Independent Component Analysis 
of Electroencephalographic Data 
Scott Makeig 
Naval Health Research Center 
P.O. Box 85122 
San Diego CA 92186-5122 
scott cplmumag. nhrc. navy. mil 
Anthony J. Bell 
Computational Neurobiology Lab 
The Salk Institute, P.O. Box 85800 
San Diego, CA 92186-5800 
tonysalk. edu 
Tzyy-Ping Jung 
Naval Health Research Center and 
Computational Neurobiology Lab 
The Salk Institute, P.O. Box 85800 
San Diego, CA 92186-5800 
jungsalk. edu 
Terrence J. Sejnowski 
Howard Hughes Medical Institute and 
Computational Neurobiology Lab 
The Salk Institute, P.O. Box 85800 
San Diego, CA 92186-5800 
errysalk. edu 
Abstract 
Because of the distance between the skull and brain and their differ- 
ent resistivities, electroencephalographic (EEG) data collected from 
any point on the human scalp includes activity generated within 
a large brain area. This spatial smearing of EEG data by volume 
conduction does not involve significant time delays, however, sug- 
gesting that the Independent Component Analysis (ICA) algorithm 
of Bell and Sejnowski [1] is suitable for performing blind source sep- 
aration on EEG data. The ICA algorithm separates the problem of 
source identification from that of source localization. First results 
of applying the ICA algorithm to EEG and event-related potential 
(ERP) data collected during a sustained auditory detection task 
show: (1) ICA training is insensitive to different random seeds. (2) 
ICA may be used to segregate obvious artifactual EEG components 
(line and muscle noise, eye movements) from other sources. (3) ICA 
is capable of isolating overlapping EEG phenomena, including al- 
pha and theta bursts and spatially-separable ERP components, to 
separate ICA channels. (4) Nonstationarities in EEG and behav- 
ioral state can be tracked using ICA via changes in the amount of 
residual correlation between ICA-filtered output channels. 
146 S. MAKEIG, A. J. BELL, T.-P. JUNG, T. J. SEJNOWSKI 
I Introduction 
1.1 Separating What from Where in EEG Source Analysis 
The joint problems of EEG source segregation, identification, and localization are 
very difficult, since the problem of determining brain electrical sources from po- 
tential patterns recorded on the scalp surface is mathematically underdetermined. 
lecent efforts to identify EEG sources have focused mostly on performing spatial 
segregation and localization of source activity [4]. By applying the ICA algorithm 
of Bell and Sejnowski [1], we attempt to completely separate the twin problems of 
source identification (What) and source localization (Where). The ICA algorithm 
derives independent sources from highly correlated EEG signals statistically and 
without regard to the physical location or configuration of the source generators. 
lather than modeling the EEG as a unitary output of a multidimensional dynami- 
cal system, or as "the roar of the crowd" of independent microscopic generators, we 
suppose that the EEG is the output of a number of statistically independent but 
spatially fixed potentiM-generating systems which may either be spatiMly restricted 
or widely distributed. 
1.2 Independent Component Analysis 
Independent Component Analysis (ICA) [1, 3] is the name given to techniques for 
finding a matrix, W and a vector, w, so that the elements, u = [u...uN] r, of 
the linear transform u = Wx + w of the random vector, x = [xl ... xv] T, are sta- 
tistically independent. In contrast with decorrelation techniques such as Principal 
Components Analysis (PCA) which ensure that {uiujl = O,Vij, ICA imposes the 
much stronger criterion that the multivariate probability density function (p.d.f.) 
of u factorizes: fu(u) = I-I= f,.(ui). Finding such a factorization involves mak- 
ing the mutual information between the ui go to zero: I(ui, uj) = O, Vij. Mutual 
information is a measure which depends on all higher-order statistics of the ui while 
decorrelation only takes account of 2nd-order statistics. 
In [1], a new algorithm was proposed for carrying out ICA. The only prior assump- 
tion is that the unknown independent components, ui, each have the same form of 
cumulative density function (c.d.f.) after scaling and shifting, and that we know this 
form, call it F,(u). ICA can then be performed by maximizing the entropy, H(y), 
of a non-linearly transformed vector: y = F(u). This yields stochastic gradient 
ascent rules for adjusting W and w: 
zxw [wr] + xr, ZXw 
(1) 
where r - [1 ... N] T, the elements of which are: 
cO cOyi [which if y -- F,(u)] cOA(ui) 
i = r2yi cOui = cOF,(ui) (2) 
It can be shown that an ICA solution is a stable point of the relaxation of eqs.(1-2). 
In practical tests on separating mixed speech signals, good results were found when 
using the logistic function, Yi = (1 + e-') -x, instead of the known c.d.f., F, of 
the speech signals. In this case i = I - 2yi, and the algorithm has a simple form. 
These results were obtained despite the fact that the p.d.f. of the speech signals was 
not exactly matched by the gradient of the logistic function. In the experiments in 
this paper, we also used the speedup technique of prewhitening described in [2]. 
Independent Component Analysis of Electroencephalographic Data 14 7 
1.3 Applying ICA to EEG Data 
The ICA technique appears ideally suited for performing source separation in do- 
mains where, (1) the sources are independent, (2) the propagation delays of the 
'mixing medium' are negligible, (3) the sources are analog and have p.d.f.'s not too 
unlike the gradient of a logistic sigmoid, and (4) the number of independent signal 
sources is the same as the number of sensors, meaning if we employ N sensors, 
using the ICA algorithm we can separate N sources. In the case of EEG signals, 
N scalp electrodes pick up correlated signals and we would like to know what ef- 
fectively 'independent brain sources' generated these mixtures. If we assume that 
the complexity of EEG dynamics can be modeled, at least in part, as a collection 
of a modest number of statistically independent brain processes, the EEG source 
analysis problem satisfies ICA assumption (1). Since volume conduction in brain 
tissue is effectively instantaneous, ICA assumption (2) is also satisfied. Assumption 
(3) is plausible, but assumption (4), that the EEG is a linear mixtures of exactly N 
sources, is questionable, since we do not know the effective number of statistically 
independent brain signals contributing to the EEG recorded from the scalp. The 
foremost problem in interpreting the output of ICA is, therefore, determining the 
proper dimension of input channels, and the physiological and/or psychophysiolog- 
ical significance of the derived ICA source channels. 
Although the ICA model of the EEG ignores the known variable synchronization of 
separate EEG generators by common subcortical or corticocortical influences [5], it 
appears promising for identifying concurrent signal sources that are either situated 
too close together, or are too widely distributed to be separated by current localiza- 
tion techniques. Here, we report a first application of the ICA algorithm to analysis 
of 14-channel EEG and ERP recordings during sustained eyes-closed performance 
of an auditory detection task, and give evidence suggesting that the ICA algorithm 
may be useful for identifying psychophysiological state transitions. 
2 Methods 
EEG and behavioral data were collected to develop a method of objectively moni- 
toring the alertness of operators of complex systems [8]. Ten adult volunteers par- 
ticipated in three or more half-hour sessions, during which they pushed one button 
whenever they detected an above-threshold auditory target stimulus (a brief in- 
crease in the level of the continuously-present background noise). To maximize the 
chance of observing alertness decrements, sessions were conducted in a small, warm, 
and dimly-lit experimental chamber, and subjects were instructed to keep their eyes 
closed. Auditory targets were 350 ms increases in the intensity of a 62 dB white 
noise background, 6 dB above their threshold of detectability, presented at random 
time intervals at a mean rate of 10/min, and superimposed on a continuous 39-Hz 
click train evoking a 39-Hz steady-state response (SSR). Short, and task-irrelevant 
probe tones of two frequencies (568 and 1098 Hz) were interspersed between the 
target noise bursts at 2-4 s intervals. EEG was collected from thirteen electrodes 
located at sites of the International 10-20 System, referred to the right mastoid, at 
a sampling rate of 312.5 Hz. A bipolar diagonal electrooculogram (EOG) channel 
was also recorded for use in eye movement artifact correction and rejection. Tar- 
get Hits were defined as targets responded to within a 100-3000 ms window, while 
Lapses were targets not responded to. Two sessions each from three of the subjects 
were selected for analysis based on their containing at least 50 response Lapses. 
A continuous performance measure, local error rate, was computed by convolving 
the irregularly-sampled performance index time series (Hit=O/Lapse=l) with a 95 
s smoothing window advanced for 1.64 s steps. 
148 S. MAKEIG, A. J. BELL, T.-P. JUNG, T. J. SEJNOWSKI 
The ICA algorithm in eqs.(1-2) was applied to the 14 EEG recordings. The time 
index was permuted to ensure signal stationarity, and the 14-dimensional time point 
vectors were presented to a 14 - 14 ICA network one at a time. To speed conver- 
gence, we first pre-whitened the data to remove first- and second-order statistics. 
The learning rate was annealed from 0.03 to 0.0001 during convergence. After each 
pass through the whole training set, we checked the amount of correlation between 
the ICA output channels and the amount of change in weight matrix, and stopped 
the training procedure when, (1) the mean correlation among all channel pairs was 
below 0.05, and (2) the ICA weights had stopped changing appreciably. 
3 Results 
A small (4.5 s) portion of the resulting ICA-transformed EEG time series is shown 
in Figure 1. As expected, correlations between the ICA traces are close to zero. The 
dominant theta wave (near 7 Hz) spread across many EEG channels (left panel) is 
more or less isolated to ICA trace 1 (upper right), both in the epoch shown and 
throughout the session. Alpha activity (near 10 Hz) not obvious in the EEG data 
is uncovered in ICA trace 2, which here and throughout the session contains alpha 
bursts interspersed with quiescent periods. Other ICA traces (3-8) contain brief 
oscillatory bursts which are not easy to characterize, but clearly display different 
dynamics from the activity in ICA trace 1 which dominates the raw EEG record. 
ICA trace 10 contains near-DC changes associated with eye slow movements in the 
EOG and most frontal (Fpz) EEG channels. ICA trace 13 contains mostly line 
noise (60 Hz), while ICA traces 9 and 14 have a broader high frequency (50-100 
Hz) spectrum, suggesting that their source is likely to be high-frequency activity 
generated by scalp muscles. 
Apparently, the ICA source solution for this data does not depend strongly on 
learning rate or initial conditions. When the same portion of one session was used to 
train two ICA networks with different random starting weights, data presentation 
orders, and learning rates, the two final ICA weight matrices were very close to 
one another. Filtering another segment of EEG data from the same session using 
each ICA matrix produced two ICA source transforms in which 11 of the 14 best- 
correlated output channel pairs correlated above 0.95 and none correlated less than 
0.894. 
While ICA training minimized mutual information, and therefore also correlations 
between output channels during the initial (alert) ICA training period, output data 
channels filtered by the same ICA weight matrix became more correlated dur- 
ing the drowsy portion of the session, and then reverted to their initial levels of 
(de)correlation when the subject again became alert. Conversely, filtering the same 
session's data with an ICA weight matrix trained on the drowsy portion of the ses- 
sion produced output channels that were more correlated during the alert portions 
of the session than during the drowsy training period. Presumably, these changes 
in residual correlation among ICA outputs reflect changes in the dynamics and 
topographic structure of the EEG signals in alert and drowsy brain states. 
An important problem in human electrophysiology is to determine a means of objec- 
tively identifying overlapping ERP subcomponents. Figure 3 (right panel) shows an 
ICA decomposition of (left panel) ERPs to detected (Hit) and undetected (Lapse) 
targets by the same subject. ICA spatial filtering produces two channels (S[1-2]) 
separating out the 39-Hz steady-state response (SSR) produced by the continuous 
39-Hz click stimulation during the session. Note the stimulus-induced perturba- 
tion in SSR amplitude previously identified in [6]. Three channels (H[1-3]) pass 
time-limited components of the detected target response, while four others (L[1-4]) 
Independent Component Analysis of Electroencephalographic Data 149 
EEG 
Fz 
Cz 
Pz 
Oz 
F3 
F4 
C3 
C4 
T3 
T4 
P3 
P4 
Fpz 
EOG 
ICA 
7  
9  
10  
4 
.... 1 sec. 
Figure 1: Left: 4.5 seconds of 14-channel EEG data. Right: an ICA transform of 
the same data, using weights trained on 6.5 minutes of similar data from the same 
session. 
150 S. MAKEIG, A. J. BELL, T.-P. JUNG, T. J. SEJNOWSKI 
Scalp ERPs 
+ 
+ 
+ 
+ 
+ 
0 0.2 0.4 0.6 0.8 1 sec 
ICA ERPs 
Detected targets -.- Undetected targets 
Figure 2: Left panel: Event-related potentials (ERPs) in response to undetected 
(bold traces) and detected (faint traces) noise targets during two half-hour sessions. 
Right panel: Same ERP signals filtered using an ICA weight matrix trained on the 
ERP data. 
Independent Component Analysis of Electroencephalographic Data 151 
components of the (larger) undetected target response. We suggest these represent 
the time course of the locus (either focal or distributed) of brain response activity, 
and may represent a solution to the longstanding problem of objectively dividing 
evoked responses into neurobiologically meaningful, temporally overlapping sub- 
components. 
4 Conclusions 
ICA appears to be a promising new analysis tool for human EEG and EPP research. 
It can isolate a wide range of artifacts to a few output channels while removing them 
from remaining channels. These may in turn represent the time course of activity 
in longlasting or transient independent 'brain sources' on which the algorithm con- 
verges reliably. By incorporating higher-order statistical information, ICA avoids 
the non-uniqueness associated with decorrelating decompositions. The algorithm 
also appears to be useful for decomposing evoked response data into spatially dis- 
tinct subcomponents, while measures of nonstationarity in the ICA source solution 
may be useful for observing brain state changes. 
Acknowledgments 
This report was supported in part by a grant (ONR.leimb.30020.6429) to the Naval 
Health Research Center by the Office of Naval Research. The views expressed in 
this article are those of the authors and do not reflect the official policy or position 
of the Department of the Navy, Department of Defense, or the U.S. Government. 
Dr. Bell is supported by grants from the Office of Naval lesearch and the Howard 
Hughes Medical Institute. 
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