eindhoven university of technology master segmentation
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Eindhoven University of Technology
MASTER
Segmentation, autoregressive modelling and clustering of the EEG
Vos, A.A.
Award date:1992
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FACULTEIT DER ELEKROTECHNIEK
TECHNISCHE UNIVERSITEIT
EINDHOVEN
VAKGROEP MEDISCHE ELEKTROTECHNIEK
SEGMENTATION,AUTOREGRESSIVE MODELLING
AND CLUSTERINGOF THEEEG
by A.A. Vos
Rapport van het afstudeerwerk
uitgevoerd van juni 1991 tot en met april 1992
in opdracht van Prof. Dr. Ir. J.E.W. Beneken
onder leiding van Dr. Ir. P.J.M. Cluitmans en Ir. N.A.M. de Beer
\J ~ ~ 1\
~2..C G/-{ l{ JOi .5' )..~:3
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c-/ 6o{;2.
DE FACULTEIT DER ELEKTROTECHNIEK VAN DE TECHNISCHE
UNIVERSITEIT EINDHOVEN AANVAARDT GEEN AANSPRAKELIJK
HElD VOOR DE INHOUD VAN STAGE- EN AFSTUDEERVERSLAGEN
SAMENVATfING
Het doel van het in dit verslag beschreven onderzoek is het vinden van EEG parameters
die mogelijk correleren met diepte van anesthesie. Het werk is verricht binnen eenonderzoeksproject van de vakgroep Medische Elektotechniek aan de TechnischeUniversiteit Eindhoven dat tot doel heeft het ontwikkelen van technieken voorneurofysiologische grootheden ten behoeve van het kunnen bepalen van anesthesie diepte.
De analyse methode die hier voorgesteld is, deelt het EEG signaal eerst op in segmentenvan variabele lengte waarvan vervolgens een set parameters geextraheerd worden.
Daaropvolgend worden de verkregen parameter vectoren gegroepeerd om zo hetonderscheidend vermogen van de parameters in relatie tot diepte van anesthesie te kunnenevalueren.
Ben software pakket is ontwikkeld waarrnee methodes voor segmentatie, parameter
extractie en clustering geevalueerd kunnen worden. Een adaptief segmentatie algoritme isgefmplementeerd dat gebaseerd is op detectie van lokale maxima in een meting voor de
"mate van stationariteit" in het EEG. Een recursief algoritme is gefmplementeerd voor hetextraheren van een set autoregressie parameters uit de verkregen EEG segmenten. Hetalgoritme berekent de kleinste kwadraten oplossing voor de autoregressie coefficientengebruikmakend van een voorwaartse en terugwaartse predictie van het signaal. Naaraanleiding van een literatuuronderzoek is een sequentieel "fuzzy" cluster algoritmeaanbevolen voor het evalueren van de bruikbaarheid van autoregressie coefficienten in het
herkennen van anesthesie-niveaus.
SUMMARY
The purpose of the research described in this report is finding EEG features that have
possible correlations with anaesthetic depth. The work was carried out within a research
project of the division of Medical Electrical Engineering at the Eindhoven University of
Technology that aims at the development of techniques for neurophysiological monitoring
of anaesthetic depth.
The EEG analysis method proposed here first divides the signal into variable length
segments of which a set of features are extracted. In a subsequent phase the resulting
feature vectors are clustered in order to evaluate the discriminating power of the features
with respect to levels of anaesthesia.
A software application was developed that enables evaluation of techniques including
segmentation, feature extraction and clustering. An adaptive segmentation technique has
been implemented that is based on the detection of local maxima in a "stationarity
difference measure" with respect to the EEG signal. A recursive algorithm for extracting a
set of autoregressive coefficients from the EEG segments has been implemented. The
algorithm is based on the least squares solution for the autoregressive coefficients using
forward and backward linear prediction. From a literature study, a sequential fuzzy
clustering algorithm is recommended for evaluating the usefulness of the autoregressive
coefficients in identifying levels of anaesthesia.
TABLE OF CONTENTS
SAMENVATIING
SUMMARY
1. INTRODUCTION 6
2. STATIONARITY ASPECfS IN EEG ANALYSIS 82.1 Introduction 82.2 Theoretical basis 82.3 Fixed-length segmentation 102.4 Variable-length segmentation methods 11
2.4.1 Segmentation with a prediction error measure 112.4.2 Segmentation with autocorrelation coefficients 122.4.3 Segmentation with a growing reference window 142.4.4 Segmentation with weighted features 152.4.5 Segmentation with a local maximum difference detection 16
2.5 Proposed segmentation method 172.5.1 Segmentation criterion 172.5.2 Window technique 182.5.3 Implementation 19
3. FEATURE EXTRACTION AND SELECTION IN EEG ANALYSIS 203.1 Introduction 203.2 Sets of features applied in EEG classifications 20
3.2.1 Time domain features 203.2.2 Autocorrelation coefficients 213.2.3 Frequency domain features 213.2.4 Autoregressive coefficients 22
3.2.4.1 Yule-Walker equations 233.2.4.2 The Burg method 24
3.2.5 Autoregressive moving average modelling 253.2.6 Kalman filtering 25
3.3 Feature selection techniques 263.3.1 Statistical approach 263.3.2 Selection with expert knowledge 263.3.3 Classifier-directed feature selection 273.3.4 Featureless pattern recognition 27
3.4 Proposed feature extraction method 27
4. CLASSIFICATION 304.1 Introduction 304.2 Parametric classifiers 304.3 Nearest neighbour classifiers 304.4 Cluster seeking 31
5. DEVELOPMENT OF AN EEG ANALYSIS TOOL 335.1 Introduction 335.2 Building the EEG analysis tool 33
5.2.1 Structured design method 335.2.2 Software development 345.2.3 Program portability 34
5.3 User interface 345.4 Preprocessing 35
5.4.1 EEG data collection 355.4.2 Filtering 36
5.5 Evaluation facilities for segmentation and feature extraction 36
6. CONCLUSIONS 376.1 Literature review 376.2 Evaluation tool 376.3 Test results 386.4 Future research 38
7. REFERENCES 39
APPENDIX A. ABBREVIATIONS 44APPENDIX B. MAIN MENU LAYOUT 45APPENDIX C. TEST RESULTS 46
1. INTRODUCTION
Before 1850 the use of ether and chloroform as anaesthetics for surgical procedures wasalready recognized and applied. However, till the end of the 19th century, no specialattention was paid to monitoring a patient's vital signs. Since then, the importance of
monitoring during anaesthesia has increased with the public demand for safety and
reliability.
Anaesthesia is in fact a highly complex combination of depression of different functions ofthe nervous system [Clu90]:
- depression of motoric functions (relaxation)- depression of sensory input processing (analgesia)
- depression of autonomic reflexes such as respiratory,circulatory and gastrointestinal reflexes and
- unconsciousness (amnesia and 'hypnosis').
These are the components of anaesthesia.
Anaesthetists try to establish and maintain an adequate depression of these components,
i.e., an adequate depth of anaesthesia. Too light anaesthesia might lead to awareness orrecall of intraoperative events by the patient, but if the patient is too deeply anaesthetized,it might cause permanent physiological damage or delayed recovery.
The main approach in improving monitoring anaesthetic depth is neurophysiologicalmonitoring that is under study in the "Anaesthetic Depth" project of the division ofMedical Electrical Engineering at the Eindhoven University of Technology. Research is
carried out on the development of quantitative measurement techniques for
neurophysiological parameters. One research field within the project iselectroencephalographic (EEG) analysis. EEGs are recordings of the spontaneous electrical
activity of the human brain cortex. It is known that changes in anaesthesia can cause
variations in the EEG.
The main goal of the study reported here is finding EEG features that have possiblecorrelations with anaesthetic depth. To derive reliable and representative features from the
EEG signal, it is important to pay adequate attention to the separation and detection of
various patterns in the signal. In other words, statistical properties of EEG epochs from
which features are to be extracted, should be taken into account in order to obtain an
accurate feature estimation. In this study emphasis is given to the first two steps within theproposed analysis method, that is, dealing with the statistical variability of the EEG and
the subsequent extraction of a set of representative features.
6
From a mathematical point of view, the EEG is a random signal that is locally stationary.Stationarity implies that the mean and variance as well as all other higher-order moments
do not change with time. In feature extraction methods the signal should, at least, be
assumed to be stationary in terms of the features to be derived. This way, the features areable to describe the signal accurately under all circumstances.
In chapter two theoretical aspects as well as several applications are discussed in order to
apply an EEG analysis method that meets 'stationarity assumptions'. In chapter threeseveral feature extraction methods are discussed in order to choose features that are
representative for the EEG during anaesthesia. The final step in the EEG analysis involves
clustering of the obtained feature vectors in order to investigate the discriminating powerof the feature set in relation to anaesthetic depth. In chapter four classification rules arereviewed briefly with clustering techniques in order to recommend a cluster method. Inchapter five the development of an analysis program is explained that is intended as a toolin the research on finding a relationship between EEG properties (features) and levels of
anaesthesia that can be determined quantitatively. It should be help in evaluating the
usefulness of a set of EEG features in identifying levels of anaesthesia. A segmentation
method (for dealing with the EEG's statistical variability) and a feature extraction methodare included in the program. In the future, a cluster algorithm can be inserted. Conclusionsfrom this study are presented in the final chapter 6.
7
2. STATIONARITY ASPECTS IN EEG ANALYSIS
2.1 Introduction
To derive features that describe an EEG signal during all the significant events of a
surgical procedure under general anaesthesia, a basic assumption is that the statistical
properties of the EEG do not change with time, i.e, that the EEG is stationary. This
assumption is rarely met. For example, from the study of McEwen and Anderson [Mce75]
it can be concluded that the variability within an EEG interval considerably increaseswhen the interval length is increased from 2 to 10 s.
Considering the signal in more detail, it can be noted that the EEG is a random signal that
has amplitude values between -200 and +200 V. The frequency can vary between 0.1 and
about 60 Hz. In the signal several 'rhythms' of different frequencies can be distinguished.
Additionally, the EEG can contain several artifacts, for example paroxysmal events
[Var88], ocular movement and muscle artifacts. During anaesthesia another artifact is the
influence of the surgery room's electrical machines on the EEG.
Several attempts have been made to deal with the randomness of the EEG for extracting
representative features. There are three basic approaches. The simplest approach is to cut
the signal into consecutive epochs of fixed length and then extract time-invariant features
from each epoch. A better approach is an adaptive segmentation technique that divides the
EEG in variable-length segments in order to ensure stationarity followed by feature
extraction. A third (computer-intensive) technique for dealing with the EEG's variability
that can be mentioned, is time-varying modelling. The latter approach can be interpreted
as a feature extraction method and it will be discussed in the next chapter (section 3.2.6).
In the following sections it is attempted to review the wide range of segmentation methods
for the EEG signal in order to apply a segmentation algorithm for EEGs under anaesthesia.
First, a theoretical contemplation about stationarity with some practical problems is given.
2.2 Theoretical basis
A random signal is said to be stationary in the strict sense, if its statistics are not affected
by a shift in the time origin. This means that mean, variance and all higher-order moments
do not change with time. Signals are called to be stationary in the wide sense if the mean
s(t1) and autocorrelation function R(t1,tJ of the signal set) are time-invariant:
and
s (t1 ) = srtr = constant
8
(2.2.1)
•R( tl' t 2 ) =R( t 1-t2 , 0) =R('t) =lim 21 JS( t) s( t+'t) dt (2.2.2)
T- T -.These conditions are sufficient for ensuring stationarity in practical cases such as EEGanalysis [Mic84].
Formulas (2.2.1) and (2.2.2) yield a mathematical basis for a segmentation criterion. Inother words, if there is a 'significant difference' between two subsequent signal intervals
in terms of mean or autocorrelation function, a "non-stationarity" has taken place.
The autocorrelation function given in formula (2.2.2) is a mathematical definition. Thelimit to infinity can only be estimated, since only a finite EEG recording is available.
Hence, in practice, a short-term autocorrelation function within a time interval [tl'~] is
calculated that is an estimation of the mathematical autocorrelation:
(2.2.3)
Similarly, a short-term mean is defined as
(2.2.4)
For a sampled signal So we obtain:
(2.2.5)
(where k =O,...,M-1 and M = number of autocorrelation coefficients)
and
(2.2.6)
Because R(k) is calculated over a finite interval, the number of terms that is averaged
depends on k. If k increases, the averaging time interval decreases and thus the reliability
of the estimation. This means that the interval length must be much larger than M.
In order to define an applicable segmentation criterion, a difference measure between two
subsequent signal epochs must be defined. This means that possibly weights for the short-
9
term mean and autocorrelation coefficients must be set. At the same time, the length of the
signal interval should be long for reliable estimation of the autocorrelation coefficients,
and short for the detection of small segments. Besides, the term "a significant difference"
should be worked out in more detail.
For EEG analysis applications other signal properties are also used for obtaining a
segmentation criterion. One often defines a segmentation criterion in terms of features thatare to be derived from the EEG in the next analysis phase.
2.3 Fixed-length segmentation
Fixed length segmentation of the EEG signal is the simplest method to deal with the
signal's variability. It is assumed that, in the determination of boundary locations between
two subsequent EEG patterns, an accuracy of the order of the length of the basic interval
itself (e.g. 2 s) is sufficient. This is, at the same time, the criticism of fixed-length
segmentation. Besides, it is noted that a pattern that is longer than the basic segment
length, will be split up into several segments that probably will be assigned to the same
group in a clustering phase.
In general, a major drawback of fixed-length segmentation is that the signal's properties
are not taken into account, while changes in signal properties do not produce epochs of
equal duration. Nevertheless, fixed-length segmentation is still applied in EEG analysis
methods. However, in many applications a fast Fourier transform is used for spectral
analysis which necessitates fixed-length intervals.
The segmentation method of Ozaki and Tong [Oza75] may be considered an intermediate
method between the fixed length segmentation methods considered thus far, and the
adaptive segmentation techniques that will be reviewed in the next section. They joined
successive nonoverlapping equal-length EEG intervals until a mathematical model "didn't
fit" the next interval. The "goodness-of-fit" was tested by applying the Akaike's
information content criterion (see [Mak75]). When the model didn't fit, the procedure
started again with a model of the current interval.
10
2.4 Variable-length segmentation methods
2.4.1 Segmentation with a prediction error measure
A more elaborate approach than fixed-length segmentation was suggested by Bodenstein
and Praetorius [Bod77]. The EEG will be split up into elementary patterns. They propose
that the EEG consists of 'quasi-stationary' segments on which transients may be
superimposed. Here, 'quasi-stationary' means that a segment may be considered to have
appreciably unvarying statistical properties.
The procedure is based upon autoregressive modelling of the EEG. Autoregressive
modelling yields a linear prediction of the next sample point of the signal. Let sn· denote
the prediction value of Sn by using p previous samples:
(2.4.1)
The coefficients ak are termed prediction coefficients. The prediction error is defined as
p
en = sn-s ; = E akSn-k ' ao=lk'=O
(2.4.2)
en is interpreted as a measure for the degree of "unexpectedness" of the value sn and this is
the basis of the applied segmentation criterion.
Bodenstein estimates the autoregressive coefficients (a1, ...,ap) of a reference window that is
positioned at the beginning of a new segment (see figure 2.1). The estimated coefficient
values are obtained as a result of the minimalization of the root mean square prediction
error. Using the calculated parameters, the prediction error en is computed according to
(2.4.2). With respect to the error signal en, a difference measure is calculated between a
fixed test window and a moving test window. The difference measure includes an
amplitude measure and a frequency measure. When the difference measure exceeds a
predefined threshold, a new segment boundary is set in the middle of the (current) moving
test window.
This method of boundary placement is rather inaccurate, as it could result in an error of
up to half the width of the moving test window. Besides, the algorithm is rather
complicated, while it could be simplified by applying a difference measure directly to the
signal rather than the linear prediction error.
11
e(tJ reference windowI (parameier eSllmaUon)
--)1
eN ---- -- ---------- ---- ------- - _l!l~~I.!'jt --- --)
1 fixed tesl window moving lesl window
--)1
figure 2.1 Segmentation by computing a linear prediction error
Various system parameters must be set: the autoregressive model order, the referencewindow length, the test window length and a threshold for segmentation. It is noted that,
to a large extent, the parameters are set empirically and it is not amenable to theoretical
evaluation.
In the analysis method autoregressive coefficients are also used as features. The
segmentation method may be interpreted as a technique to obtain stationary features ratherthan stationarity in a mathematical sense.
2.4.2 Segmentation with autocorrelation coefficients
In this method the defined segmentation criterion is derived from the first autocorrelationcoefficients of EEG data within a reference and a moving window. The segmentationmethod is developed by Michael. A detailed description can be found in [Mic84]. The
method will be discussed here briefly.
The difference in power spectrum between a reference window and a moving window is
used for the segmentation criterion. A difference d is defined as:
12
(2.4.3)
where Sr(oo) and Sm(oo) denote the power spectrum of respectively a reference window and
a moving window.
According to the Wiener-Khintchine theorem, the relationship between the power spectrum
S(oo) and the autocorrelation function R('t) for a real signal can be defined as:
•S(<a» ::: ...l..JR(~) cos (<a>~) en
2n -.or in a discrete case:
Sk ::: ...l..[R(O) + 2E R(k) cos (<a>k)]2n k=l
(2.4.3) and (2.4.4) yield for the difference criterion:
(2 •4 .4)
(2.4.5)
Integration results in
(2.4.7)
The first term of (2.4.7) could be interpreted as an energy distance measure dA and the
second term as a spectral distance measure dp• A normalized total difference measure dtolal
is defined as:
(2.4.8)
Since the EEG's power spectrum is limited (to about 60 Hz), dp can be calculated by
computing the first autocorrelation coefficients. TA is an energy threshold and Tp is a
frequency threshold. The segmentation criterion could be specified in "familiar" terms, as
a percent change in amplitude, in frequency or in both. TA and Tp are determined in such
a way that when dwta' exceeds the value 1.0, a boundary is assumed to be detected. Anadditional procedure is used to determine the exact position of the boundary. Mter a
segmentation has occurred, the length and the first nine autocorrelation coefficients of the
entire segment are stored to be used during clustering. The reference window is
repositioned at the beginning of the new segment and the procedure is repeated.
13
Because of the additional boundary placement procedure, better results were obtained incomparison with the method of Bodenstein. Besides, the method of Michael is simpler,since a difference measure is derived directly from the EEG signal. However, thecorrelation between the first autocorrelation coefficients is rather strong, so that theirinformation value is rather low.
________________________~I!(ipg )s[q
1reference window
t---------'1moving window
-)t
figure 2.2 Segmentation with a fixed and a moving window
2.4.3 Segmentation with a growing reference window
Appel [App83] introduced a segmentation method in which a reference window is growingbeside a moving window (see figure 2.3). Autoregressive modelling was applied to the
time series within respectively the reference window, the moving window and the
concatenation of the two. The autoregressive coefficients and the residual prediction errorenergies were computed for each time series.
The residual prediction errors E1,s-I' ES,s+L-l and E1,s+L-l of respectively the (growing)reference window, the moving window and the concatenation of the two were used for thesegmentation criterion. The segmentation criterion d was formulated as [App83]:
d= (5+£-1) lnE(l.S+L-l) - (5-1) In(E1 • S - 1 ) - (L) In (ES•S+L-1) (2.4.9)
This was used for both segmentation and (optimum) positioning of the boundary.
Three system parameters had to be adjusted in the proposed procedure, i.e, the order of the
autoregressive model, the moving window length and the threshold for the difference
measure. Some principles for parameter settings were given, but it was noted that heuristic
14
measures had to be used also.
An important advantage of this method in comparison with the previous methods is thefact that no procedure for the exact position of the segment boundaries is necessary. Onthe other hand, the presented method is more calculation intensive. Besides, the
segmentation algorithm is developed with respect to nonstationary stochastic time series ingeneral. The autoregressive modelling as a basis for the segmentation criterion should
perhaps be reconsidered with respect to the set of features to be extracted from an EEG
signal.
reference window
s(q ~!~~~ __)
I moving window
1 s s+L-l --)t
figure 2.3 Segmentation with a growing reference window
2.4.4 Segmentation with weighted features
Bankman and Gath [Ban87] used a segmentation criterion that is clearly based on the
features to be derived. They segmented and classified the EEG during anaesthesia. From
each segment nine features were derived and classified. During the segmentation phase thefeatures were also calculated of a reference and a moving window (see figure 2.2). Therelative difference dj for each feature is estimated as:
i=1, ... ,9 (2.4.10)
where Fr,i and Fm,i denote the ith feature of the reference and the moving window
respectively. A total difference measure d is calculated as:
15
(2.4.11)
(2.4.12)
where aj is a weight for the ith feature. When the difference measure exceeds a predefinedthreshold a new reference window is positioned at the beginning of a new segment.Otherwise the moving window is shifted and the difference is calculated again. Thecoefficients aj and the segmentation threshold were determined heuristically by using
simulated signals containing different combinations of three frequency components
according to the frequency distribution of the EEG during anaesthesia.
A major drawback of this method is the great number of parameters that needs to be setheuristically. Besides, the influence of short-time nonstationarities in the EEG is not taken
into account in the simulated signals and thus in the setting of the algorithm parameters.
2.4.5 Segmentation with a local maximum difference detection
Skrylev ([Skr84] referred to by [Bar8S] and [Var88]) introduced the idea of using two
equally long consecutive moving windows (Xl and X2; see figure 2.4), instead of areference and a moving window. By computing the Fast Fourier Transform (FFT) of both
windows the difference between the power spectra Xl(w) and X2(w) is observed by thefollowing equation [Kra91]:
G =max (.,) {~[;: ::: + ~ ::n -1} (0)0)
One expects that a change in stationarity manifests itself by the local maxima of the
difference measure. Formula (2.4.12) results in one G value. When the moving windows
are shifted one sample, new spectra are calculated and a second G value is obtained, etc.
Another window is used that slides along the G values for detecting local maxima. The
length of the latter window determines the "detailedness" of the segmentation: the shorter
the window length, the more maxima will be detected.
A major benefit of this segmentation method compared with previous methods is that the
(critical) segmentation threshold is not necessary. Due to the local maximum approach, a
more or less detailed segmentation and a less critical algorithm setting are obtained. Twosystem parameters need to be set: the length of the moving windows and the length of the
"maximum detection" window.
16
moving window Xl moving window X2
811dlng8(1) - - - - - - - - - - - - - - • - - - >
1
G
1
-->t
-->t
figure 2.4 Segmentation with two moving windows and a mutual difference measure
Varri used a simpler difference measure that includes an amplitude and frequency
measure. Besides, the relationship between this difference measure and the features that
are used in his application [Var88] is also more obvious. Two more coefficients needed to
be set: an amplitude and a frequency weight.
2.5 Proposed segmentation method
2.5.1 Segmentation criterion
Gasser ([Gas83] referred to by [Gev84]) notes that the real issue is not whether the
stationarity assumption is true, but whether a stationarity criterion is adequate for a
particular application. The same EEG segment mayor may not be considered stationary
depending on the signal's features that are used to characterize the process under
investigation.
With respect to this consideration, there should be a significant relationship between the
EEG properties that are used for a segmentation criterion on one hand and the set of
features that are subsequently derived from each segment on the other hand.
17
As will be explained in the next chapter, in the application proposed in this study
autoregressive coefficients will be used as features that represent the EEG segments and
enables classification of the EEG during anaesthesia. Therefore, autoregressive coefficients
should be used as a basis for the segmentation criterion.
2.5.2 Window technique
Another point that requires attention is the way to use windows. The use of a (fixed)
reference window at the beginning of a new segment is possibly too arbitrary, as (during
segmentation) comparisons are always made with reference to the beginning of thesegment (see figure 2.5). However, the difference between the last moving test window of
a segment and the (connecting) reference window of the next segment could have been
very small.
reference window moving window [new) referencewindow
segment boundary
-)t
figure 2.5 Difference measure with a fixed reference window and a moving window. The
difference between the moving window and the latter reference window could
have been very small but it is not taken into account.
This limitation is overcome by the paired moving window technique presented by Skrylev
[Skr84]. Segment boundaries are placed where two connected windows most differ in the
sense of the segmentation criterion. As a result, no complicated procedure for segment
boundary position is necessary, but they are exactly placed at the local maxima of the
difference measure. In addition, the (critical) setting of a segmentation threshold is
omitted.
18
2.5.3 Implementation
The paired moving window technique is implemented in an evaluation tool in order to beable to get an optimum algorithm setting. According to Gasser [Gas83], a suitablesegmentation criterion should hold a detection of change in autoregressive coefficientsbetween the moving windows, since these coefficients are also used for describing the
EEG segments. The detection of a parameter change should be accounted for in onemeasurement value. The windows are to be moved one sample and the autoregressiveestimate will be repeated resulting in a second difference measure. The parameter thatneeds to be adjusted is the autoregressive model order.
The previously discussed segmentation criterion results in a computationally complex
algorithm, because after each step of one sample two autoregressive models are estimated.It is decided to start first with a simple segmentation criterion that contains an amplitude
and a frequency difference measure. The frequency difference measure contains asummation of the absolute differences in value between two consecutive samples of the(digitized) EEG. This summation can be looked upon as a parameter that is related to themean frequency of the measured signal [Var88]. The total difference measure G applied tothe signal sn is now defined as:
where L is the length of one moving window and a and b are appropriate weights for the
amplitude and frequency measure respectively.
The proposed amplitude and frequency difference measure can be interpreted as basicproperties of the signal's power spectrum. Since the power spectrum can be calculated by
using the autoregressive coefficients, the amplitude and frequency measure can also be
seen as a (strong) reduction of the information in the autoregressive coefficients.
Therefore, it is noted here that the "allowance" of this reduction must be investigated moredetailed. When it appears that the segmentation criterion contains too little information, ithas to be modified.
19
3. FEATURE EXTRACTION AND SELECTION INEEG ANALYSIS
3.1 Introduction
The purpose of feature extraction is to find a measurable quantitative relationship between
levels of anaesthesia and the EEG signal. In connection with the segmentation methods
reviewed in the previous chapter, essential information should be derived from the EEG
segments in order to classify them. Single feature methods yield the extraction of one
feature of each segment. In [Th091] single features significantly correlated with
anaesthetic depth, but both the "within-patient" and the "between-patient" variability were
great. If a multiparametric method is applied, the classification accuracy may be increased.
At least, a set of features will lead to more information about the EEG epoch in question.
One method is taking a set of features that is expected to be representative for the
particular application. Another approach is listing a lot of possible features and applying a
feature selection technique that takes a small (optimum) number of them according to
some predefined criteria. In section 3.2 feature extraction methods according to the first
method are discussed. Section 3.3 deals with feature selection techniques.
3.2 Sets of features applied in EEG classifications
3.2.1 Time domain features
In early studies time domain analysis methods were quite popular; calculations were
simple and straightforward. More advanced applicable theory, however, was not available.
Features like maximum amplitude, mean and variance could be easily calculated with the
inefficient computers of the time. In 1970, Hjorth [Hj070] defined three normalized slope
descriptors (amplitude, mean frequency and frequency range) that are later used in
combination with other features as well (see for example [Ban87] and [Var88]). It is noted
that the Hjorth parameters also partly belong to the frequency domain.
20
3.2.2 Autocorrelation coefficients
Thomsen et al. extract the first eleven autocorrelation coefficients of 2-s EEG segmentssampled at 100 Hz and filtered with a 25 Hz antialiasing filter in the studies [Th087],[Th089] and [Th091] dealing with assessment of anaesthetic depth. The final featurevector that was used for classification of the EEG segments, consisted of ten normalizedautocorrelation coefficients and the root mean square (RMS) amplitude. Normalized
autocorrelation coefficients NR(k) were calculated according to:
NR(k) = R(k)R(O)
R(k) is calculated using (2.2.5). The RMS amplitude is calculated according to:
( 3 • 2 • 1 )
RMS = cy'R{OT (c for weighted feature) (3.2.2)
The autocorrelation coefficients as final features were also used by others (see for example
[Mic84]), but their use should be thoroughly reconsidered. When the EEG is sampled at100 Hz or some higher frequency, the information value of the first autocorrelation
coefficients is rather low, since they correlate strongly. Lowering the sample frequencycould diminish the correlation, but it must be high enough to keep a precise description ofshort-time nonstationarities in the EEG signal.
3.2.3 Frequency domain features
By frequency analysis many spectral features were calculated in EEG classification
studies. For example, the power contents of EEG frequency bands (rhythms) are oftenused as EEG descriptors. A popular method to display the results of spectral analysis is to
plot the frequency spectrum as a function of time. This technique is termed as compressedspectral array (CSA). An example is presented in figure 3.1.
One method for estimating spectral features is the fast Fourier transform (FFf). Moredetails about EEG spectrum evaluation and feature extraction with FFT can be found in
[VeI91].
The alternative method to FFT is autoregressive (AR) modelling that is based on linear
prediction [Wie49]. In AR modelling a mathematical model is fitted to the signal epochs.The power spectrum can be derived from the mathematical model (see for example
[lan81D. Therefore, autoregressive modelling is known as a parametric method. In
contrast, Fourier transformation techniques are termed as nonparametric methods, since the
spectrum is determined directly from the signal. The estimation of the mathematical model
21
will be described in more detail in the next section. A major advantage of autoregressivemodelling in comparison with FFT is that the segment lengths can be flexible. Besides, itis reported that the spectral performance is also better (for more details on the comparison
of both methods see [Bar85]).
as.8
a....
..... 7
1_.8 H.,U,,: as.8
figure 3.1 Compressed spectral array representation of five EEG epochs
3.2.4 Autoregressive coefficients
In many EEG analysis studies the coefficients of the underlying mathematical model in
autoregressive modelling are used as features for classifying the EEG (see for example[Ben91], [Cer85] and [Jan81]) . These autoregressive coefficients contain all the
(statistical) information for calculating the EEG's power spectrum and computing spectralfeatures. Besides, all the coefficients take part "at the same level" and thus no appropriateweight for each coefficient is needed.
Autoregressive modelling is based on the linear prediction theory that was presented in
1949 by Wiener [Wie49]. Since then, several algorithms have been developed forautoregressive coefficient estimates. In AR modelling, a mathematical model with order p
that is fitted to each EEG segment, can be defined as
(3.2.3)
where So is the signal's amplitude at sample time n and eo is the error that is made bypredicting the current sample with a weighted linear combination of previous samples.
Applying model (3.2.3) to each EEG segment involves the computation of the coefficients
a1,...,ap• Two basic approaches for computing the autoregressive coefficients will be
22
considered here briefly.
3.2.4.1 Yule-Walker equations
The Yule-Walker technique of estimating the model coefficients is based on finding a
least-square fit of the autoregressive model to the EEG segment in question. This is
achieved by finding those coefficient values for which the squared prediction error is
minimal. (3.2.3) can be reformulated as:
p
en = sn + a1 sn-l + ••• + apsn _p = sn + E alesn - lele-l
The total squared error Ep is
Ep is minimized by setting
(3.2.4)
(3.2.5)
(3.2.6)
From (3.2.5) and (3.2.6) we obtain the set of equations:
p
E aleE Sn-leSn-i = -E SnSn-i t l~i~ple=l n n
(3.2.7)
As the autoregressive modelling is applied to EEG segments, Ep in (3.2.5) is minimized
over a finite interval, say 1 :s; n :s; N. (3.2.7) then reduces to
where
p
E alecplei = -CPOi' l~i~plc=1
N
cP lei = E Sn-leSn-in"'l
(3.2.8)
(3.2.9)
Equations (3.2.8) are known as the Yule-Walker equations [Mak75]. It is noted from
(3.2.8) and (3.2.9) that also values of the signal So with -p+1 :s; n :s; 0 are included. This,
however, doesn't make sense if the model is to be fitted to interval 1 :s; n :s; N. In EEG
applications based on solving Yule-Walker equations, it is implicitiy assumed that the data
outside the observation interval are zero. If the interval includes one long data sample,
then this "null extension" is not harmful. However, if the data consist of many short
23
intervals to be modelled and the ratio of ends to data is high, the method discussed here
may cause significant inaccuracies.
Additionally, from Jansen's study [lan81] it may be concluded that the Yule-Walker
method should not be used as it often results in unstable models.
3.2.4.2 The Burg method
The Burg technique of estimating autoregressive coefficients, always produce stable
models ([Var88] and [Jan81n. The essential point of this method is that only the datawithin the interval is used.
The prediction error value en in (3.2.4) can be interpreted as the output of filter (1,a1,...,ap)
if the data series is passed through this filter in a forward direction. The average output
power is the squared prediction error that is to be minimized. If the time series is passed
through the filter in the backward direction, a backward prediction value bn is obtained.
Under the assumption of a stationary signal interval, the average output power is the same
for both passing directions and the autoregressive coefficients could also have been
estimated by minimalization of the squared backward prediction error [Bur75].
The Burg method implies that the autoregressive coefficients are computed by applying
both a forward and backward prediction error. The "end effect problem" of the Yule
Walker approach will be avoided.
Considering time series {Sl,... ,SN} and model order p, a forward and backward prediction
error are defined as:
p p
f n = sp+n + E alcsp +n - lc = E alcsp +n - lc a o=llc=l lc-O
p P
bn = sn + E alcsn +lc = E alcsn +lc ' a o=lJc:l lc..O
(3.2.10)
(3.2.11)
with 1 s n s N-p.
To obtain estimates of the autoregressive coefficients a1,...,ap of time series {Sl,...,SN}, Burg
minimized the sum of the forward and backward prediction error energies:
(3.2.12)
A detailed description of a technique to minimize Ep in (3.2.12) is given in [Bur75].24
3.2.5 Autoregressive moving average modelling
An extension of autoregressive analysis is autoregressive moving average (ARMA)
technique. In this technique not only the signal itself is expressed as a linear combination
of its own immediate past but the error signal as well. The linear relationship of an
ARMA model of signal Sn and error en is:
(3.2.13)
Computational requirements increase because of the estimation of two sets of coefficients
even though the order (r+s) for an ARMA model is smaller than for an AR model for a
given accuracy [Bar8S]. As the stability requirements of the AR model are easily met and
coefficients are faster to calculate, AR analysis has been applied more often [Var88].
Further details on the comparison of AR and ARMA modelling can be found in [Boh73].
3.2.6 Kalman nItering
The classic linear prediction theory for stationary signals ([Wie49]) is modified by Kalman
[KaI60] so that it could also be used for nonstationary signals. The method is known as
Kalman filtering and was first introduced to nonstationary EEGs by Bohlin [Boh71].
Kalman filtering is a recursive technique ("tracking device") in which the autoregressive
model coefficients are updated continuously as a new sample becomes available. The
update is proportional to the difference between the new observation and the predicted
value given the present model coefficients. As a result, no preceding segmentation of theEEG signal is necessary, as opposed to previously (and later) described feature extractions.
The disadvantage of this method is the computational complexity, while it results in data
expansion rather than compression; with each sample new autoregressive coefficients are
calculated. An additional layer of processing should be required [lan91]; in EEG analysis
methods the estimated coefficients are averaged over fixed-length intervals (e.g. 1 s).
Besides, as the method uses past information for estimating new model coefficients, an
occurrence of a short-term nonstationarity in the signal influences the model coefficient
estimates for several seconds thereafter [lan81].
25
3.3 Feature selection techniques
The simplest solution in choosing features is to list possible features and take a small
number of them. However, usually it is better to assess the discriminating power of theselected feature somehow.
3.3.1 Statistical approach
A statistical method like principal component analysis (peA) selects those features that
maximize the amount of variance in the resulting feature vector ([Har76]). Unfortunately,
a small amount of residual variance could have been the key to distinguish some definedclasses. This drawback is even more serious if a linear transform technique is performed.A linear transform can be applied to reduce the number of final features. The variance in
some features that are unaccounted for in the transformation will be rejected. Generally,
statistical methods maximize some criteria, but the selected features may be irrelevant fordistinguishing clinical categories.
3.3.2 Selection with expert knowledge
If expert knowledge about what patterns are to be classified is available, it can be helpfulin selecting features. For example, various measures of the traditional EEG frequency
bands (delta band, theta band, alpha band and beta band; see table 3.1) have often been
used as features. However, heuristic features may be highly correlated with each other.
• lgna11 ••c
frequency........ (Hz)
8-4
delta
4 - •
theta
• - 12
alpha
12 - 31
table 3.1 Definition of BEG frequency rhythms (bands) (the applied frequency ranges canvary from one publication to another)
26
3.3.3 Classifier-directed feature selection
Another approach in feature selection is a 'closed loop' analysis in contrast with the 'open
loop' feature selection methods described above. The 'sensitivity' of the set of features
can be increased by using a classifier-directed feature extraction method. The classification
accuracy can be maximized. An often used algorithm is stepwise discriminant analysis
(SWDA). Features are selected one by one to evaluate the discriminating power and
intercorrelation of each feature [Jen77]. Methods such as SWDA that select features one at
a time have a major limitation: "the set of best features chosen one at a time is generally
not as good as the best set of features chosen in combination". This is known as the
Cover's paradox [Cov74].
As a matter of fact, this approach involves a supervised clustering technique, since the
classes are assumed to be known beforehand. In identifying levels of anaesthesia with
EEG features, however, we are interested in the usefulness of some selected features.
Therefore, the obtained feature vectors are to be grouped in an unsupervised fashion to
investigate the discriminating power of the features in relation to anaesthetic depth.
3.3.4 Featureless pattern recognition
The difficulties in choosing the best set of features have induced Gersch [Ger79] to argue
for 'featureless' pattern recognition. The difference between time series is calculated by a
Kullback-Leibler dissimilarity measure that is defined by Kullback [KuI58]. This measure
is a statistical number measure of the difference between two time series rather than a
property of an individual time series as a feature is. In an initial application a high
classification accuracy is obtained. However, it is not known whether this technique could
be useful in neurophysiological monitoring (see also [Gev80]). Also, the method has not
been reported to have been used by others.
3.4 Proposed feature extraction method
In literature, no EEG features are found that exceptionally well correlate with anaesthetic
depth. In many studies investigated EEG features show correlations with changes in
anaesthesia in initial applications, however, general applicable conclusions have not been
drawn yet. This can be partly motivated by the fact that a complete understanding of the
EEG generating mechanism and an explicit definition of "anaesthetic depth" is lacking.
With respect to these considerations, it is decided to describe the EEG, in a first
application, as accurately as possible under all circumstances during anaesthesia in order
to lose as little information as possible before classification. Later, redundant features
27
could be removed and possibly substituted for other features.
Since autoregressive coefficients are a basis for the calculation of the power spectrum andextraction of (spectral) features, they can be a good candidate for describing the EEGsignal in a general way. As can be concluded from section 3.2.4, the Burg method isclearly more accurate than the Yule-Walker approach for estimating autoregressive
coefficients. Besides, the Yule-Walker estimate is even not allowed to be used, since dataoutside an EEG segment are needed. In feature extraction studies, one aims at a
description of the data within the segments.
Marple [Mar80] developed a computationally efficient recursive algorithm that computesthe autoregressive coefficients according to the Burg method. The algorithm aims at theleast squares solution of the prediction error energy defined by Burg. The algorithm willbe outlined briefly.
The prediction error energy is minimized by setting its derivatives with respect to theautoregressive coefficients to zero. Substituting the forward and backward linear prediction
errors, one obtains (using (3.2.10) and (3.2.11» the set of equations:
(3.4.1)
where
N-p
r(i,j) = L (Sk+P-iSk+P-j + Sk+iSk+i)k"'l
The minimum prediction error energy Ep can be found to be
Expressions (3.4.1) and (3.4.3) can be combined in a matrix form as
(3.4.2)
(3.4.3)
r(O,O)
r (p, 0)
• r(O,p) 1a 1
. r (p,p) ap
28
=
o
(3.4.4)
The matrix in (3.4.4) may be decomposed into products of Toeplitz matrices!:
(3.4.5)
Matrix T is an (N-p)x(p+l) Toeplitz matrix of data samples,
8 p +1 8 p 8 1
8 p +2 8p +1 . . 8 2
T= (3.4.6)
8 N 8 N- 1 . 8 N-P
T denotes the transposed matrix of T. T denotes the reversed matrix of T:
8 1 8 2 8p +1
8 2 8 3 . . 8p +2
T I = (3.4.7)
8 N-P 8 N-P +1 . . 8 N
It is this special structure that allows a computationally efficient recursive algorithm to be
generated. Further details on the development of the algorithm can be found in [Mar80].
The autoregressive algorithm is implemented in a software tool in order to investigate its
usefulness in EEG analysis for identifying levels of anaesthesia. The development of the
software tool will be described in chapter five in more detail.
lA Toeplitz matrix is symmetric and the elements along anydiagonal are identical
29
4. CLASSIFICATION
4.1 Introduction
When feature vectors of EEG segments have been calculated, the discriminating power ofthe features has to be investigated. The vectors will be clustered according to some
classification rule. In this chapter classification rules with clustering techniques arereviewed briefly in order to implement (in future) a suitable clustering algorithm withinthe analysis tool.
4.2 Parametric classifiers
The Bayes' classifier is a statistical method in which the probability of a pattern (featurevector) belonging to a class Q is calculated. Misclassification is minimized in a statistical
sense. For more details see [Tou74].
Yunck discussed in [Yun80] classifiers based on the probability density functions fromeach class. These classifiers were significantly less effective than classifiers based on
nearest neighbour rules that will be discussed in section 4.3.
Another point of view is considering the EEG as a finite number of recurrent states.Changing from one state to another is associated with transition probabilities. A transition
probability model is indicated as a Markov model. The Markov model could be used for
estimating parameters in the Bayes' classifier or in rule-based automatic scoring systems.For more details see [Kem87].
4.3 Nearest neighbour classifiers
Varri [Var88] pointed out that the nonparametric 'k-nearest neighbour density' estimation
('k-NN' rule) is one of the most effective classifiers. k nearest distances are calculated ofeach cluster to the feature vector to be classified. The feature vector is classified to the
cluster with a majority of shortest distances. In case of a tie the choice is made randomly.
Yunk [Yun80] discussed classifiers based on the k-NN rule. Best results were obtainedwith a classifier in which statistical properties of the classes are included in the distance
measure. For each class Wi a covariance matrix ~ is calculated. ~ is defined as
(4.3.1)
Ej {.} denotes the expectation operator over the vectors x in class Wi and m j denotes the
30
mean vector of class wj and is defined as
(4.3.2)
The applied difference measure of the mean vector mj of class wj to vector a to beclassified is now defined as
(4.3.3)
Equation (4.3.3) is also known as the Mahalanobis distance measure and is a general formof the well-known Euclidean distance measure. The resulting classifier is a combination ofa parametric (statistical) classifier and a nearest neighbour classifier.
4.4 Cluster seeking
The aim of clustering is to investigate the discriminating power of the calculated EEG
features with respect to changes in anaesthesia. In EEG analysis studies dealing withassessment of anaesthetic depth, two basically different techniques are applied in obtaining
a grouping of feature vectors: hierarchical clustering and sequential fuzzy clustering. Sinceclusters are not known beforehand, these techniques are said to be "unsupervised".
In hierarchical clustering one merges the two nearest clusters by applying a distancemeasure. Merging is done step by step starting with the initial number of clusters andending with the number of clusters that is preferred in the particular study. The distance
measure that is applied, could be an Euclidean distance or a Mahalanobis distance. The
weakness of hierarchical clustering is the fact that, when two clusters are merged, they are
joined permanently and are a basis for later merges.
In sequential fuzzy clustering the feature vector can belong with "different degrees of
membership" to two or more clusters at the same time. Therefore, the position of the
vector in the feature space is determined more accurately than "rounding" it to the nearest
cluster. Besides, cluster centroids are updated continuously.
At the start, the first feature vector becomes the centroid of the first cluster. When the
distance of the second vector to the first one exceeds a predefined threshold, it becomes
the centroid of a second cluster. Otherwise, the centroid of the first cluster is updated as
the average of both vectors. This procedure repeats, however, when two or more clusters
have been created, a degree of membership of a new vector in each cluster is calculated
according to [Ban87]:
31
(4.4.1)
where dj is a (metric) distance measure (e.g. Euclidean distance measure) of the vector tothe centroid of cluster i, and n is the number of clusters at that moment. With each new
vector all centroids are updated taking the degree of membership into account.
Sequential fuzzy clustering enables the visualization of both "area's with many vectors"
and "outliers" in the feature space. Area's with many vectors will result in "heavy"clusters, while outliers result in single vector clusters. The preset clustering thresholdcontrols the number of final clusters and the cluster sizes: the lower the threshold, themore clusters will be formed with, generally, fewer vectors in each of them.
It appears that sequential fuzzy clustering imposes less strict "constraints" on vectorclustering than hierarchical clustering does and therefore it may be a better clusteringtechnique to start with. More details on the use of a sequential fuzzy clustering algorithm
can be found in [Ban8?] and [Gat80].
The two reviewed clustering techniques could be used to obtain a "natural" grouping ofthe feature vectors during a so-called "training" or "learning" phase of the EEG
classification. When some useful clusters have been found and new data is to be classifiedto those clusters, a classifier has to be defined. This is termed a test phase. At themoment, it is only desired to detect dissimilarities (learning phase) between feature vectorsobtained from the EEG during different stages of anaesthesia.
Besides, it is noted that neural networks become rather popular in pattern classification.They can be used for (unsupervised) clustering (Le., the training phase) and developing a
classifier for a subsequent test phase. Some neural network properties are: robustness, high
computation rates and the capability of adapting classification rules during a test phase dueto current input data. Lippmann reviewed many different adaptive classifiers that are basedon neural networks. More details on using neural networks in pattern classification can be
found in [Lip8?] and [Lip89]. They are beyond the scope of this report.
32
5. DEVELOPMENT OF AN EEG ANALYSIS TOOL
5.1 Introduction
The purpose of the analysis program is to enable research on the usefulness of a (new) set
of EEG features in identifying levels of anaesthesia. The application is meant to evaluate
the EEG segmentation, feature extraction and clustering. Researchers should be enabled toevaluate each part easily. Therefore, parameter settings can be adjusted and evaluated.
EEG analysis methods are partly developed using empirical research. It is probable that afuture user wants to adjust a particular analysis method or even substitute it for analternative method. The analysis tool should be built up conveniently so that all parts ofthe program can be modified or substituted without too much effort.
In first instance, the evaluation will be done by analyzing recorded EEGs. The applicationyields an off line EEG processing that is split up into two parts. First, segmentation and
subsequent feature extraction are to be carried out. Processing is done directly on the timesignal. Calculation results are written to a file. Secondly, a clustering technique can be
applied to the stored results. A general structure of the software tool is implemented in
which the aforementioned segmentation method and feature extraction are included. Infuture, a clustering algorithm can be inserted.
In the next sections the development of the EEG analysis tool is outlined briefly. A
detailed program description is in a separate text available at EH 3.03.
5.2 Building the EEG analysis tool
5.2.1 Structured design method
Easy adaptation possibilities can be provided by a "top-down structured design" of the
analysis tool (see [Som86]). This implies that the system is designed from a functional
point of view. At first, a main function is defined. Then, the main function is refined into
smaller functions resulting in a more detailed design, etc. This technique is applied to the
EEG analysis tool.
33
5.2.2 Software development
The software is developed according to the design concept (described above) in a topdown fashion. The top (first) level of the proposed design is worked out while the second
level is represented by empty blocks. The second level is then worked out by filling theempty blocks. This results in new empty blocks, representing the third level, etc.
H the lowest level has been worked out, functions that belong together to some extent
(level or task), are grouped together in a separate source file. For example, a file is createdthat takes care of the preprocessing of the EEG recordings.
A small task that is to be executed at several places in the program (for example, getting a
filename) is implemented at one place in a separate function. This results in "standardized"library files containing basic functions for the analysis tool. In addition, no "hard code"filenames or constants are used, since they may need alteration in future. Such identifiersare to be grouped together, where a future user can easily modify them.
Due to flexible and efficient memory management, memory for data arrays that are neededduring processing and that have a length, unknown beforehand, can be dynamically
allocated. Static memory allocation would result in data structures that are partly not inuse. Especially if data arrays become rather large, one should use the limited amount ofmemory efficiently. On the other hand, a clear program structure is greatly desired so that
sometimes a static memory allocation is more convenient.
5.2.3 Program portability
The last couple of years, all software implementations that are developed within the
Anaesthetic Depth project have been made in the programming language "C". The analysisprogram proposed here is also implemented in "C", as it could be combined conveniently
with previously or (future) developed programs. Besides, the ANSI standard for the "C"
programming language is applied as well as possible and a separate (external) graphicslibrary ([Med88a] and [Med88b]) is used for operating the monitor display.
5.3 User interface
Menus were made for entering application facilities and easy adjustment of parameter
settings. As the EEG processing is divided into two separate parts a main menu was made
for choosing. The main menu also provides the entrance to a help function that may be
developed in future due to complexity increase. The main menu layout is given in
appendix B.
34
If the first part is entered (time data processing) a subsequent menu provides the entrance
to two edit menus and a procedure for starting the EEG analysis. The edit menus provides
facilities for adjusting preprocessing and calculation settings respectively. The following
parameters are categorized as preprocessing settings: the sampling frequency, the
maximum EEG frequency and FIR filtering (yes/no; for further details see section 5.4.2).
In the second edit menu parameters can be adjusted that are inherent to the applied
segmentation method and feature extraction. At the moment, it consists of the lengths of
the moving windows and the difference window, weights for both the amplitude measure
and frequency and the order of the autoregressive modelling.
The latter set of parameters is crucial in the evaluation of the applied methods and will be
adjusted many times in order to obtain an optimum algorithm adjustment. Due to the
probably intensively repeated adjusting of the calculation settings the user is enabled to
save the settings, as he does not want to adjust the settings all over again at a next start.
5.4 Preprocessing
5.4.1 EEG data collection
The available EEG data within the Anaesthetic Depth project was acquired in clinical
sessions performed for auditory evoked potential (AEP) studies. AEP analysis is another
field of interest within the project; the influence of anaesthetics on AEPs is studied.
Evoked potential studies yield the recording of a patient's EEG while a sensory organ is
stimulated.
A sampling frequency of 5 kHz was used to record the stimulus evoked responses (see
[Clu90]). The EEG analysis tool proposed here is intended to evaluate analysis techniques
with respect to the raw EEG. Hence, we are only interested in the range 0 to about 100
Hz of the recording and a low pass filtering algorithm is necessary that will be explained
in the next section.
Measurements of different levels of anaesthesia sometimes required different settings for
the calibration and offset values. It implies a multiplication factor and deviation on zero
input that is used for calibration of the samples to proper units in micro-Volts. For this, a
record was kept for the calibration and offset values of each measurement.
35
5.4.2 Filtering
Since we want to analyze the raw EEG, only the frequency range from 0 to about 60 Hzis interesting. In other words, we would like to lower the sampling rate to an artificialsampling rate that is twice (or slightly more) the maximum significant EEG frequency(that is adjustable in the analysis tool, see section 5.3). As it is explained in [VeI91], dueto aliasing the high frequency components occurring in the stimulus evoked responses caninfluence the signal below a reduced sampling rate. Hence, before the sampling frequencyis lowered, the frequency components above the maximum significant EEG frequencyshould be removed from the data. For this, a finite impulse response (FIR) filter technique
is used. The filter that is applied, "smooths" the signal. The filter is defined by:
L
I = 1 r sn 2£+1 LJ n+k
k=-L
(5 • 1 )
in which sn is the input signal and rn is the output signal. The values rn represent theaverage value of sn around sample n. A detailed description of the applied FIR filteringalgorithm can be found in [VeI91].
5.5 Evaluation facilities for segmentation and feature extraction
As described previously, the analysis tool is intended for evaluating the applied EEGanalysis methods. Plotting the time signal and detected segment boundaries on a display
can be a help for evaluating the calculation settings of the segmentation algorithm (seealso appendix C).
Therefore the major part of the display area (a monitor screen) is reserved for the timedata of the EEG channels. The evoked potential system stores 2 channels of EEG so that
usually 2 channels will be analyzed and displayed. However, the number of channels to be
analyzed and displayed can be set by the user. The display area reserved for time data isautomatically divided with respect to the number of channels to be displayed.
Additionally, the number of seconds to be plotted on one screen can be set by the user.
The settings of the algorithms are stored in the header of the file in which the processingresults will be stored. This "result" file can be used as a primary source in the clustering
phase.
36
6. CONCLUSIONS
6.1 Literature review
The purpose of the study described in this report is to extract features from the EEG that
may significantly correlate with anaesthetic depth. On the basis of the reviewed literature,autoregressive coefficients are proposed as a set of features for describing the EEG duringsurgical intervention.
Theoretically, in autoregressive modelling it is assumed that the EEG signal is stationary.To meet this stationarity assumption an adaptive segmentation method is applied to thesignal. The method is based on the detection of local maxima of measures of difference
between two equally long consecutive windows sliding along the signal. The difference
measure consists of an amplitude and frequency measure.
The final step in the EEG analysis is a clustering phase by which the discriminating power
of the set of features in identifying levels of anaesthesia can be investigated. Based onfindings in the literature, a sequential fuzzy clustering algorithm is recommended, as no"crisp" assumptions are made with respect to the clusters that will be created. Therefore, itis probably the most suitable method to start with.
At the moment, an evaluation tool is developed in which the segmentation method and
autoregressive modelling are inserted.
6.2 Evaluation tool
The evaluation tool can be used for investigating the usefulness of the proposed analysismethods in identifying levels of anaesthesia.
The EEG analysis methods are partly based on empirical research and the algorithms need
some parameters to be set. Therefore, a menu structure was chosen for easy adjustment ofparameters. Evaluation of specific parameter settings is provided with a monitor display.
A hierarchical tool design is applied so that a well-structured program is obtained in whicha particular algorithm can be modified or substituted easily.
37
6.3 Test results
A few tests on the implemented segmentation algorithm have been carried out that will bedescribed here briefly.
With the segmentation algorithm the "detailedness" of the segmentation can be controlled.
If the length of the window is decreased that is used for detecting local maxima in
measures of difference between two consecutive windows sliding along the EEG, more
maxima (i.e., boundaries) will be detected. An example of this is explained in appendix C.
In addition, if the length of the two abovementioned consecutive windows is decreased, it
means that a measure of difference is based on fewer EEG samples and short-term
nonstationarities in the EEG will be less "smeared out". In appendix C it can be seen that
such a decrease also results in a more detailed segmentation. However, in general, the
boundaries don't coincide with previous ones.
When a more detailed segmentation is desired (e.g. due to an increase of the
autoregressive model order in the feature extraction phase) the length of the "maximum
detection" window must be set smaller. To obtain a reliable difference measure, the
length of the two consecutive moving windows must be taken long enough.
6.4 Future research
The program intended here is meant as a beginning of a more general analysis tool in
which several EEG analysis methods can be evaluated in relation to anaesthesia. To givedirection to this development, some extensions to consider could be:
the implementation of the proposed sequential fuzzy clustering algorithm. The
user-entrance to the clustering phase has already been provided in the program
structure. An important aspect to think about is the evaluation for the cluster
method.
the display of 'characteristic' calculation results. The values can now only be
reviewed in a result file. In particular, the autoregressive coefficients or prediction
errors could be displayed in order to obtain a better evaluation of the accuracy of
the autoregressive modelling.
adding (or substituting) other EEG properties to the feature vector. However, this
becomes only interesting when the segmentation method and the autoregressive
coefficients are thoroughly evaluated.
38
7. REFERENCES
[App83]
[Ban87]
[Bar85]
[Ben91]
[Bod77]
[Boh71]
[Boh73]
[Bur75]
[Cer85]
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v
APPENDIX A. ABBREVIATIONS
AEPANSI
ARARMA
CSAEEG
FFfFIRpeA
RMS
auditory evoked potential
American National Standards Institute
autoregressive
autoregressive moving average
complex spectral array
electroencephalogram
fast Fourier transform
finite impulse response
principal component analysis
root mean square
44
APPENDIX B. MAIN MENU LAYOUT
EEGRNAL: softMare tool far Ilg analysis
+ Plot Datil (1)
Plot Cluster results (2)
Help (3)
Quit (4)
45
APPENDIX C. TEST RESULTS
In the next three pages a 5-s EEG epoch is plotted with different settings in the
segmentation algorithm. The parameters that are varied are the length of the twoconnected windows that slide along the EEG signal and the length of the "maximumdetection" window. The parameter values that are used, are given in table c.l.
page moving window maximum detection window
upper 40 30middle 150 30lowest 150 100
Table c.l. Parameter values2 that are used in the following pages. The settings are givenin number of samples.
From the middle and the lowest page, it can be concluded that extra boundaries are
detected when local maxima of difference measures are searched for with a smallerwindow. From the upper page, it can be noted that boundaries are located at other
positions, since other difference values have been obtained. Besides, a decrease of the
length of the connected moving windows results in a more detailed segmentation.
2The sample frequency is taken 100 Hz.
46
autoregressive modelling and clustering of
the EEG." (by A.A. Vas)
autoregressive modelling and clustering of
the EEG." (by A.A. Vos)
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