Groupwise independent component decompos (1)

www.elsevier.com/locate/ynimg
NeuroImage 35 (2007) 1103 – 1112

Groupwise independent component decomposition of
EEG data and partial least square analysis
Natasa Kovacevic a,⁎ and Anthony Randal McIntosh a,b
a

Rotman Research Institute Baycrest Centre 3560 Bathurst Street, Toronto, Ontario, Canada M6A 2E1
Department of Psychology, University of Toronto, Toronto

b

Received 20 July 2006; revised 10 November 2006; accepted 12 January 2007
Available online 27 January 2007
This paper focuses on two methodological developments for analysis of
neuroimaging data. The first is the derivation of robust spatiotemporal
activity patterns across a group of subjects using a combination of
principal component analysis (PCA) and independent component
analysis (ICA). In applications to ERP data, the space dimension is
typically represented in terms of scalp electrodes. The signal recorded

by high density electrode caps is known to be highly correlated due in
part to volume conduction. Consequently, this redundancy is also
reflected in spatiotemporal patterns characterizing signal differences
across experimental conditions. We present an alternative spatial
representation and signal compression based on PCA for dimensionality reduction and ICA conducted across all subjects and conditions
simultaneously. The second advancement is the use of partial least
squares (PLS) analysis to assess task-dependent changes in the
expression of the independent components. In an application to
empirical ERP data, we derive an efficient number of independent
component maps. Comparative PLS analysis on the independent
components versus original electrode data shows that task effects are
not only preserved under compression, but also enhanced statistically.
© 2007 Elsevier Inc. All rights reserved.

Introduction
PLS is a multivariate technique that has been utilized in a
variety of neuroimaging applications including ERP, MEG, fMRI
and PET (McIntosh, 2004; Lobaugh et al., 2001; Duzel et al.,
2003; Hay et al., 2002; Addis et al., 2004; Itier and Taylor, 2002).
One of the main uses of PLS has been in detecting changes in

neuroimaging data due to experimental manipulations of cognitive
tasks and describing the changes in terms of spatiotemporal
patterns. In applications to functional neuroimaging data representing a group of subjects recorded over several conditions, PLS can
detect major experimental effects describing differences in signal
intensity across conditions, consistently across subjects. The

⁎ Corresponding author.
E-mail address: nkovacev@rotman-baycrest.on.ca (N. Kovacevic).
Available online on ScienceDirect (www.sciencedirect.com).
1053-8119/$ - see front matter © 2007 Elsevier Inc. All rights reserved.
doi:10.1016/j.neuroimage.2007.01.016

experimental effects are further characterized in terms of their
expression in space and time.
In most ERP analyses, including PLS, space is represented in
terms of electrode potentials and time is represented in terms of
latency offsets from time-locking events. Electrodes receive a
summed signal from simultaneously active brain sources, and as
the signal passes through the skull it becomes spatially smeared
across electrodes. In this paper we show how to obtain reduced and

efficient spatial representation of an ERP signal as an input to PLS.
The representation consists of a set of spatial maps capturing major
modes of task related activation for a given event related
experiment.
Our spatial data reduction is based on PCA dimensionality reduction followed by ICA rotation. The PCA/ICA analysis is
performed across all subject and conditions in order to identify
robust spatiotemporal patterns. Many applications of ICA to EEG
data extract meaningful components at the individual subject level.
Subject-specific components are then combined based on similarity
metrics (Makeig et al., 2004). While there is reason to believe that
such an approach will yield similar results to the group-based ICA we
propose, there is an important assumption behind our approach
versus subject-specific ICA. In our derivation, the assumption is that
there are enough similarities across individuals in cortical anatomy/
geometry that a group-based metric is a reasonable topographic
summary of task-dependent effects. As such, the components we
extract can be considered as a set of spatial filters that are optimized
to project subject data into a common spatial reference. The approach
is similar in concept to that used in fMRI, where data at the subject
level are converted to a common spatial reference, and group analyses performed to extract the most reliable effects across the sample

(whether through mixed effects or conjunction analysis (Friston et
al., 1999) or resampling (e.g., Strother et al., 2002; McIntosh, 2004)).
Group ICA components are fixed scalp maps with mutually
independent time courses. They are viewed as a new and reduced
coordinate system for the spatial representation of the EEG data.
Single trial time series of the group ICA components are calculated
as weighted sums of electrode activations. Individual subject
average time series (wave forms) of group ICA are calculated by
averaging single trial time series. This component based spatio-

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temporal data representation is then analyzed with PLS in order to
detect and characterize main task related effects across the group.
The construction of the new spatiotemporal representation and
its effect on the PLS results are illustrated through an application to
a cross-modal EEG experiment. Comparison between standard
PLS analysis of electrode data and the new PLS analysis of group

ICA data shows overall similarity in the detection of task effects.
However, there are two main differences: (1) spatiotemporal
patterns of task effects are often more efficiently captured and
separated in the component space then in the electrode space, (2)
task effects tend to be more statistically robust in the component
space compared to the electrode space.
Materials and methods
Experiment
Twelve healthy adult subjects aged 18–33 (8 males) were
presented with two stimuli: a high or low pitch binaural tone and a
checkerboard square presented left or right of fixation (Fig. 1). Each
stimulus was presented for 250 ms. The auditory stimulus
represented a cue, while the visual stimulus represented a target.
In one block of trials, the C1 task, the cue was presented first and
was followed by the target. In another block of trials, the C2 task,
the cue was presented second and was preceded by the target. The
inter-stimulus interval was 1000 ms. After the second stimulus
subjects responded by button press. The tone’s pitch indicated
whether a response was required to be spatially compatible or
incompatible, i.e., with the hand on the same or opposite side of the

target. High pitch (250 Hz) and low pitch (4000 Hz) tones were used
to indicate compatible and incompatible responses, respectively.
The pitch was randomly varied across trials. Subjects were given
1050 ms to respond after the second stimulus. This was followed by
an inter-trial interval that varied between 800 and 1200 ms.
Control tasks were run where the tone had no meaning and the
response rule was fixed as either compatible or incompatible within
a block of trials. These were denoted C1c and C2c, depending on
whether the auditory stimulus was presented first or second. Each

of the four tasks (C1, C2, C1c, C2c) contained four conditions
determined by the side of the target and compatibility of the
response (LC = left compatible, LI = left incompatible, RC = right
compatible, RI = right incompatible), bringing the total number of
conditions to 16.
EEG recordings and preprocessing
Continuous electroencephalogram (EEG) recordings were
digitized using NeuroScan 4.0 with a 65 channel ElectroCap at a
250 Hz sampling rate. Electrodes were referenced to Cz during the
recording. In addition, electro-oculogram (EOG) recordings were

made and subsequently used for PCA based correction of ocular
artifacts in continuous EEG data (Picton et al., 2000). The
continuous data were re-referenced to an average reference and
bandpass filtered (0.5–45 Hz). Data were epoched into 2200 ms
epochs (550 time points at 250 Hz sampling rate) time-locked to
the onset of the first stimulus and 200 ms prestimulus baseline. The
epoch length was sufficient to include both stimuli and the
response. Epoched data sets containing trials with correct
responses were further cleaned of artifacts using independent
component analysis (ICA) as implemented in EEGLAB software
(Delorme and Makeig, 2004) and run in MATLAB (Mathworks
Inc.). Since most of the ocular artifacts were previously corrected,
ICA based artifact removal and correction consisted of the
following steps: (1) trials contaminated with excessive amplitudes
were removed first, (2) an ICA decomposition was performed on
the remaining concatenated trials and (3) components carrying
residual ocular and muscle artifacts were subtracted. Each subject’s
data set was divided into 16 condition-specific sets of trials. The
number of artifact-free, correct-response trials per subject, per
condition was between 20 and 56, with average 45.

Data organization for group ICA
Data from all subjects and conditions were combined into a
single matrix in order to: (1) incorporate data from all subjects and
conditions, (2) equalize number of trials across subjects and

Fig. 1. EEG experiment. In C1 task, auditory cue was presented first, before visual target. In C2 task, auditory cue was presented second, after visual target. In
both tasks, button press was required after the second stimulus. Response compatibility was indicated by the cue.

N. Kovacevic, A.R. McIntosh / NeuroImage 35 (2007) 1103–1112

conditions, (3) increase signal-to-noise ratio while preserving
temporal dynamics and (4) reduce the computational load for
subsequent ICA decomposition. We utilized the following sorting
and subaveraging procedure. Subject and condition-specific trials
were sorted with respect to the response time (RT), from faster to
slower. Sorted trials were binned into 5 bins with approximately
the same number of trials per bin (9 on average). Data were
averaged within each bin, resulting in a set of 5 subaveraged trials
per subject and condition. RT was calculated as an offset in ms
from the second stimulus onset. The average RT and average

standard deviation of RT across subjects and conditions were
460 ms and 114 ms, respectively. Thus, the activation of motor
response typically ranged by at least 200 ms. Subaveraging across
trials with vastly different response times would introduce
temporal smearing and obscure response locked activations. We
first ordered the trials with respect to RT so that the subsequent
binning and subaveraging would preserve the overall temporal
characteristics of single trials in terms of both stimulus and
response locked activation patterns. In view of the constraints
presented by the number of available trials, RT variability and the
computational load, the number of bins was experimentally
determined as most appropriate.
The subaveraged trials were concatenated into a single data set
representative of all conditions and subjects. The resulting data
matrix X was 65 × m in size, where 65 = number of electrodes and
m = number of conditions * number of subjects * number of subaveraged trials * number of time points per trial = 16 * 12 * 5 * 550 =
528,000.

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PLS analysis in electrode space

Spatial dimensionality reduction via PCA followed by Infomax
ICA decomposition was performed on the group data matrix X,
described above. X was initially decomposed with PCA and
spatially reduced to a subspace spanned by a proposed number of
components. The basis of the subspace was then rotated using the
Infomax algorithm as implemented in EEGLAB. The effect of the
initial PCA procedure was to determine a subspace that captured a
portion of the variance across electrodes and was spanned by an
orthogonal basis. The purpose of the subsequent Infomax
procedure was to find another basis for the same subspace such
that spanning components were no longer necessarily orthogonal,
but rather maximally temporally independent in the Infomax sense,
i.e., with maximum component joint entropy. For a given model
with p components, the PCA followed by ICA decomposition
resulted in a p × 65 weighting matrix, which expressed each
component as a weighted sum of electrodes (see Appendix A for
details). A single trial time series of the derived components were
obtained by multiplying the electrode single trial time series by the

weighting matrix.

A complete description of PLS can be found in Lobaugh et al.
(2001) and McIntosh (2004). Here we present the essential details
with a brief mathematical description in Appendix B. PLS starts
with a data matrix composed such that the rows correspond to
subjects within conditions and the columns correspond to time
points within electrodes. Each row of the matrix consists of a
condition and subject-specific average time series, horizontally
concatenated across electrodes. In the grand mean deviation
analysis, grand average time series for each condition are
calculated and the data matrix is mean-centered column-wise with
respect to condition-specific grand averages.
The mean-centered matrix is decomposed using singular value
decomposition (SVD) to produce a set of mutually orthogonal
latent variables (LVs, which are the left and right singular vectors
from the SVD) with decreasing order of magnitude (analogously to
PCA). Each LV consists of: (1) a singular value, (2) a design LV
and accompanying design saliences (weights within the right
singular vector) representing a task contrast and (3) scalp LV and
accompanying electrode saliences (weights within the left singular
vector) representing the optimal spatiotemporal relation to the
identified contrast. The relative strength of each LV can be
evaluated by computing the percentage of cross-block covariance
accounted for. This is the ratio of the squared singular value over
the summed squared singular values for all LVs. This metric is not
to be confused with the percentage of total variance accounted for
as it pertains only to the covariance between measured brain
activity and experimental design and thus is dependent on the
parameterization of the design.
The figure of merit for PLS is provided by statistical assessment
using resampling procedures. Firstly, the singular value for each
LV is tested for significance based on permutation tests, which
randomly reassign conditions within subjects. Secondly, the
electrode saliences of the significant LVs are further tested for
stability across subjects, by bootstrap resampling of subjects within
conditions. The ratio of the salience to the bootstrap standard error
is approximately equivalent to a z-score and is used as a measure of
stability. Thresholding bootstrap ratios allow identification of
electrodes and time points (spatiotemporal pattern) of stable LV
expressions. In summary, grand mean deviation PLS analysis
identifies main data driven task effects (e.g., as in Fig. 2) together
with their respective spatiotemporal signatures, which are stable
across subjects.
In the non-rotated (hypothesis driven) version of PLS analysis,
a set of a priori contrasts is constructed and the sums-of-squares for
the projection of each contrast on the data are computed (McIntosh,
2004). Once again, statistical assessment assigns a p-value to the
sums-of-squares for each contrast projection and identifies
corresponding stable spatiotemporal patterns.

ðcomponent activationsÞptime ¼ ðweighting matrixÞp65

PLS analysis in component space

Group ICA

Tðelectrode activationsÞ65time
An optimal number of ICA components was determined using
Bayesian Information Criterion (BIC) (Hansen et al., 2001).
Models with the number of components ranging from 1 to 65 were
considered, thus covering the entire theoretical range, and a
Bayesian probability of each model was evaluated. The model
with maximum probability was selected for subsequent PLS
analysis.

PLS analysis of the group ICA component space operated in the
same way as in the electrode space, except that the spatial
dimension was now expressed in terms of group ICA components.
The data matrix was composed so that the rows corresponded to
subjects within conditions and the columns corresponded to time
points within group ICA components. Each row of the matrix
consisted of a condition and subject-specific average time series,
concatenated horizontally across components. The new spatial

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N. Kovacevic, A.R. McIntosh / NeuroImage 35 (2007) 1103–1112

Fig. 2. Probability distribution across models varying in number of group
ICA components. Number of ICA components is limited by the number of
electrodes (65). Shown are probabilities for models 1–30; for higher models
probabilities were close to 0. The maximum BIC probability was achieved
with 11 group ICA components.

representation of the data also implied a new interpretation of the
task contrasts in terms of the spatiotemporal patterns. Both meancentering and non-rotated versions of PLS were used in the
analysis of the component data.
Comparison of PLS results in electrode and component spaces
In the first set of PLS analyses we used a mean-centering
approach in order to identify the main effects due to condition
differences (LC, LI, RC, RI) within four main tasks (C1, C2, C1c
and C2c). We used a randomization scheme with 500 permutations
for contrast significance estimation and 500 bootstrap samples for
the estimation of the stability of spatiotemporal contrast saliences.
We compared task contrasts of the first three latent variables in
electrode and component analyses, along with their corresponding
p-values calculated by the permutation tests and cross-block
covariance contributions.
In the second set of analyses we used a non-rotated version of
PLS in order to assess statistical properties of three a priori
contrasts. With a condition ordering LC, LI, RC and RI, the
contrasts were: visual field (1, 1, − 1, − 1), compatibility (1, − 1, 1,
− 1) and hand of response (1, − 1, − 1, 1). LC and RI both require a
left-hand response, while LI and RC require a right-hand response.
As with the mean-centered analysis, the non-rotated PLS analysis
was done within the four main tasks. This gave us an opportunity
to make a direct comparison between four sets of electrode and
component analyses using identical contrasts. For each of the three
contrasts, we compared significance and percent cross-block
covariance.
Comparison of PLS results between original electrode data,
filtered electrode data and component data
To foreshadow, we found overall enhancement of task effects in
the component space compared to the electrode space, as a result of
data reduction and filtering (see Results). In order to investigate the
effect of group ICA filtering directly, we back-projected the
component signal into the electrode space (see Appendix A for

details). We performed mean-centering PLS analyses on the
filtered electrode data and compared the results with those from
the PLS analyses on the original, unfiltered electrode data. We then
calculated the dot products between the design LV vectors from
filtered and unfiltered data analysis to assess their similarity.
Because the vectors are unit length, the dot products are cosines or
correlations.
Direct comparison between spatiotemporal patterns of task
related differences was investigated using the three contrasts. For
this purpose, we calculated the dot product between saliences in
the original and filtered electrode spaces both of which were scaled
to unit length.
Finally, we performed a three-way comparison between original
electrode data, filtered electrode data and component data. We used
a mean-centering PLS approach in order to identify the main
effects within task pairs (C1 and C1c, C2 and C2c, C1 and C2, C1c
and C2c). Each task pair consisted of 8 conditions. This allowed
more extensive statistical assessment over increased number of
conditions with potential for larger number of orthogonal contrasts.
We compared electrode and component PLS results in terms of the
number of significant LVs and corresponding percent cross-block
covariances. Because mean-centered PLS produces orthogonal
contrasts, we summed up the total cross-block covariance across
significant LVs. This was taken as a measure of the portion of the
cross-block covariance captured by the significant contrasts. We
also calculated the relative weight of stable spatiotemporal patterns
in the following way. For each significant LV, we calculated the
number of space–time points that stably expressed the design
contrast across subjects (absolute bootstrap ratio > 3.3). The
number was then represented as a percent of the total number of
space–time points to adjust for the differing number of spatial
coordinates in electrode and components spaces. This measure was
taken as an estimate of the efficiency for a given data
representation: larger percent of space–time with stable contrast
expression indicated more efficient representation.
Results
Group ICA components
The maximum BIC probability was obtained for the model
with 11 group ICA components, as shown in Fig. 2. The data set
was accordingly reduced and decomposed into 11 maximally
temporally independent modes whose topographic scalp maps
together with grand average time series in all conditions from C1
and C2 tasks are shown in Fig. 3. Two last components were
identified as artifactual based on their scalp maps and time courses
across subjects and subaveraged trials, using similar criteria as in
single subject artifact rejection (Delorme and Makeig, 2004).
Unlike task related components, artifactual components lack
consistent time-locked and task related amplitude variations, as
illustrated in Fig. 4. The last two components were dropped from
further analysis.
The nine task related components exhibit a great deal of
temporal specificity pointing to separate functional roles. For
example, components 2 and 3 are mostly involved in visual
response because their highest activation amplitudes are occurring
50–300 ms after the onset of the visual stimulus and are otherwise
at the baseline level. In particular, component 3 shows strong
differentiation between left and right visual field, which extends for
at least 800 ms following the onset of the visual stimulus.

N. Kovacevic, A.R. McIntosh / NeuroImage 35 (2007) 1103–1112

1107

Fig. 3. Scalp maps of the eleven group ICA components and their grand average time series across four conditions in C1 and C2 tasks. Scalp maps were produced
using spherical spline interpolation. In time series plots, Y-axis represents component activation amplitude in μV and X-axis represents time. 0 and 1000 ms
correspond to stimulus onsets. Within each of the two tasks, shown are grand average time series for 4 conditions: left compatible (LC), left incompatible (LI),
right compatible (RC) and right incompatible (RI). Conditions can be grouped depending on the handedness of the response, e.g., LC and RI require left hand
response (Lh).

Components 4 and 6 activate strongly 50–300 ms after the onset of
the auditory stimulus. Motor response is mostly carried by
components 5, 6 and 9, with strong differentiation for left hand
(LC and RI) and right hand (LI and RC) response. Component 8
shows weak task related activation and further investigation of its
single trial time series and power spectrum indicated that this
component captured alpha rhythms with sporadic stimulus locking
(data not shown), consistent with its topographic map indicative of
the visual cortex.
PLS results in electrode and component spaces
Results from mean-centering PLS analyses across four main
tasks in electrode and component spaces are shown in Fig. 5. For
both analyses, the obtained sets of design LVs are overall
expressing three contrasts: left visual field vs. right visual field

(Lvf vs. Rvf), high vs. low tone frequency, i.e., compatible vs.
incompatible (C vs. I), and left vs. right hand response (Lh vs. Rh).
Table 1 shows the comparison of the non-rotated PLS analysis
in terms of significance and percent cross-block covariance. The
comparison of the spatiotemporal patterns characterizing the three
contrasts is more complicated because of the different spatial
representations. In general, the electrode space exhibited patterns
with more overlap in both space and time. This is illustrated in Fig.
6. It shows spatiotemporal patterns for the Lvf vs. Rvf contrast in
the C2 task. In both spaces the signal differentiation for left and
right visual field expresses strongly during 150–250 ms after
stimulus onset and then re-emerges during the slow wave period
(400–800 ms) when subjects memorize the side of the visual field
while waiting for the cue. While this differentiation extends over
several electrodes in the electrode space, it is compactly captured
by a single group ICA component, namely component 3.

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N. Kovacevic, A.R. McIntosh / NeuroImage 35 (2007) 1103–1112

Fig. 4. Component activations across sorted group data are visualized using ERP image tool of EEGLAB. Trials are stacked vertically with task order C1, C2,
C1c and C2c from bottom to top, and within each task in condition order LC, LI, RC and RI from bottom to top. Trial time interval (from −200 to 2000 ms)
corresponds to the horizontal axis and color represents activation amplitude in μV. Visual stimulus onset is at 1000 ms in C1 and C1c tasks and at 0 ms in C2 and
C2c tasks. Component 3 (on the left) shows activation time-locked to the visual stimulus and consistent across conditions and subjects, with strong differentiation
between left and right visual fields. By contrast, component 10 (on the right) does not show consistent stimulus time-locked activations. Its scalp map also
suggests residual ocular artifact, mostly carried by a single subject (red horizontal lines repeating in regular intervals indicate trials of the same subject).

PLS results in original electrode data, filtered electrode data and
component data
Results from the comparison between original and filtered
electrode data via dot products of design LVs from mean-centering
PLS are shown in the left column of Fig. 7. Products on the
diagonal are close to 1, and off the diagonal are close to 0. This
indicates that the sets of contrasts were not only similar across all

four tasks, but their ordering by the contribution to the cross-block
covariance was also the same. Though the contrast sets were highly
similar, they were not identical.
To investigate spatiotemporal patterns for identical experimental effects we subsequently performed non-rotated PLS analyses
with the three a priori contrasts and then compared the associated
spatiotemporal patterns of the original and filtered electrode
analyses. The resulting dot products of the normalized salience

Fig. 5. Mean-centering PLS analysis of electrode data (left) and component data (right) across the four main tasks. Shown are three design LVs from each
analysis, along with their corresponding p-values and percent cross-block covariance. Design LVs express contrasts between 4 conditions, LC, LI, RC and RI.

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N. Kovacevic, A.R. McIntosh / NeuroImage 35 (2007) 1103–1112
Table 1
p-values for the three ideal contrasts in electrode (E) and component (C) analyses
C1

E

C

Lvf vs. Rvf
C vs. I
Lh vs. Rh
Lvf vs. Rvf
C vs. I
Lh vs. Rh

C2

C1c

C2c

p

Cc (%)

p

Cc (%)

p

Cc (%)

p

Cc (%)

0
0
0.04
0
0.04
0

37
40
24
47
19
34

0.03
0.4
0.08
0
0.7
0

39

0
0.03
0.2
0
0.4
0

46
30

0.04
0.7
0.7
0
0.7
0

39

41
42

48
37

36
51

For significant LVs (p < 0.05) corresponding percent cross-block covariance (cc) is also shown.

vectors are shown in Fig. 7 on the right. Once again, the dot
product matrices resemble the 3 × 3 identity matrix, which indicates
high degree of similarity between the two sets of spatiotemporal
patterns of the a priori contrasts.
Results from the three-way comparison between PLS analyses
of the original electrode data, filtered electrode data and
component data are summarized in Table 2. Mean-centering
PLS analyses were performed on paired tasks. For each task pair
and data type, shown is the number of significant LVs, the
corresponding cross-block covariance contributions and percent
of space–time with stable contrast expression. In general, analysis
of component data produced the largest number of significant
effects and stable time points, whereas the original electrode data
produced the fewest. This was most evident on the analysis of C2
vs. C2c, where the analysis of component data yielded 3
significant LVs, while the original data yielded only one. The
filtered data produced an intermediate result, with 2 significant
LVs.
Discussion
In the standard ERP analysis, the spatiotemporal representation
of data uses time series of the electrode recordings averaged across

repeated trials for each subject. Spatial smearing and signal
redundancy of the recorded signal are also reflected in analysis
results. This can make identification and spatiotemporal separation
of task effects difficult. In this paper, we introduced an alternative
approach to ERP signal representation. We utilized group PCA
data reduction and group ICA filtering in order to re-express the
signal in a compressed and efficient way, with optimum balance
between goodness of fit and model complexity as determined by
Bayesian Information Criterion. In an application to real EEG we
were able to compress the spatial representation of the data to a
small set of maximally temporally independent scalp topographies
(group ICA components), with relatively specialized functional
relevance.
Similar spatiotemporal PCA and ICA based techniques have
been previously used for data reduction and filtering (Spencer et
al., 1999; Curran and Friedmann, 2004; Makeig et al., 1999). In
these studies the analyses were performed on either grand averaged
electrode time series (Makeig et al., 1999) or on combined subject
averages (Spencer et al., 1999; Curran and Friedmann, 2004). Both
averaging procedures may impact temporal specificity, especially
in experiments with large variability in brain response latency. This
is commonly observed in experiments requiring behavioral
responses such as a button press. In order to increase the signal-

Fig. 6. Spatiotemporal patterns in electrode and component spaces characterizing Lvf vs. Rvf contrast in C2 task where visual stimulus onset starts at 0 ms. Each
colored horizontal line represents electrode or component salience across time. Hot colors signify space–time points with positive contrast expression, i.e., where
signal is higher for left than for right visual filed. Analogously, cool colors signify points with negative contrast expression, i.e., where signal is higher for right
than for left visual field. Black circles identify space–time points for which contrast expression is stable across subjects (absolute bootstrap ratio >3.3).

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N. Kovacevic, A.R. McIntosh / NeuroImage 35 (2007) 1103–1112

Fig. 7. Comparison across four task PLS results between original electrode data and filtered electrode data. Left column shows absolute value dot products
between original design LVs produced by mean-centered PLS (E) and those in filtered electrode space (FE). The contrasts are arranged in a decreasing order of
singular values, i.e., contribution to the cross-block covariance. Right column shows dot products between normalized salience vectors corresponding to three a
priori contrasts in the original and filtered electrode spaces.

to-noise ratio and at the same time preserve temporal specificity,
we chose the middle ground between single trial data and subject
averages. This was done by a subaveraging procedure, which
divided each subject’s trials into several temporally consistent bins
and then calculated the average time series for each bin. The data
matrix combining the subaverages from bins across all subjects and
conditions was analyzed and compressed using PCA and ICA. The

resulting set of ICA components was representative of the group
across all experimental conditions.
Under the spatial compression from full electrode space onto
group ICA space, task effects were not only preserved, but also
further enhanced in terms of statistical properties. This was
demonstrated by an increased number of significant task effects in
the group ICA space, compared to both original and filtered

Table 2
Comparison of significant task effects in mean-centering PLS analyses of original electrode (E), filtered electrode (FE) and component (C) data across combined
tasks

E

FE

C

sig LVs
cc (%)
st (%)
sig LVs
cc (%)
st (%)
sig LVs
cc (%)
st (%)

C1, C1c

C2, C2c

C1, C2

C1c, C2c

3
39 21 14 (74)
12 5 5 (22)
3
39 22 14 (75)
14 5 5 (24)
4
38 27 13 9 (87)
8 8 4 4 (24)

1
65 (65)
13 (13)
2
64 11 (75)
14 3 (17)
3
32 25 23 (80)
8 8 4 (20)

2
63 9 (72)
18 8 (26)
2
64 9 (73)
20 9 (29)
4
38 21 14 12 (85)
10 11 6 3 (30)

2
60 12 (72)
11 4 (15)
2
63 11 (74)
14 5 (19)
4
35 25 16 11 (87)
8 14 4 3 (29)

For each analysis, sig LVs denotes number of significant LVs (p < 0.05), cc denotes percent cross-block covariance for significant LVs with sum over all
significant LVs given in parentheses and st denotes percent of space–time that stably expresses significant LVs (absolute bootstrap ratio >3.3) with sum over all
significant LVs given in parentheses.

N. Kovacevic, A.R. McIntosh / NeuroImage 35 (2007) 1103–1112

electrode spaces (Table 2). Note that there was no attempt to
preserve maximum variance by the compression. For example, the
subspace spanned by initial 11 PCA/ICA components captured
93% variance of the data matrix variance. After rejecting 2 artifactrelated components, the space spanned by the remaining 9 ICA
components captured only 82% of the variance. However, task
effects exhibited by the 9 group ICA components were enhanced.
Although filtered electrode data showed some enhancement of
task effects compared to the original electrode data (greater or
equal number of significant contrasts with larger contributions to
cross-block covariance and enhanced stability of spatiotemporal
patterns), it was not nearly as good as in the component data.
Despite filtering with ICA, it is likely that the residual noise from
less heavily weighted electrodes continues to attenuate task
effects.
Overall, group ICA component space offers efficient spatial
representation with increased sensitivity to task related signal
differences and can therefore be used as an alternative or as a
complement to the more traditional electrode space.
Acknowledgments
This work was supported by CIHR and J.S. McDonnell
foundation. We thank Stephen Strother for helpful suggestions and
discussions. We also thank Mackenzie Glaholt, Maya Stefanovic
and Andrea Diaconescu for data acquisition and preprocessing. All
code used for Group ICA and for PLS analysis can be accessed
through www.rotman-baycrest.on.ca/pls or by contacting the
authors. The Group ICA module will also be made available as a
plug-in for EEGLAB.
Appendix A
We present a description of the data transformation using
PCA dimensionality reduction followed by ICA rotation and
further reduction. Let X be a data matrix containing time series
concatenated across subaveraged trials, as described in the
Materials and methods section. The size of X is 65 × m, where
65 = number of electrodes and m = number of time points from
the concatenated subaveraged trials. The matrix W of eigenvectors of the matrix of observed covariances C = XXT, is defined
by:
XXT ¼ WEWT ;
where W is orthogonal and E is diagonal and both matrices are
65 × 65 in size. Projection of X onto a subspace defined by the
first p principal components is obtained as:
Y ¼ WpT X;
where Wp is a 65 × p matrix containing the first p columns of W.
Y is subsequently rotated with ICA into a new coordinate space
of temporally independent components

1111

spanned by the first q components (after possibly resorting the
rows of R so that unwanted components are last):
Zq ¼ Rq Y;
where Rq denotes matrix containing the first q rows of R. ICA
filtered version of Y signal is obtained by back-projecting the Zq
space
YF ¼ ðR 1 Þq Zq ¼ ðR 1 Þq Rq Y;
where (R− 1)q denotes a p × q matrix containing the first q
columns of R− 1. It is easy to check that Rq (R− 1)q = Iq, where Iq
denotes the identity matrix of size q × q.
Finally, PCA and ICA filtered version of the original electrode
signal is obtained by back-projecting the YF signal into the
electrode space
XF ¼ Wp YF ¼ Wp ðR 1 Þq Rq Y ¼ Wp ðR 1 Þq Rq WpT X:
In summary: (1) the relationship between the original electrode
signal and retained ICA component signal is given by Zq = L X,
where L= Rq WpT is a q × 65 weighting matrix and (2) PCA–ICA
filtered electrode signal is given by XF = P X, where P= Wp (R− 1)q
Rq WpT is a 65 × 65 filtering matrix. It can be easily shown that Wp
(R− 1)q is the Moore–Penrose pseudoinverse of L.
This filtering process can now be applied to every set of subject
and condition-specific single trial data. If x denotes a data matrix of
size 65 × n containing the original electrode single trial time series
with n time points, then the matrix of single trial activations for the
group ICA components is given by zq = L x, and filtered single trial
electrode time series is given by xF = P x.
Appendix B
B.1. Grand mean deviation PLS analysis
Assume a rectangular matrix M with n observations (subjects)
and k conditions as the n * k rows. The columns of the data matrix
contain the signal measured for each electrode or independent
component at each time point. The first column has intensity for
the first electrode/component at the first time point, the second
column has the intensity at the second time point. With m
electrodes/components and t time points, there are m * t columns in
the matrix M. Column-wise averages are created within each task,
yielding matrix T, a k by m * t matrix of task means. Grand mean
deviation matrix Tdev is defined as
Tdev ¼ T

1Tð1T TTÞ=k;

ð1Þ

where matrix 1 is a column vector of ones of length k and T
denotes a matrix transpose. Tdev is a column-wise mean-centered
matrix (for this reason, this version of PLS is also called the
“mean-centered” task PLS). The operation:
½ScalpLV; S; DesignLVŠ ¼ SVDðTdevT Þ where :

ð2Þ

Z ¼ RY;

ScalpLVTSTDesignLVT ¼ TdevT

ð3Þ

where R is an invertible p × p matrix. Letting p range between 1
and 65, the corresponding ICA spaces are evaluated using
Bayesian Information Criterion and optimal p is selected (for our
data set, the optimal p was 11). Subsequent ICA filtering of
residual artifacts is achieved by restricting Z to the subspace Zq

provides ScalpLV (or ComponentLV if independent component
maps are analyzed), an m * t × k orthonormal matrix containing
the electrode/component saliences, DesignLV, an k × k orthonormal matrix of design saliences, and S, a diagonal matrix of
the k singular values. The final diagonal element of S is zero,

1112

N. Kovacevic, A.R. McIntosh / NeuroImage 35 (2007) 1103–1112

representing the grand mean, which is eliminated through
mean-centering.
B.2. Non-rotated PLS
We start with a set of contrasts C comparing specific tasks (e.g.,
Helmert contrasts, dummy coded contrasts). Next the contrasts are
projected on to matrix T:
CT TT ¼ E:

ð4Þ

The sums-of-squares for each vector in E are computed and
treated to the same permutation assessment as the singular values
derived in Eq. (2). The weights within each vector of E are the
electrode/component saliences, whose reliability is assessed with
bootstrap resampling. While the non-rotated PLS has the advantage
of allowing a direct assessment of hypothesized experimental
effects, the interpretation may be difficult if non-orthogonal
contrasts are used.
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