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CHAPTER 3
ALGORITHMS FOR P300-BASED BCI SYSTEMS
3.1 Introduction
Clearly, in all of the P300-based BCI systems described in the previous chapter, algorithms that
can infer the command a user wants to execute from the EEG signals are necessary. The input for
these algorithms is the EEG signals recorded during presentation of stimuli, together with the
sequence and timing of stimuli. The output is the identity of the stimulus that was chosen by the
user, i.e. the identity of the target stimulus. To compute this output, the same general approach is
employed mainly in all of the algorithms described in the literature (recall figure 2.1); data
processing operation and classification.
The direct classification algorithm that has been used with success in several P300 BCIs
in the literature consists of the following steps. First, a subset of electrodes positioned at the
locations on the scalp where strong P300 amplitudes are expected is selected. Then, the raw
signals from these electrodes are bandpass filtered and down-sampled. Finally the filtered and
down-sampled signals from the selected electrodes subset are concatenated into feature vectors
and fed into a machine learning algorithm to be classified.
This general approach was used in many algorithms in the literature, such as in the
algorithms described in [48] and [49]. In the method described in [48], a ten electrode
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configuration consisting of the midline electrodes, the parietal-occipital electrodes PO7, PO8, P3,
P4 and the central electrodes C3, C4 was used. A support vector machine (SVM) with Gaussian
kernels was used for the classification step. This method was one of the winning entries for the
P300 dataset from the BCI competition II, 2003 [11, 12].
In the method described in [49], a set of 25 central and parietal electrodes was used. In
addition to the down-sampled signals, estimates of the time-derivatives of the signals were used.
According to their study, the use of the time-derivatives improves the accuracy of the classifier.
An SVM with a Gaussian kernel was used for classification. The method was tested with several
P300 speller datasets and showed very good performance. Unfortunately, the method was not
tested with publicly available datasets and thus a direct comparison with the method presented in
[48] is impossible.
An alternative to manually fixing parameters for feature extraction (e.g. filter settings and
subset of electrodes) is to let an algorithm select the optimal features from a set of predefined
features. This idea is implemented in the stepwise discriminant analysis (SWDA) algorithm and
was used in the studies described in [23, 29, and 74]. In these studies filter settings and a subset of
electrodes were fixed, however SWDA was used to select time points relevant for P300
classification within EEG segments. In a recent comparison of classification methods for the
P300 speller, SWDA stated to be one of the best methods in terms of classification performance
and in terms of effort needed for implementation of the method [11].
The principle of automatically selecting features was also used in [81]. In the proposed
algorithm an over-complete dictionary of continuous wavelets was used to transform the raw
EEG signals into the time-scale space. During training a t-test was used to identify points in time
domain at which the difference between the mean wavelet coefficients from P300 segments and
non-P300 segments is high and at which the variance around these means is small. The wavelet
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coefficients with the best t-test results were fed into a linear discriminant analysis (LDA)
classifier for the classification. The proposed method was tested with the P300 datasets in the BCI
competition 2003 [11 and 12] and was among the winning entries.
Still another algorithm which used the principle of automatic feature selection was
presented in [6]. In this algorithm recursive feature selection with the SVM was used to find an
optimal subset of EEG electrodes. To further improve the performance, several SVM classifiers
were learned from different subsets of the training data. This approach is based on the assumption
that the distribution of the P300 and non-P300 segments in the training set is variable and thus
cannot be appropriately modeled by a single classifier. The method was tested with on the BCI
competition III, 2004 P300 dataset [11 and 12] and gave very good results where it was the
winning entry for the competition.
In addition to the algorithms based on filtering for feature extraction and the algorithms
based on feature selection a third group of algorithms can be identified. The algorithms in this
group use independent component analysis (ICA) for spatial feature extraction as in [1, 3, 28, 40,
43, 46, and 57] and may also include Discrete Wavelet Transformation (DWT) or Continues
Wavelet Transformation (CWT) as feature extractors. The first step in all algorithms use ICA is
to compute independent components from the training data sets. Then the components that
present well the P300 are selected (note that this step may be optional). This can be either done
manually, i.e. by visually inspecting the data as in [40], or by defining criteria that allow to
automatically select P300 like components as in [28 and 57]. When the algorithm is applied to
new data, the data is projected on the retained independent components and then classified.
Different types of classifiers were used in combination with ICA as the feature extractor. In [57],
the use of LDA was proposed while in [28] a neural network was used. The method in [28] was
only tested on proprietary datasets, while the algorithm described in [57] was tested on the 2003
P300 competition datasets and was one of the winning entries. In addition to ICA, some studies
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introduced the use of principle component analysis (PCA) to reduce the dimensions of the filtered
EEG data before applying ICA algorithm to extract features. This may increase the computational
efficiency and the robustness of ICA. Examples of these studies are described in [5 and 43].
After this review of several structures of algorithms that have been used in the literature,
we can now conclude that the main components of an algorithm for any P300-based BCI system
are the data pre-processing and feature classification. Data pre-processing operation may include
data filtering, winsorization, down-sampling, feature extraction and/or independent component
analysis. Classification stage is the use of deterministic machine learning algorithms to learn and
classify signal features, the outcome of the first stage, and make the decision regarding the
existence of P300. In Section 3.2 we describe the mostly used data pre-processing techniques;
filtering, windsorization and blind source separation (BSS) as a type of signal sources extraction.
Only two of the widely used BSS methods are detailed; Principle Component Analysis and (PCA)
and Independent Component Analysis (ICA). The features of the P300 wave (and their extractors)
that can be useful in the classification step are described in Section 3.3. In Section 3.4 we give
some details about some used machine learning algorithms. In Section 3.5, we describe some
evaluation metrics that have been used in the literature to evaluate and test P300-based BCI
systems. Finally, in Section 3.6 we describe some other issues that are relevant to the
development and design of a P300-based BCI system.
3.2 EEG Raw Data Processing
Several methods and techniques are used to remove noise and other artifacts from the captured
raw EEG signals. In this section, we describe two well known techniques of the data processing
schemes; filtering and Windsorization. Information about other artifacts removing methods such
as using EOG/EEG correlations can be found in some literatures such as [1 and 28].
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3.2.1 Filtering
To remove high frequency components, noise, and artifacts, the EEG raw data is fed to a low-
pass filter or a band-pass filter. The desired frequency band depends on the type of the
neurophysiological signal that needs to be classified; in this thesis it is the P300. Consequently,
the filtering step here allows only the band that carries the most information of the P300 wave to
be available.
Many of the researchers have suggested that the P300 component is primarily formed by
transient oscillatory events in the delta and theta frequency bands of EEG waves, and some of the
events in the alpha frequency band [45] (see Table 2.1).
3.2.2 Windsorization
Eye blinks, eye movement, muscle activity, or subject movement can cause large amplitude
outliers in the EEG. To reduce the effects of such outliers, the data from each electrode is
windsorized. For the samples from each channel or electrode a specified lower and upper
percentiles (e.g. 10
th
and the 90
th
, see figure 3.1) are computed and amplitude values lying below
the lower percentile or above the upper percentile are then replaced by the lower percentile or the
upper percentile, respectively [80].
Figure 3.1: Data Windsorization
0 10% 90% 100%
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3.2.3 Blind Source Separation
Blind source separation (BSS) methods are based on the hypothesis that the observed signals
from a multi-channel recording are produced from a mixture of several distinct signal sources.
They attempt to isolate the original source signals by applying a transform to the set of observed
signals. Usually, the cocktail party problem is used as a classical example to illustrate the
functionality of BSS methods. In the “cocktail party,” there is a room with several people
speaking simultaneously, and their voices are considered to be the independent sources in this
problem. There are also several microphones set up throughout the room recording a mixture of
all the voices (sources). Using the information from all of the recording channels (microphones),
the BSS methods attempt to transform this data into a set of the original independent signal
source sources. The BSS methods accomplish this by finding a set of basis vectors to transform
the original data, where the different methods use different optimization criteria to find these
basis vectors. The observed signals X(t) = [x
1
(t), x
2
(t), x
3
(t), . . . , x
n
(t)] consisting of n channels
are assumed to originate from some unknown linear mixing of p source signals S(t) = [s
1
(t), s
2
(t),
s
3
(t), . . . , s
p
(t)].
(1)
Here, A is the unknown mixing matrix of dimensions n×p. It should be noted that in order to
solve this problem, the mixing matrix must be over-determined (i.e., n ≥ p). If there are more
sources than recording channels, it is impossible to completely isolate each source. In this work,
an assumption is made for simplification that the number of sources is equal to the number of
channels, p = n. Therefore, the mixing matrix A is n×n. The BSS method then attempts to find
the corresponding demixing matrix W that best estimates the original source signals.
(2)
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Here,
is the estimate of the source components S(t). It is also possible to find an estimate of
the original mixing matrix A by taking an inverse of the resulting demixing matrix, as in W
−
1
.
Using the mixing matrix A, it is then possible to project the components back to reconstruct the
original data.
(3)
It is also possible to select only a single source component
and project it back to find the
contribution from component j.
(4)
The variable a
j
refers to the j
th
row in A, and w
j
refers to the j
th
column in W.
The demixing matrix W = [w
1
, w
2
, w
3
, . . . , w
n
] consists of a set of basis vectors, where
each column vector w
i
is associated with a single source, and can be considered as a spatial filter.
Each basis vector provides weights for a linear mixture of the channels from the recorded data X(t)
that results in a single source component. This is especially relevant when it is known that the
sources are spatially distributed across the recording channels. Therefore, there will be many
references to the spatial filters associated with sources, which are derived from the associated
basis vector.
Principal Component Analysis
PCA is a method to find a linear transformation of the data that maximizes the variance of the
transformed data. Using PCA, the transformation is constrained to be orthogonal. This problem is
solved using the eigenvectors of the covariance matrix X
T
X, as shown in:
XTXα = λα (5)
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Where α is an eigenvector with a corresponding eigenvalue λ. The set of all eigenvectors
constitute the new orthogonal basis that the data is projected on.
PCA can be used for BSS on EEG data recorded with n channels by applying it to the
covariance matrix across the n dimensions. The bases obtained from this process are linear
combinations of the n channels, which represent the set of spatial filters for the source
components.
Independent Component Analysis
ICA is a concept that can be applied to any set of random variables to find a linear transform that
maximizes the statistical independence of the output components [4]. While PCA relies only on
the second order statistics of covariance, ICA can be seen as a higher order generalization of PCA
that does not require orthogonality. Kachenoura et al., [3] defined ICA as an optimization
problem to minimize the mutual information between the source components. They presented an
efficient algorithm using higher order statistics to measure the notion of non-Gaussianity that
corresponds with statistical independence.
(a) (b)
Figure 3.2: The difference between PCA and ICA on a non-orthogonal mixture of two distributions that are
independent and highly sparse (peaked with long tails). a) PCA. b) ICA [3]
To understand how non-Gaussianity relates to statistical independence, it is necessary to
understand the central limit theory, which states that the sum of many independent processes
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tends towards a Gaussian distribution. Therefore, if S(t) is assumed to be a set of actually
independent sources, the observed mixed signal X(t) will be more Gaussian by the central limit
theory. A single estimated source
is a linear mixture of X(t) given by the weights in the
spatial filter w
i
. The w
i
that maximizes the non-Gaussianity of
is used to find the closest
approximation to the true independent source
. Consequently, the optimization criterion is to
find the demixing matrix that maximizes non-Gaussianity in all of the source components.
When used for P300 classification, ICA has been applied and showed its ability to isolate
the P300 signal into source components as mentioned above.
In [68, 69 and 70], ICA was applied to averaged ERP trials and it was found that the
observed signal is comprised of many spatially distinct and independent brain processes. As a
result, the application of BSS to P300 trials has the potential advantage of finding the
corresponding spatial filters to isolate these independent sources. ICA was applied to P300 data in
[57] and a priori information about the spatial and temporal characteristics of the standard P300
response was used to select the most related source components. Their algorithm selects
components with larger amplitudes from 250 to 400 ms window and stronger contributions from
electrodes Cz, C1, and C2 that were later used for classification. Although it worked well for that
single user, as explained above, the disadvantage of using a priori information is that each user’s
P300 response can entirely vary, especially in amyotrophic lateral sclerosis (ALS) users. ICA was
also applied in [28 and 46] and both used different forms of a posteriori template matching to
select the most related source components. Spatially constrained ICA was applied to P300 trials
in [71] with the use of an a posteriori template matching algorithm, but it used the manual
selection of the best component to use as a template. Their results showed that this method
increased character classification on the BCI Competition II dataset [11]. They also applied
recursive feature elimination (RFE) to the resulting source components but found that although
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many components did not contribute to the performance, the elimination of these irrelevant
components did not increase the accuracy.
There are many different implementations of ICA that each uses different metrics for
statistical independence. Based on the comparison of several ICA algorithms applied to BCI
applications in [3], we have chosen to use FastICA [2, 16, 63 and 77], which displayed good
performance and uses kurtosis as a measure of non-Gaussianity.
Kurtosis is a fourth-order statistic given by E{X
4
} – 3 for a signal X with a mean of zero
and unit variance. It indicates whether a probability distribution is sub-Gaussian, Gaussian, or
super-Gaussian. It uses the hypothesis that white noise is Gaussian and the most independent
sources are furthest from a Gaussian distribution. A signal with negative kurtosis is sub-Gaussian,
while a signal with positive kurtosis is considered as super-Gaussian. Gaussian distribution has a
kurtosis equal to zero. A signal that is super-Gaussian with a higher kurtosis means that much of
the variation in the signal is caused by large deviations that occur infrequently causing a heavy
tailed distribution that is more common in many independent signals. FastICA finds the set of
source components that correspond to the kurtosis extreme [2 and 4].
The basic form of the FastICA algorithm for one unit is as Follows [4]:
1. Center the data to make its mean zero.
2. Whiten the data to give z.
3. Choose an initial (e.g. random) weight vector w.
4. Let w = E{zg(w
T
z)} − E{g'(w
T
z)}w.
5. Let w = w/||w||.
6. If not converged, go back to 4.
Convergence means that dot product of the old and new value of weight w is equal or
almost equal to 1, i.e. they point in the same direction.
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