ORIGINAL PAPER
Comparing ICA-based and Single-Trial Topographic ERP
Analyses
Marzia De Lucia
•
Christoph M. Michel
•
Micah M. Murray
Received: 2 September 2009 / Accepted: 10 April 2010 / Published online: 27 April 2010
Springer Science+Business Media, LLC 2010
Abstract Single-trial analysis of human electroencepha-
lography (EEG) has been recently proposed for better
understanding the contribution of individual subjects to a
group-analyis effect as well as for investigating single-
subject mechanisms. Independent Component Analysis
(ICA) has been repeatedly applied to concatenated single-
trial responses and at a single-subject level in order to
extract those components that resemble activities of inter-
est. More recently we have proposed a single-trial method
based on topographic maps that determines which voltage
configurations are reliably observed at the event-related
potential (ERP) level taking advantage of repetitions across
trials. Here, we investigated the correspondence between
the maps obtained by ICA versus the topographies that we
obtained by the single-trial clustering algorithm that best
explained the variance of the ERP. To do this, we used
exemplar data provided from the EEGLAB website that are
based on a dataset from a visual target detection task. We
show there to be robust correpondence both at the level of
the activation time courses and at the level of voltage
configurations of a subset of relevant maps. We addition-
ally show the estimated inverse solution (based on low-
resolution electromagnetic tomography) of two corre-
sponding maps occurring at approximately 300 ms post-
stimulus onset, as estimated by the two aforementioned
approaches. The spatial distribution of the estimated
sources significantly correlated and had in common a right
parietal activation within Brodmann’s Area (BA) 40.
Despite their differences in terms of theoretical bases, the
consistency between the results of these two approaches
shows that their underlying assumptions are indeed
compatible.
Keywords Single-trial Independent Component
Analysis (ICA) Event-Related Potential (ERP)
Introduction
Classical analysis and interpretation of ERPs in human EEG
is based on averaging peri-stimulus electrical responses to
generate a single time series for each electrode within a
given scalp montage. Although this has the advantage of
increasing to a great extent the signal-to-noise ratio, it relies
on the simplistic assumption that the signal related to the
stimulus is stationary in time and that any activity that is not
fixed in time is ‘‘noise’’. On the other hand, single-trial
This is one of several papers published together in Brain Topography
on the ‘‘Special Topic: Cortical Network Analysis with EEG/MEG’’.
M. De Lucia (&) M. M. Murray
Electroencephalography Brain Mapping Core of the Lemanic,
Center for Biomedical Imaging, CHUV 07.081, Rue du Bugnon
46, 1011 Lausanne, Switzerland
e-mail: Marzia.De-Lucia@hospvd.ch
C. M. Michel
The Functional Brain Mapping Laboratory, University of
Geneva, Geneva, Switzerland
M. M. Murray
Neuropsychology and Neurorehabilitation Service, Department
of Clinical Neuroscience, Vaudois University Hospital Center
University of Lausanne, Lausanne, Switzerland
M. M. Murray
Radiology Department, Vaudois University Hospital Center
University of Lausanne, Lausanne, Switzerland
M. M. Murray
Department of Hearing and Speech Sciences, Vanderbilt
University, Nashville, TN, USA
123
Brain Topogr (2010) 23:119–127
DOI 10.1007/s10548-010-0145-y
methods are made problematic by the presence of many
known and unknown sources of noise (physiological and
instrumental) that can obfuscate the signal of interest. As a
consequence a priori hypotheses about the brain processes
underlying the measured signal are required. ICA is cur-
rently a typical single-trial analysis approach (Bell and
Sejnowski 1995; Makeig et al. 1999, 2002). This technique
relies on the hypothesis that brain activity is the result of a
superimposition of a number of independent components in
a number less than or equal to the total number of elec-
trodes. Each of these components has an associated time
course of the activity in every trial and a scalp map, rep-
resenting the strength of the volume-conducted component
activity at each scalp electrode. The applicability of ICA to
ERP analyses has been shown repeatedly in a context in
which it is possible to attribute a physiological meaning to
one or more components (Makeig et al. 2002; Debener et al.
2004), for artifacts detection (Vigario 1997) and more
generally for EEG pattern recognition and classification
(Naeem et al. 2006; De Lucia et al. 2008). Numerous other
approaches have been developed in the area of blind source
separation (Belouchrani et al. 1997; Tang et al. 2005;
Barbati et al. 2006), and several methods at the level of
single waveforms either based on assuming stationary
stereotypic wave shapes (Knuth et al. 2006) or on filtering
and de-noising (Quiroga and Garcia 2003; Georgiadis et al.
2005).
More recently, a novel single-trial clustering algorithm
based on topographic information has been proposed. This
method stems from the hypothesis that event-related
potentials at a single-trial level exhibit a semi-stationary
temporal structure, characterized by a few representative
topographic maps that appear over short time periods on
the order of at least 10–20 ms duration. This hypothesis has
been explored both at the single-subject (De Lucia et al.
2007a) and at a group level of analysis (De Lucia et al.
2007b) on a set of data from an auditory object discrimi-
nation experiment. The suitability of this model can be
demonstrated by computing the amount of explained var-
iance, as we will detail below, as well as by showing that it
provides sufficient information so as to allow an above
chance classification accuracy of independent datasets
(Tzovara et al. 2010). The advantages of this approach are
that it offers a flexible tool for estimating which voltage
configurations appear reliably across trials, their latencies,
and their differences across experimental conditions.
Moreover, it takes full advantage of the reference-inde-
pendent information conveyed by the spatial characteristics
of the electric field measured at the scalp and does not
make explicit a priori assumptions about the frequency or
temporal features of the EEG signal.
Because these various single-trial analysis approaches
stem from very different assumptions, it is an obvious
question whether they detect/extract consistent information
and to which extent they are comparable. Here, we com-
pared the results of an ICA-based analysis and those
obtained by the single-trial topographic clustering algo-
rithm on a dataset derived from a visual target detection
task. Despite their differences in terms of a priori
assumptions and theoretical bases, one common goal is to
estimate components that are consistent across trials so as
to provide insights about the spatio-temporal profile of
event-related brain activity (i.e. its time course and voltage
distribution at the scalp), which ultimately reflects the
activity of underlying sources.
Materials and Methods
Subjects, Stimuli and Task
Ten subjects participated in the experiment. ERPs were
recorded while the subjects attended a sequence of visual
stimuli appearing briefly in any of five squares arrayed
horizontally above a central fixation cross. In each exper-
imental block, one (target) box was differently colored
from the rest. Whenever a square appeared in the target
box, the subject was asked to respond quickly with a right
thumb button press. The subject was asked to ignore circles
presented either at the attended location or at an unattended
one (for full details see Makeig et al. 1999). The dataset we
consider here contains only target stimuli presented at the
two attended locations in the left visual field for a single
subject (downloadable from the EEGlab website,
http://sccn.ucsd.edu/eeglab/).
EEG Acquisition and Preprocessing
EEG data were collected from 30 scalp electrodes mounted
in a standard electrode cap at locations based on a modified
International 10–20 system, and from two periocular
electrodes placed below the right eye and the left outer
canthus. Signals were referenced to the right mastoid and
sampled at 512 Hz. Before the analysis, the dataset was
down-sampled to a 128 Hz sampling rate and 40 Hz low-
pass filtered. In total, we consider here 80 trials (including
1 s of baseline and 2 s of post-stimulus responses) base-
line-corrected and common average re-referenced, con-
catenated one after the other.
ICA Analysis
The ICA analysis was performed using EEGLAB, ver-
sion 6.01b, a freely available open source toolbox
120 Brain Topogr (2010) 23:119–127
123
(http://sccn.ucsd.edu/eeglab/). We performed the indepen-
dent component decomposition based on the ‘infomax’
ICA algorithm (Bell and Sejnowski 1995). The suitability
of this ICA decomposition for ERP analysis is discussed in
(Makeig et al. 1999).The output comprised a total of 32
components (i.e. equal to the number of electrodes) (for a
complete methodological description of the ICA analysis
on this dataset see Makeig et al. 1999). After visual
inspection of the scalp maps and of the time-course of their
activation, we selected the components accounting for
artifacts. One of these components was clearly related to
eyeblinks and therefore it was eliminated. The EEG data
were back-projected to the subset of remaining 31 com-
ponents. All the analyses we report in the following refer to
this ‘clean’ dataset.
Single-Trial Topographic Analysis
Model Estimation
We consider each topography (or map) as an N-dimen-
sional vector
m = {m
1
(t),m
2
(t),…,m
N
(t)}, with N number
of electrodes, for each trial and time-point (Fig. 1a). Each
vector
m is normalized by its global field power so as to not
take into account instantaneous strength (Lehmann 1987;
Michel et al. 2001, 2004; Murray et al. 2008). We would
like to emphasize that at this point all the information about
latencies and trial assignment is lost, as all the maps are
treated as points in an N-dimensional space without any
tracking of their original order in time. It is also worthwhile
to remind the reader that analyses based on topographic
information are inherently independent of the reference
electrode (cf. Michel et al. 2004; Murray et al. 2008 for a
treatment of this issue).
In the attempt to represent our dataset in a number of
representative maps, we propose to model the ensemble
{m} as a mixture of Gaussians (GMM) (Fig. 1b):
pðm l
j
; rÞ¼
X
k
p
k
G
k
ðl
k
; r
k
Þ; k ¼ 1; ::; Q ð1Þ
where G
k
is the kth Gaussian distribution with mean l
k
,
covariance r
k
, and p
k
prior probability. The mean of each
of these Gaussians will be referred to as template map and
considered as a prototypical voltage map for all those sets
of maps that have been clustered together in one of the
Gaussian. Q is the total number of Gaussians, which needs
to be decided a priori before estimating the model’s
parameters.
The GMM is estimated by an expectation–maximization
algorithm, Baum-Welch algorithm (Dempster et al. 1977),
which iterates the estimation of the model parameters in
order to maximize the likelihood. This algorithm requires
the parameters of the GMM to be initialized. Here we
consider as initial means those obtained by a k-means
clustering algorithm (Bishop 1995). The initial guess of the
covariance (here restricted to be diagonal) is obtained by
considering the topographies closer to each of the means as
estimated by the k-means algorithm. The priors, {p
k
}, are
obtained by the relative number of topographies for each
cluster. In this GMM estimation, the value of the total
number of Gaussians is fixed a priori. In order to find the
optimum value of Q, we estimate a GMM model for a set
of values of Q ranging from 4 to 28 and we choose the
value of Q corresponding to a value of explained variance
above a certain threshold.
ERP Analysis Based on the GMM
Once the optimal GMM model has been estimated, it is
possible to assign to each map m, a posterior probability for
each of the Gaussians. An example of posterior probability
is provided in the inset of Fig. 1b for one of the maps. In
this example, the cluster colored ‘blue’ is the one providing
the highest posterior probability among the three; this map
is therefore best represented by the template map corre-
sponding to the blue Gaussian. By rearranging these pos-
terior probabilities in the original order of trials and time
(Fig. 1c), we can investigate which maps are best repre-
sented by one template map across trials and locked in time
(Fig. 1d).
Specifically, we are interested in estimating at which
point in time the average posterior probability exhibits a
significant modulation with respect to pre-stimulus base-
line. The presence of these modulations is indicative of the
degree to which the model is representative of stimulus-
related activity and of the presence of one specific template
map across trials and at a certain latency. This statistical
analysis was performed by means of a non-parametric test
(Kruskall–Wallis) which contrasts—at each time-frame—
the posterior probability values and corresponding median
along the baseline across trials. For each of the estimated
GMM, we consider therefore the total number of Gaussians
Q and the subset of these Gaussians, Q’, whose posterior
probability was significantly higher than baseline in some
temporal intervals during the post-stimulus period. In
general, not all the template maps will exhibit a posterior
probability with a significant modulation with respect to
baseline, and therefore Q’ will be lower than or equal to Q.
We further constrain our analysis by considering as ‘active’
only those template maps with posterior probabilities sig-
nificantly higher than baseline for at least 10 consecutive
data-points, here corresponding to approximately 78 ms.
This is a means of correcting for temporal auto-correlation
in the data (e.g. Guthrie and Buchwald 1991).
Brain Topogr (2010) 23:119–127 121
123
In order to choose the best model, we compute for each
total number of maps Q, the global explained variance
(GEV) on the whole dataset and on those time periods
where there was a significant modulation of the posterior
probability. The GEV is based on the correlation between
the template maps and the GFP-normalized voltage maps
recorded at each time point and each trial and the instan-
taneous GFP. This notion of explained variance is an
established measure in the context of microstate analysis,
where the correlation is computed between template maps
(estimated at average ERP level) and instantaneous voltage
configuration of the average ERP (Murray et al. 2008;
Pourtois et al. 2008). We choose the value of Q which
provides a maximum or local maximum of the explained
variance over these sub-periods (Fig. 2, red line).
Comparison Between Single-Trial and ICA Analyses
After selecting the mixture of Gaussians we considered
within the set of template maps only those whose posterior
probability was deemed ‘active’ according to the above-
mentioned criteria. As our aim is to compare the information
Fig. 1 Flow-chart of the GMM modeling of the ERP dataset and
statistical analysis. a Voltage maps are pooled together irrespective of
time and trials in an N-dimensional space, where N is the total
number of electrodes; (b) the ensemble of observations {m} are
modeled as a GMM. In this panel we provide an example of three
Gaussians in the mixture. Model’s parameters allows to assign to each
map a vector of posterior probabilities as shown for one exemplar
map belonging to the ‘blue’ Gaussian; (c) These set of posterior
probabilities are re-ascribed with respect to time and trials; (d)
Averaging across trials the posterior probabilities for each Gaussian
and at each time-point, we can infer the presence of template maps
during the post-stimulus period with respect to baseline, indicative of
the degree of stimulus-related modulation of maps presence
Fig. 2 Explained variance as a function of number of Gaussians in
the mixture of Gaussians model. The blue line refers to the explained
variance computed over the entire dataset. The red line refers to sub-
periods where the posterior probabilities across trials were signifi-
cantly higher than baseline. The tendency to obtain a higher explained
variance when computed over those sub-periods shows how the
model explains mostly those parts of the data which is event-related
and locked across trials
122 Brain Topogr (2010) 23:119–127
123
conveyed by ICA and single-trial topographic clustering
methods for ERP interpretation, we selected those ICA scalp
maps that best correlated spatially with the Q’ template
maps. In parallel, we computed the average activations of
these scalp maps and compared the latencies of their maxima
with those of the corresponding average posterior probabil-
ities as obtained by the single-trial topographic analysis. It is
worth emphasizing that a resemblance of the spatial maps
obtained by the two analyses does not presuppose a similar
temporal profile of the corresponding average activations.
Finally, we computed the EEG current source locations
based on low-resolution electromagnetic tomography
(LORETA) (Pascual-Marqui et al. 1994) of corresponding
maps in the two approaches at latencies that were related to
known ERP components. LORETA uses a three-shell
spherical head model including scalp, skull, and brain
compartments, registered to the digitized Montreal Neu-
rological Institute (MNI) MRI template (Talairach and
Tournoux 1988). The solution space corresponds to cortical
gray matter sampled at 6-mm resolution, resulting in a total
of 3005 voxels.
Results
The total explained variance of the GMM model increased
with the total number of maps in the model when computed
on the overall dataset (Fig. 2, blue line). The explained
variance on those temporal intervals during which some of
the posterior probabilities exhibited a significant modula-
tion with respect to baseline (i.e. were ‘active’), peaked at
two values of total number of maps Q (Fig. 2, red line). We
therefore chose Q = 11 as this was providing the relative
maximum contribution of explained variance (68%). The
total number of active template maps Q’, was 5. We
therefore refer to these five template maps in the analyses
that follow. The average posterior probabilities across trials
for these template maps are shown in Fig. 3a together with
the intervals of significant modulation with respect to
baseline for each of them (thicker lines). The correspond-
ing template maps are shown in Fig. 4a.
Among the 31 scalp projections identified by ICA, we
selected those providing the highest spatial correlation with
the abovementioned Q’ template maps (Fig. 4; Table 1).
We discuss here only those scalp projections that were the
most correlated with the Q’ template maps even if several
others also produced an high and significant correlation.
The mean activations of the selected scalp projections
exhibited a temporal pattern closely resembling those of
the posterior probabilities of corresponding template maps
(Fig. 3a,b). In particular, the latencies of the peaks were
matching when the maxima of the average posterior
probabilities fell within periods of statistically significant
modulation. The latencies of these peaks are indicated by
arrows in Fig. 3. For example, the first template map
peaked at 297 ms (39th data point) post-stimulus onset, and
the ICA component whose scalp projection was most
highly correlated with the first template map peaked at
305 ms (40th data point) post-stimulus onset. That is to
say, their latency differed by only one data point. A full
description of the periods of activity of the five template
maps, their latencies and differences with the mean acti-
vation latencies of the ICA components is listed in Table 1.
It is worth noting that the peaks of activations in both
panels of Fig. 3 occurred between 305 and 437 ms post-
stimulus onset (here we focus only on the absolute peak of
each activation, although other earlier peaks are also
important and possibly accounting for early visual com-
ponents). The appearance of the earliest of these compo-
nents (component 1, blue trace in Fig. 3) at 297 and
305 ms, respectively, is consistent with the so-called P300
component, related to attending to novel stimuli. The later
subset of components peaking between 391 and 437 ms,
possibly comprised activities related to the motor response.
This pattern of components has been extensively described
in the original publication (Makeig et al. 1999).
In correspondence to the first of these components, we
computed the inverse solution based on standard LORETA
and we compared the results between the blue-framed
maps obtained in the two approaches (Fig. 5). A quanti-
tative comparison was possible only at the level of spatial
correlation since, based on one single subject dataset, we
are not in the position to assess statistically which sources
were significantly active. The spatial (Pearson) correlation
between the 3005 voxels within the inverse solution points
was r =
0.57 (p \ 10
-15
). To assess the existence of
spatially overlapping sources, we looked at peaks of the
inverse solution values as a percentage of the absolute
maximum for each of the two solutions. At 80% of the
maximum value for each of the two inverse solutions, we
found the first overlapping voxels, whose peak was located
at 34, 33, 57 mm using the Talairach and Tournoux (1988)
coordinate system. This peak falls within Brodmann’s Area
(BA) 40 of the right hemisphere (Fig. 4, coronal view).
Discussion
The results reported here support the consistency between
an ICA-based ERP analysis and a recently introduced
single-trial topographic clustering algorithm. Several
common lines of interpretation can be derived from these
results. Both methods uncovered the presence of ERP
components that matched each other both with respect to
the latencies of their activation peaks and also their spatial
configurations. In particular, three template maps estimated
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