Download Independent Components Analysis of Single Trial CNV data

4th International Conference “Neural Networks and Expert Systems in Medicine and Healthcare”
20-22 June 2001, Milos Island, Greece
NNESMED 2001
Independent Components Analysis of Single Trial CNV data
J.H. Britton & B.W. Jervis
Sheffield Hallam University
Sheffield, UK
ABSTRACT: Established techniques for the analysis of Event Related Potentials (ERPs) involve averaging of time-locked sections
of the EEG signal over many trials to obtain the ERP waveform. Such techniques are necessary as single trial ERP signals are
obscured by ongoing EEG activity, with signal to noise ratios below -10dB. The Independent Components Analysis (ICA) method is
used to determine unknown source signals which have been transmitted through and linearly mixed in an unknown system to
produce mixed output signals. ICA was applied to multi-channel CNV data in order to extract and analyse single trial ERP
waveforms and their underlying source signals. Variations in the extracted single CNV waveform during the recording session were
observed. Analysis of the underlying source signals suggests that these variations are the result of changes to the transmission path
of the source signals.
INTRODUCTION
The aim of this study is to apply the Independent Components
Analysis (ICA) method to event related potential (ERP) data in
order to extract and analyse single trial ERP waveforms and
their source signals.
ERPs are electrical signals produced by the brain in response to
stimuli or cognitive activity. They are usually obtained by
averaging sections of EEG recorded during many repetitions
(or trials) of a simple cognitive or motor task. Averaging over
many trials is necessary because each single trial ERP is
obscured by random fluctuations in the ongoing EEG.
multi-channel ERP data to obtain the underlying source signals
and single trial CNV waveforms.
The study is based on the assumption that the signal recorded
at each electrode is a linear combination of a number of
unknown source signals. Many of these source signals may be
produced by neural generators close to the surface of the scalp,
and can be considered to represent EEG noise and artefacts
unrelated to the ERP. However, it is likely that some of the
source signals are produced by specific neural generators
located in regions of the brain responsible for the production of
the ERP.
THEORY
The use of cognitive and motor ERPs has been investigated as
a means of diagnosing neurological disorders [1], [2]. Such
studies have been held back by several factors. These include
the limited volume of data collected from each individual (a
single averaged ERP waveform) and practical difficulties
associated with collecting ERPs from some patient groups. To
overcome some of these difficulties, and provide new insights
into the how ERPs change during a recording session, methods
have been proposed for the extraction of single trial ERPs.
Examples include Adaptive Multi-resolution Analysis [3] and
Time Sequence Adaptive Filtering [4].
This study uses an ERP called the Contingent Negative
Variation (CNV), which is generated by a cued reaction time
task. Each CNV paradigm consists of a pair of tones (a
warning tone and an imperative tone) separated by a fixed
interval of 1 second. The participant is instructed to press a
button as quickly as possible in response to the imperative
tone. Typically at least 30 single CNV trials are averaged.
Methods have been devised to determine unknown source
signals which have been transmitted through and linearly
mixed in an unknown system to produce mixed output signals
(the measured signals). The determination of these source
signals is known as blind source separation. ICA provides a
method to achieve this. Here we apply the ICA method to
The Infomax approach [5] to ICA was employed here. The
unknown mutually time independent source signals s are
linearly mixed by the mixing matrix A to produce the signals
as measured x , see Figure 1.
s1
s2
:
A
x1 W
u1
x2
u2
:
:
:
sn
xn
g(.)
:
:
un
y1=g1(u1)
y2=g2(u2)
:
:
yn=gn(un)
Figure 1: Infomax ICA algorithm
The aim is to find the unmixing matrix W  A 1 which
unmixes the x s to produce outputs u  s . The infomax
approach is to maximise the mutual information between the
inputs x and the outputs y of the nonlinear functions g( u ).
The g( u ) should be the cumulative probability density
functions of the source signals. This also minimises the mutual
information between the outputs y [6]. Further since the
mapping between the u and the y is invertible the mutual
information between the u is minimised. Thus the u
 
W  W T
1
 1  2y x T
produced by the CNV paradigm. A source signal was
considered to be part of the CNV waveform if it fulfilled two
criteria:

The signal contained little or no energy before the warning
stimulus and after the imperative stimulus
The signal consisted of a single transient peak

6
15
4
Voltage (uV)
10
Voltage (uV)
approximate the time independent source signals s according
to the accuracy of the estimated weights in W . Maximisation
of the mutual information was shown to equate to the
maximisation of the entropy of the outputs y [5]. By
maximising this entropy with respect to W an iterative
algorithm was found for calculating W in terms of the
incremental changes in the weights per iteration. This involved
matrix inversion and the convergence time was decreased by
introducing the natural gradient [7] . This algorithm applied to
super-Gaussian sources. An extended algorithm was developed
to include sub-Gaussian sources [8]. Thus for super-Gaussian
sources with N inputs and N outputs:
5
0


-2
-5
0
1
(2)
(3)
The components of the source signals measured at the
electrodes x c are given by:
x c  W 1u
2
Time (s)
3
-4
0
4
1
2
Time (s)
3
4
Figure 2: Underlying source signals
identified using ICA. Left: ERP source
signal. Right: noise source signal
applies for the extended algorithm in which the – sign is
associated with super-Gaussians and the + sign with subGaussians. The estimates of the source signals are:
u  Wx
0
(1)
for a sigmoidal nonlinearity with g (u)  (1  e u ) 1 ,
and
W  I  tanhuuT  uuT W
2
(4)
When extracting ERP components rows of u which
correspond with EEG or artefactual sources are set to zero.
METHODS
ERP data were digitally recorded (sampled at 125Hz) from a
healthy subject using a montage of 25 equally spaced scalp
recording electrodes, distributed symmetrically around the
central - midline position (Cz). Linked mastoids were used as a
reference, and two additional electrodes were positioned
around the eyes to record the EOG. Each single trial recording
started 1 second before the warning stimulus, and ended 2
seconds after the imperative stimulus, giving 4 seconds, or 500
data points for each channel. The data were pre-processed to
correct for baseline drift, and low pass filtered to remove high
frequency EEG energy.
The remaining sources consisted of EEG noise and artefacts.
For each single trial recording a small number of CNV source
signals were identified. Figure 2 shows waveforms for one
ERP source signal and one noise source signal. Denoised single
trial CNV were obtained by setting rows of the source signal
matrix that contained EEG and artefacts to zero, and
multiplying the resulting matrix by the mixing matrix (the
inverse of the unmixing matrix). The latency (relative to the
onset of the warning stimulus) and peak voltage of the
extracted CNV were analysed. The single trial CNV can be
reconstructed at any of the 25 scalp electrodes used during the
recording process. For the purposes of this study, the
waveforms obtained at the central-midline position Cz will be
used as the CNV is known to be most prominent at this point.
The matrix of unmixed source signals produced by the ICA
algorithm is ordered according to the variance in each source
signal. Due to the random nature of the noise contaminating
each trial, the ERP source signals occur on different rows of
the matrix on each trial. To enable the ERP sources to be
compared across trials, the rows of each source signal matrix
were re-ordered according to the position in time of the peak
voltage in each ERP source signal relative to the warning
stimulus. Figure 3 shows the first 5 rows of the re-ordered
source signal matrix for one single trial.
20
0
-20
20
1
3
1
3
1
3
1
3
0
The 25 scalp recordings and two EOG signals for a single trial
(the mixed signals) were presented to the ICA algorithm as an
N*M matrix where N is the number of data channels, and M is
the number of points in each channel. This gave the unmixing
matrix once the algorithm had converged. From this and the
input signals, the source signals, their components at the
electrodes, the individual ERPs at the electrodes, and the
average of the ERPs at the electrodes over all trials were
calculated.
The original ICA algorithm was used [5] because the extended
algorithm [8] resulted in incorrect ERP waveforms.
For each single trial, 27 unmixed signals were plotted and
inspected visually in order to identify those which were
-20
20
0
-20
20
0
-20
20
0
-20
0
0.5
1
Time (s)
1.5
2
Figure 3: ERP source signals for trial
1 (warning stimulus at time t=0)
Columns of each corresponding mixing matrix were similarly
re-ordered to allow comparisons across trials. The mixing
matrix for a single trial can be viewed as a set of filters through
which all of the underlying source signals for that trial are
passed to generate the measured mixed signals. One row of the
mixing matrix combines all of the source signals to produce the
measured signal at a single electrode. As the measured signal at
the Cz electrode position is of interest, analyses of the mixing
matrix have been carried out only on the corresponding row.
6
4
Voltage (uV)
2
The normalised cross-correlation coefficient at lag = 0, 12(0),
between two waveforms x1 and x2 was calculated thus:
12 ( j ) 
r12 ( j )
1  N 1 2 N 1 2 
x 2 ( n) 
 x1 (n)
N  n 0
n 0

(5)
1/ 2
0
-2
-4
-6
-8
-10
0
r12 
1
N
Figure 5: Average of extracted single
trial CNVs at Cz (solid line) & average
measured CNV at Cz (broken line).
Warning stimulus at 1s, imperative
stimulus at 2s
N 1
 x ( n) x
n 0
1
2
( n)
4
3
2
Time (s)
1
where
(6)
The cross-correlation coefficient between the extracted single
trial CNV waveforms at Cz for trial number 1 and each
subsequent trial was calculated. The cross-correlation
coefficient between the row of the mixing matrix
corresponding to the Cz electrode at trial number 1 and that of
each subsequent trial was also calculated.
The peak amplitude and latency (the time between the warning
stimulus and the peak CNV amplitude) of each extracted single
trial CNV at site Cz is shown in Figure 6. The CNV power for
each extracted single trial CNV at site Cz is shown in Figure 7.
1.1
0
1
-10
Extracted single trial CNV waveforms
0.9
Latency (s)
Peak amplitude (uV)
RESULTS
-20
-30
0.8
0.7
0.6
-40
Figure 4 shows an example set of single trial CNV waveforms
extracted using the ICA technique reconstructed at the Cz
electrode (the central-midline site).
5
10
0
0.5
-50
0
5
10
15
20
Trial number
25
30
0.4
0
5
10
15
20
Trial number
25
30
Figure 6: Voltage (upper left) and
latency relative to warning stimulus
(upper right) of extracted single trial
CNV peak at Cz
-20
-30
20
-5
15
-10
-40
-50
0
1
2
Time (s)
3
-15
0
4
1
2
Time (s)
3
4
10
5
10
5
RMS power (uV)
Voltage (uV)
Voltage (uV)
0
-10
5
0
0
Voltage (uV)
Voltage (uV)
0
-5
0
5
10
15
20
Trial number
25
30
Figure 7: RMS power of extracted
single trial CNV at Cz
-5
-10
-10
-15
-15
0
1
2
Time (s)
3
4
-20
0
1
2
Time (s)
3
4
Figure 4: Single trial CNV waveforms
at Cz. Warning stimulus at 1s,
imperative stimulus at 2s
It is seen in Figures 6 and 7 that the peak CNV amplitude,
latency and the CNV RMS power vary significantly from trial
to trial and do not appear to change systematically during the
experimental session.
Underlying source signals & mixing matrix
The accuracy of the denoised signals can be estimated by
comparing the average of the measured single trials with the
average of the denoised single trials. Results show that the
average of the denoised signals deviates little from the average
of the recorded signals for each electrode site in the region
where the ERP is located. Figure 5 shows the averaged noisy
CNV recorded at Cz and the average of the extracted single
trial CNV.
All of the recorded single trial CNVs are made up of 3 to 5
source signals. Only small variations in the shape and position
(relative to the warning stimulus) of these source signals are
observed across the trials for which 5 source signals have been
identified. In cases where there are less than 5 source signals,
the waveforms have similar shape and latency to those
observed when 5 sources are present, but one or more of the
source waveforms seen when 5 sources are present are absent.
Inspection of the denoised single trials shows significant trial
to trial variations in the measured CNV for all trials. These
variations are primarily the result of changes in the mixing
matrix for each trial, as they are not reflected in the underlying
source signals. The solid line in Figure 8 shows the correlation
between the single trial CNV at Cz extracted for trial number 1
and each subsequent trial. The broken line in Figure 7 shows
the correlation between the appropriate row of the mixing
matrix for trial number 1 and each subsequent trial.
were found to vary from trial to trial. These changes were not
reflected in the underlying source signals, which suggests that
trial to trial variations in the CNV are result of changes to the
transmission path through which the underlying source signals
propagate.
Further work is necessary to extend the findings presented here
and to apply the ICA method to a larger dataset.
REFERENCES
1
1.
Jervis, B. W., Saatchi, M. R., Allen, E. M., Hudson, N. R.,
Oke, S., and Grimsley, M., 1993, “Pilot study of
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schizophrenic, and Parkinson's disease patients using the
Contingent Negative Variation”, Medical and Biological
Engineering and Computing, 31, 31-38
2.
Saatchi, M.R., and Jervis, B. W., 1991, “PC-based
integrated system developed to diagnose specific brain
disorders”, Computing Control Engineering Journal, 2,
61-68
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Saatchi, M.R., Gibson, C., Rowe, J.W.K., and Allen, E.M.,
1997, ‘Adaptive multiresolution analysis based evoked
potential filtering’, IEE Procedings on Science &
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4.
Ferrara, E. R. and Widrow, B., 1981, “The time-sequenced
adaptive filter” IEEE Transactions ASSP, 29, 3, 776-770
5.
Bell A.J., and Sejnowski T. J., An InformationMaximisation Approach to Blind Separation and Blind
Deconvolution, Neural Computation, 7, 1129-1159, 1995.
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Nadal J.-P. and Parga N., Non linear neurons in the low
noise limit: a factorial code maximises information
transfer, Network, 5, 565-581, 1994.
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Amari S., Cichocki A., and Yang H.H., A New Learning
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Girolami M., and Fyfe C., Generalised Independent
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Correlation coefficient
0.8
0.6
0.4
0.2
0
-0.2
-0.4
0
5
10
15
20
Trial number
25
30
Figure 8. Solid line: Correlation
between extracted trial 1 and
subsequent
trials.
Broken
line:
Correlation between mixing matrix row
for trial 1 & all subsequent trials.
It is seen in Figure 8 that the correlation between the mixing
matrix row for trial 1 at Cz and the rows for subsequent trials
follows a similar pattern to the correlation between the
extracted single trial CNV waveforms.
DISCUSSION
Extracted single trial CNV
Results suggest that the signals extracted using the ICA
technique reflect the shape of the underlying single trial CNV.
The similarity between the average of the recorded (noisy)
single trials and that of the extracted single trials shows that the
extracted single trial CNVs are not systematically distorted by
the ICA method. The power, peak amplitude, and latency of
the extracted CNV waveforms vary randomly across trials.
Underlying source signals & mixing matrix
Analyses of the unmixed source signals show that the CNV is
made up of a small number of underlying sources which
remain fairly constant during the course of the CNV
experiment. Trial to trial variations in the measured signals are
primarily the result of changes in the unmixing matrix. This
suggests that trial to trial variations in the CNV are due to
changes in the transmission path through which the underlying
source signals are propagated to the scalp electrode recording
positions.
CONCLUSION
ICA offers a means to identify the source signals underlying
the CNV and extract single trial CNVs. The CNV waveforms