supervised classifier which had the complete
label information available and has been
trained on the same amount of training
data as MIX after a short ramp-up.
In this section, we reviewed the most
promising unsupervised adaptation and
unsupervised learning methods for
ERP-based BCIs. It is of course also
possible to combine the best of the two
worlds. While an unsupervised adaptation method crucially relies on a pretrained classifier, unsupervised learning
methods can certainly also benefit from
a good initialization of the model
parameters based on historic labeled (or
unlabeled) data. A study by Kindermans
et al. [70] showed how transfer learning
significantly improves the EM algorithm. Even if the model is initialized
poorly, unsupervised learning methods
have a high chance of learning a good
classifier which is not the case for unsupervised adaptation methods.
III. Methods

The main goal of the current paper is to
verify the promising results of the MIX
study in an online study. Even though
authors of offline simulations try hard to
1

DOI: http://doi.org/10.5281/zenodo.192684.

may 2018 | IEEE ComputatIonal IntEllIgEnCE magazInE

http://doi.org/10.5281/zenodo.192684

Table of Contents for the Digital Edition of IEEE Computational Intelligence Magazine - May 2018