{"title": "Independent Component Analysis of Electroencephalographic Data", "book": "Advances in Neural Information Processing Systems", "page_first": 145, "page_last": 151, "abstract": null, "full_text": "Independent Component Analysis \nof Electroencephalographic Data \n\nScott Makeig \n\nNaval Health Research Center \n\nP.O. Box 85122 \n\nSan Diego CA 92186-5122 \n\nAnthony J. Bell \n\nComputational Neurobiology Lab \nThe Salk Institute, P.O. Box 85800 \n\nSan Diego, CA 92186-5800 \n\nscott~cplJmmag.nhrc.navy.mil \n\ntony~salk.edu \n\nTzyy-Ping Jung \n\nNaval Health Research Center and \nComputational Neurobiology Lab \nThe Salk Institute, P.O. Box 85800 \n\nSan Diego, CA 92186-5800 \n\nTerrence J. Sejnowski \n\nHoward Hughes Medical Institute and \n\nComputational Neurobiology Lab \nThe Salk Institute, P.O. Box 85800 \n\nSan Diego, CA 92186-5800 \n\njung~salk.edu \n\nterry~salk.edu \n\nAbstract \n\nBecause of the distance between the skull and brain and their differ(cid:173)\nent resistivities, electroencephalographic (EEG) data collected from \nany point on the human scalp includes activity generated within \na large brain area. This spatial smearing of EEG data by volume \nconduction does not involve significant time delays, however, sug(cid:173)\ngesting that the Independent Component Analysis (ICA) algorithm \nof Bell and Sejnowski [1] is suitable for performing blind source sep(cid:173)\naration on EEG data. The ICA algorithm separates the problem of \nsource identification from that of source localization. First results \nof applying the ICA algorithm to EEG and event-related potential \n(ERP) data collected during a sustained auditory detection task \nshow: (1) ICA training is insensitive to different random seeds. (2) \nICA may be used to segregate obvious artifactual EEG components \n(line and muscle noise, eye movements) from other sources. (3) ICA \nis capable of isolating overlapping EEG phenomena, including al(cid:173)\npha and theta bursts and spatially-separable ERP components, to \nseparate ICA channels. (4) N onstationarities in EEG and behav(cid:173)\nioral state can be tracked using ICA via changes in the amount of \nresidual correlation between ICA-filtered output channels. \n\n\f146 \n\nS. MAKEIG, A. l . BELL, T.-P. lUNG, T. l. SEJNOWSKI \n\n1 \n\nIntroduction \n\n1.1 Separating What from Where in EEG Source Analysis \n\nThe joint problems of EEG source segregation, identification, and localization are \nvery difficult, since the problem of determining brain electrical sources from po(cid:173)\ntential patterns recorded on the scalp surface is mathematically underdetermined. \nRecent efforts to identify EEG sources have focused mostly on verforming spatial \nsegregation and localization of source activity [4]. By applying the leA algorithm \nof Bell and Sejnowski [1], we attempt to completely separate the twin problems of \nsource identification (What) and source localization (Where). The leA algorithm \nderives independent sources from highly correlated EEG signals statistically and \nwithout regard to the physical location or configuration of the source generators. \nRather than modeling the EEG as a unitary output of a multidimensional dynami(cid:173)\ncal system, or as \"the roar of the crowd\" of independent microscopic generators, we \nsuppose that the EEG is the output of a number of statistically independent but \nspatially fixed potential-generating systems which may either be spatially restricted \nor widely distributed . \n\n1.2 \n\nIndependent Component Analysis \n\nIndependent Component Analysis (leA) [1, 3] is the name given to techniques for \nfinding a matrix, Wand a vector, w, so that the elements, u = (Ul .. . uNF, of \nthe linear transform u = Wx + W of the random vector, x = [Xl ... xNF, are sta(cid:173)\ntistically independent. In contrast with decorrelation techniques such as Principal \nComponents Analysis (peA) which ensure that {UiUj} = 0, Vij, ICA imposes the \nmuch stronger criterion that the multivariate probability density function (p .d.f.) \nof u factorizes: fu(u) = n::l fu.(ud . Finding such a factorization involves mak(cid:173)\ning the mutual information between the Ui go to zero: I(ui,uj) = O,Vij. Mutual \ninformation is a measure which depends on all higher-order statistics of the Ui while \ndecorrelation only takes account of 2nd-order statistics. \n\nIn (1], a new algorithm was proposed for carrying out leA. The only prior assump(cid:173)\ntion is that the unknown independent components, Ui, each have the same form of \ncumulative density function (c.d.f.) after scaling and shifting, and that we know this \nform, call it Fu(u). ICA can then be performed by maximizing the entropy, H(y), \nof a non-linearly transformed vector: y = Fu(u) . This yields stochastic gradient \nascent rules for adjusting Wand w: \n\nwhere y = (:ih ... YN F, the elements of which are: \n\n, \nYi = - - whic \n\na 0Yi (h \n0Yi OUi \n\nif y = Fu U \n\n( )] \n\n(1) \n\n(2) \n\n_ Ofu(Ui) \nOFu(Ui) \n\nIt can be shown that an leA solution is a stable point of the relaxation of eqs.(1-2) . \nIn practical tests on separating mixed speech signals, good results were found when \nusing the logistic function, Yi = (1 + e- u\u2022 )-1, instead of the known c.d.f., Fu, of \nthe speech signals. In this case Yi = 1 - 2Yi, and the algorithm has a simple form. \nThese results were obtained despite the fact that the p.d.f. of the speech signals was \nnot exactly matched by the gradient of the logistic function. In the experiments in \nthis paper, we also used the speedup technique of prewhitening described in [2] . \n\n\fIndependent Component Analysis of Electroencephalographic Data \n\n147 \n\n1.3 Applying leA to EEG Data \n\nThe leA technique appears ideally suited for performing source separation in do(cid:173)\nmains where, (1) the sources are independent, (2) the propagation delays of the \n'mixing medium' are negligible, (3) the sources are analog and have p.d.f.'s not too \nunlike the gradient of a logistic sigmoid, and (4) the number of independent signal \nsources is the same as the number of sensors, meaning if we employ N sensors, \nusing the ICA algorithm we can separate N sources. In the case of EEG signals, \nN scalp electrodes pick up correlated signals and we would like to know what ef(cid:173)\nfectively 'independent brain sources' generated these mixtures. If we assume that \nthe complexity of EEG dynamics can be modeled, at least in part, as a collection \nof a modest number of statistically independent brain processes, the EEG source \nanalysis problem satisfies leA assumption (1) . Since volume conduction in brain \ntissue is effectively instantaneous, leA assumption (2) is also satisfied. Assumption \n(3) is plausible, but assumption (4), that the EEG is a linear mixtures of exactly N \nsources, is questionable, since we do not know the effective number of statistically \nindependent brain signals contributing to the EEG recorded from the scalp. The \nforemost problem in interpreting the output of leA is, therefore, determining the \nproper dimension of input channels, and the physiological and/or psychophysiolog(cid:173)\nical significance of the derived leA source channels. \n\nAlthough the leA model of the EEG ignores the known variable synchronization of \nseparate EEG generators by common subcortical or corticocortical influences [5], it \nappears promising for identifying concurrent signal sources that are either situated \ntoo close together, or are too widely distributed to be separated by current localiza(cid:173)\ntion techniques. Here, we report a first application of the ICA algorithm to analysis \nof 14-channel EEG and ERP recordings during sustained eyes-closed performance \nof an auditory detection task, and give evidence suggesting that the leA algorithm \nmay be useful for identifying psychophysiological state transitions. \n\n2 Methods \n\nEEG and behavioral data were collected to develop a method of objectively moni(cid:173)\ntoring the alertness of operators of complex systems [8] . Ten adult volunteers par(cid:173)\nticipated in three or more half-hour sessions, during which they pushed one button \nwhenever they detected an above-threshold auditory target stimulus (a brief in(cid:173)\ncrease in the level of the continuously-present background noise). To maximize the \nchance of observing alertness decrements, sessions were conducted in a small, warm, \nand dimly-lit experimental chamber, and subjects were instructed to keep their eyes \nclosed . Auditory targets were 350 ms increases in the intensity of a 62 dB white \nnoise background, 6 dB above their threshold of detectability, presented at random \ntime intervals at a mean rate of 10/min, and superimposed on a continuous 39-Hz \nclick train evoking a 39-Hz steady-state response (SSR). Short, and task-irrelevant \nprobe tones of two frequencies (568 and 1098 Hz) were interspersed between the \ntarget noise bursts at 2-4 s intervals. EEG was collected from thirteen electrodes \nlocated at sites of the International 10-20 System, referred to the right mastoid, at \na sampling rate of 312.5 Hz. A bipolar diagonal electrooculogram (EOG) channel \nwas also recorded for use in eye movement artifact correction and rejection. Tar(cid:173)\nget Hits were defined as targets responded to within a 100-3000 ms window, while \nLapses were targets not responded to. Two sessions each from three of the subjects \nwere selected for analysis based on their containing at least 50 response Lapses. \nA continuous performance measure, local error rate, was computed by convolving \nthe irregularly-sampled performance index time series (Hit=O/Lapse=l) with a 95 \ns smoothing window advanced for 1.64 s steps. \n\n\f148 \n\nS. MAKEIG, A. l. BELL, T.-P. lUNG, T. 1. SEJNOWSKI \n\nThe leA algorithm in eqs.(1-2) was applied to the 14 EEG recordings. The time \nindex was permuted to ensure signal stationarity, and the 14-dimensional time point \nvectors were presented to a 14 ---. 14 leA network one at a time. To speed conver(cid:173)\ngence, we first pre-whitened the data to remove first- and second-order statistics. \nThe learning rate was annealed from 0.03 to 0.0001 during convergence. After each \npass through the whole training set, we checked the amount of correlation between \nthe leA output channels and the amount of change in weight matrix, and stopped \nthe training procedure when, (1) the mean correlation among all channel pairs was \nbelow 0.05, and (2) the leA weights had stopped changing appreciably. \n\n3 Results \n\nA small (4.5 s) portion of the resulting leA-transformed EEG time series is shown \nin Figure 1. As expected, correlations between the leA traces are close to zero. The \ndominant theta wave (near 7 Hz) spread across many EEG channels (left paneQ is \nmore or less isolated to leA trace 1 (upper right), both in the epoch shown and \nthroughout the session. Alpha activity (near 10 Hz) not obvious in the EEG data \nis uncovered in leA trace 2, which here and throughout the session contains alpha \nbursts interspersed with quiescent periods. Other leA traces (3-8) contain brief \noscillatory bursts which are not easy to characterize, but clearly display different \ndynamics from the activity in leA trace 1 which dominates the raw EEG record. \nICA trace 10 contains near-De changes associated with eye slow movements in the \nEOG and most frontal (Fpz) EEG channels. leA trace 13 contains mostly line \nnoise (60 Hz), while ICA traces 9 and 14 have a broader high frequency (50-100 \nHz) spectrum, suggesting that their source is likely to be high-frequency activity \ngenerated by scalp muscles. \n\nApparently, the ICA source solution for this data does not depend strongly on \nlearning rate or initial conditions. When the same portion of one session was used to \ntrain two leA networks with different random starting weights, data presentation \norders, and learning rates, the two final ICA weight matrices were very close to \none another. Filtering another segment of EEG data from the same session using \neach ICA matrix produced two ICA source transforms in which 11 of the 14 best(cid:173)\ncorrelated output channel pairs correlated above 0.95 and none correlated less than \n0.894. \n\nWhile ICA training minimized mutual information, and therefore also correlations \nbetween output channels during the initial (alert) leA training period, output data \nchannels filtered by the same leA weight matrix became more correlated dur(cid:173)\ning the drowsy portion of the session, and then reverted to their initial levels of \n(de)correlation when the subject again became alert. Conversely, filtering the same \nsession's data with an leA weight matrix trained on the drowsy portion of the ses(cid:173)\nsion produced output channels that were more correlated during the alert portions \nof the session than during the drowsy training period. Presumably, these changes \nin residual correlation among ICA outputs reflect changes in the dynamics and \ntopographic structure of the EEG signals in alert and drowsy brain states. \n\nAn important problem in human electrophysiology is to determine a means of objec(cid:173)\ntively identifying overlapping ERP subcomponents. Figure 3 (right paneQ shows an \nleA decomposition of (left paneQ ERPs to detected (Hit) and undetected (Lapse) \ntargets by the same subject. leA spatial filtering produces two channels (S[I-2]) \nseparating out the 39-Hz steady-state response (SSR) produced by the continuous \n39-Hz click stimulation during the session. Note the stimulus-induced perturba(cid:173)\ntion in SSR amplitude previously identified in \n[6] . Three channels (H[I-3]) pass \ntime-limited components of the detected target response, while four others (1[1-4]) \n\n\fIndependent Component Analysis of Electroencephalographic Data \n\nJ 49 \n\nEEG \n\nleA \n\nFz ~V~~~hI'o/A. \nCz ~~MvN'N{\\~vI*~vw~Y!\"'~.fW'Iwi'fr.\"'I \n\nT4 ~~~~ \n\n10 ~~~~~ \n\nP3 v\"V'v\"\"Nv\\~\"'-'V \n\n11 1~IVVV~\\fvv{iJYlw~~ \n\nP4 M'-VVI/<{WY'V0,Ww~ \nFpz ~\\~I\"IVlV';.~~ \nEOG~~~ \n\n12/\u00a5v\\~~ \n\n13~~~~~~~ \n\n14 ~~\\\"W!~~~~~ \n\n- - 1 sec. \n\nFigure 1: Left: 4.5 seconds of 14-channel EEG data. Right : an l e A transform of \nthe same data, using weights trained on 6.5 minutes of similar data from the same \nseSSlOn. \n\n\f150 \n\nS. MAKEIG, A. J. BELL, T.-P. JUNG, T. J. SEJNOWSKI \n\nScalp ERPs \n\nICAERPs \n\nFz ~~~~...., \n\nCz \n\npz \n\nOz \n\n+ \n;., ~~P \u2022. ..-.woiQfiS$i \n-... + \"-,;r::> Gtr~ --,.~ \n+ \n+ \n~ .,. \n+ \n\n, Q . . . \u00a2I,;;\" '''iIi 04\"'. \n\nF4 \n\nC3 \n\n+ \n\n.... '''''''S \n\nF3 ~ \"\"~~n;; \n:1 ~;f'O\"IV'~~ 'tV; \n+ \n-., ' 1;so~ ; _ \n+ \n;;., ,~, coA'C>\"\",~ .... ,W Ii ::v; \n+ \n~ 1\"\u00b7\" ,,~\"\" ~;t;!\u00a5 ;Nft~h'\" \n+ \n;'+~~t ~~~.\"w \n+ - .J \n1 c ......... r::c;.,.~4&f' ! c 44c;c;e \n\nP3 \n\nC4 \n\nT3 \n\nT4 \n\n+ \n~.\" 0\u00ab '4 ~~;. '\" \n+ \n\nP4 \n\n\u2022 j\" \"\"*+ \n\n+ \n\nFPZ~n~~~ \u2022. \nEOG;\"\"1 \n+ \no \n\n... ~ ... '1* \n0.6 \n\n:: -.........-\n\nit~ \n1 sec \n\n0.2 \n\n0.8 \n\n0.4 \n\nH2;c _'_~4W. ;11 \n\n- I \n\n+ \n\nH3 ~ \u2022 ...,p.~~ Rep ~ \nL1 -..,~. v.. ..At '~\"lf\"'o ~ \n+ \n- +~~\"4 = e . . . . . ~ \n+ \n\nL2 \n\n+ \n\nL4 \n\n+ \n\nL3 ::\"I-\u00b7~~ ~ \n-1$ f- ...... \u00b7 A.E:::::;? <:::!>

\"\" ,;I6'O'~' t'4ac*'\" , \nU3 -.... ro1~C--_ 'k . \u2022 ... -\nUS :+~[P'~Q\"\"'~ \"' ..... ~ .. _ \n\nU4 ~~ 111(ok i. tdt .. 'IWoio'\" \n\n\"M I~ C \n\n+ \n\n+ \n\n- Detected targets \n\n- Undetected targets \n\nFigure 2: Left panel: Event-related potentials (ERPs) in response to undetected \n(bold traces) and detected (faint traces) noise targets during two half-hour sessions. \nRight panel: Same ERP signals filtered using an leA weight matrix trained on the \nERP data. \n\n\fIndependent Component Analysis of Electroencephalographic Data \n\n151 \n\ncomponents of the (larger) undetected target response. We suggest these represent \nthe time course of the locus (either focal or distributed) of brain response activity, \nand may represent a solution to the longstanding problem of objectively dividing \nevoked responses into neurobiologically meaningful, temporally overlapping sub(cid:173)\ncomponents. \n\n4 Conclusions \n\nICA appears to be a promising new analysis tool for human EEG and ERP research. \nIt can isolate a wide range of artifacts to a few output channels while removing them \nfrom remaining channels. These may in turn represent the time course of activity \nin longlasting or transient independent 'brain sources' on which the algorithm con(cid:173)\nverges reliably. By incorporating higher-order statistical information, ICA avoids \nthe non-uniqueness associated with decorrelating decompositions. The algorithm \nalso appears to be useful for decomposing evoked response data into spatially dis(cid:173)\ntinct subcomponents, while measures of nonstationarity in the ICA source solution \nmay be useful for observing brain state changes. \n\nAcknowledgments \n\nThis report was supported in part by a grant (ONR.Reimb .30020.6429) to the Naval \nHealth Research Center by the Office of Naval Research. The views expressed in \nthis article are those of the authors and do not reflect the official policy or position \nof the Department of the Navy, Department of Defense, or the U.S. Government. \nDr. Bell is supported by grants from the Office of Naval Research and the Howard \nHughes Medical Institute. \n\nReferences \n\n[1] A.J. Bell & T.J. Sejnowski (1995). An information-maximization approach to \n\nblind separation and blind deconvolution, Neural Computation 7:1129-1159 . \n[2] A.J. Bell & T.J. Sejnowski (1995). Fast blind separation based on informa(cid:173)\n\ntion theory, in Proc. Intern. Symp. on Nonlinear Theory and Applications \n(NOLTA), Las Vegas, Dec. 1995. \n\n[3] P. Comon (1994) Independent component analysis, a new concept? Signal \n\nprocessing 36:287-314. \n\n[4] A.M. Dale & M.1. Sereno (1993) EEG and MEG source localization: a linear \n\napproach. J. Cogn. Neurosci. 5:162. \n\n[5] R. Galambos & S. Makeig. (1989) Dynamic changes in steady-state poten(cid:173)\n\ntials. In Erol Basar (ed.), Dynamics of Sensory and Cognitive Processing of \nthe Brain, 102-122. Berlin:Springer-Verlag. \n\n[6] S. Makeig & R. Galambos. (1989) The CERP: Event-related perturbations \nin steady-state responses. In E. Basar & T.H. Bullock (ed.), Brain Dynamics: \nProgress and Perspectives, 375-400. Berlin:Springer-Verlag. \n\n[7] T-P. Jung, S. Makeig, M. Stensmo, & T. Sejnowski. Estimating alertness from \n\nthe EEG power spectrum. Submitted for publication. \n\n[8] S. Makeig & M. Inlow (1993) Lapses in alertness: Coherence of fluctuations \nin performance and EEG spectrum. Electroencephalog. din. N europhysiolog. \n86:23-35. \n\n\f", "award": [], "sourceid": 1091, "authors": [{"given_name": "Scott", "family_name": "Makeig", "institution": null}, {"given_name": "Anthony", "family_name": "Bell", "institution": null}, {"given_name": "Tzyy-Ping", "family_name": "Jung", "institution": null}, {"given_name": "Terrence", "family_name": "Sejnowski", "institution": null}]}