Detecting Neonatal Seizures using Short Time Fourier Transform and

Frechet Distance

Aleksandar Jeremic

and Dejan Nikolic

Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON, Canada

Physical Medicine and Rehabilitation, University Childrens Hospital, Faculty of Medicine,

Keywords:

Seizure Detection, Information Fusion, Machine Learning.

Abstract:

Recently there has been an increase in the number of long-term cot-bed EEG systems being implemented in

clinical practice in order to monitor neurological development of neonatal patients. Consequently a signiﬁcant

research effort has been made in the development of automatic EEG data analysis tools including but not

limited to seizure detection as seizure frequency and/or intensity are one of the most important indicators of

brain development. In this paper we propose to evaluate time dependent power spectral density using short

time Fourier transform and using Frechet distance measure to detect presence and/or absence of seizures. We

propose to use three different distance measures as they capture different properties of the corresponding PSD

matrices. We evaluate the performance of the proposed algorithms using real data set obtained in the NICU of

the McMaster University Hospital. In order to benchmark performance of our proposed techniques we trained

and tested a support vector machine (SVM) classiﬁer.

1 INTRODUCTION

Continuous EEG monitoring and analysis remain im-

portant clinical tools in neonatal intensive care units

(NICU) for early stage evaluation / detection / diag-

nosis of various types of encephalopathies. In the re-

cent decade there has been a signiﬁcant advancement

in utilizing advanced EEG techniques for improving

outcomes for neonatal patients experiencing various

degrees of neurological developmental issues.(Faul,

2005). To this purpose long-term EEG monitoring

is being applied to cot-beds for a wider spectrum of

patients and not only to those with severe neurolog-

ical problems (Temko et al., 2015). Consequently

the amount of data being generated by such sys-

tems cannot be reviewed by experts due to the lim-

ited resources (number of personnel, time, etc.) One

of the most important and critical emergencies phe-

nomenons that is being monitored in NICUs is oc-

currence of seizures as it allows better understand-

ing of brain function in a variety of patients, from the

extremely premature newborn to the term baby with

acute injury. In addition, neonatal EEG facilitates

rapid diagnosis of seizures, identiﬁcation of epileptic

encephalopathy, and may provides useful prognostic

information.

A seizure is deﬁned clinically as a paroxysmal al-

teration in neurologic function, i.e., behavioural, mo-

tor, or autonomic function. It is a result of exces-

sive electrical discharges of neurones, which usually

develop synchronously and happen suddenly in the

central nervous system (CNS). It is critical to recog-

nize seizures in newborns, since they are usually re-

lated to other signiﬁcant illnesses. Seizures are also

an initial sign of neurological disease and a potential

cause of brain injury (Volpe, 2001). In a clinical set-

tings physicians are able to detect seizures based on

EEG data however the process may be time consum-

ing considering the number of cot-beds in regular size

NICU department. To this purpose development of

computer-aided diagnosis would be extremely bene-

ﬁcial as such system would be important from both

academic and clinical standpoint of view. From the

academic stand point automatic recording of seizures

and consequently analysis of these data would pro-

vide insight into frequency of occurrence and corre-

late it with the dynamic of neurological development.

From clinical standpoint it has been demonstrated that

the neonatal patient outcomes can be improved due to

early detection of certain encephalopathies.

In the last decade a signiﬁcant number of short-

time Fourier transform and wavelet transform tech-

342

Jeremic, A. and Nikolic, D.

Detecting Neonatal Seizures using Short Time Fourier Transform and Frechet Distance.

DOI: 10.5220/0009178703420347

In Proceedings of the 13th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2020) - Volume 4: BIOSIGNALS, pages 342-347

ISBN: 978-989-758-398-8; ISSN: 2184-4305

niques have been proposed. Wavelet transform tech-

niques commonly attempt to decompose the sig-

nal into the frequency bands of interest and thus

achieve discriminatory goals. On the other hand,

STFT attempts to analyze non-stationary properties

by analyzing various features contained in the time-

dependent power spectral density. To this purpose

several machine learning algorithms have been imple-

mented but their performance relies heavily on sig-

niﬁcant amount of data which may not be available

since the patient-to-patient variability of seizure fea-

tures is signiﬁcant. In our previous work, we pro-

posed two distributed detection algorithms for neona-

tal seizure detection using some of the commonly

used single channel seizure detection algorithms and

extended this approach to the detection of seizures us-

ing Frechet distance measure of sample EEG covari-

ances. In this paper we develop a distributed detec-

tion algorithm using a single-channel detection algo-

rithm based on short-time Fourier transform (STFT)

and three Frechet distance based detectors between

the training ensemble of STFT matrices and actual

data.

First, we present an estimator of the Frechet mean

of the power spectral density (PSD) matrix on the

manifold M using the different measures of Rie-

mannian distances. Then we introduce the Fr

echet

mean based on two Riemannian distances and dis-

cuss computational algorithms for calculating the pro-

posed distance means. In Section 3 we illustrate ap-

plicability of our results using data set of NICU pa-

tients. Finally, in Section 4 we discuss future direc-

tions.

2 SIGNAL MODEL

2.1 Short-time Fourier Transform

Let x(t) denote the uniformly sampled EEG signal,

then the discrete STFT can be written as

F {F(n,k)} =

M−1

∑

m=0

f (n − m)w(m)e

−2πmk/N

(1)

where f (n) is the EEG signal, w(m) is a support-

ing window, M is the window length, and N is the

number of samples used for calculating STFT. There-

fore this algorithm can be viewed as a continuous cal-

culation of STFT using a sliding windows and hence

contains in itself temporal variation of the EEG fre-

quency spectrum. The visual representation of matrix

F is commonly referred to as a spectrogram of the

1 2 3 4 5 6 7 8

Time

100

120

Frequency

(a) First quarter

1 2 3 4 5 6 7 8

100

120

(b) Second quarter

1 2 3 4 5 6 7 8

Time

100

120

Frequency

1 2 3 4 5 6 7 8

Time

100

120

Frequency

(d) Fourth quarter

Figure 1: PSD matrices in the presence of seizures - 1s

epoch with 25% overlap.

1 2 3 4 5 6 7 8

Time

100

120

Frequency

(a) Figure E

1 2 3 4 5 6 7 8

Time

100

120

Frequency

(b) Figure F

1 2 3 4 5 6 7 8

100

120

1 2 3 4 5 6 7 8

Time

100

120

Frequency

(d) Figure H

Figure 2: PSD matrices in the absence of seizures - 1s

epoch.

corresponding signal. In order to apply the Frechet

distance measure to the ensemble of the correspond-

ing STFT spectrograms F

we calculate the corre-

sponding power spectral density matrix given by

= F

(2)

where superscript H denotes Hermitian transpose

due to the fact that the entries of F are complex num-

bers. In Figures 1 we illustrate sliding window PSD

output of STFT for an arbitrary seizure epoch and in

Figure 2 we illustrate similar results ﬁn the absence

of seizures.

2.2 Frechet Distance

To measure the distance between two M × M covari-

ance matrices A and B on manifold of positive deﬁnite

Detecting Neonatal Seizures using Short Time Fourier Transform and Frechet Distance

343

matrices M , we consider the metrics which have been

developed to measure distance between two points on

the manifold itself.

The ﬁrst metric is obtained by measuring distance

between projections on the subspace spanned by uni-

tary matrices (Li and Wong, 2013)

(A,B) =

Trace(A) + Trace(B)− 2Trace(A

)

(3)

The second metric is obtained by measuring the

distance between their projections on the subspace

spanned by identity matrices. It has been shown (Li

and Wong, 2013) that this distance is equivalent to:

(A,B) =

Trace(A) + Trace(B)− 2Trace(A

)

(4)

Let the points A,B ∈ M and let X be a the point on

the manifold at which we construct a tangent plane ( it

is usually denoted as T

X). According to the inner-

product

A,B

= Trace(X

−1

B) the log- Rie-

mannian metric is given as (Moakher, 2005):

(A,B) =



log(A

−

)



∑

i=1

log

)

(5)

where the L

’s are the eigenvalues of the matrix

−1

B (Absil et al., 2009). (Metric d

has been de-

veloped in various ways and has, for a long time, been

used in theoretical physics).

In order to solve the corresponding minimization

problems we presented detailed computational algo-

rithms for calculating these distances in (Jahromi et

al., 2015). In all the cases certain iterative proce-

dures are necessary however we demonstrated exis-

tence of unique solutions (means) for all the proposed

distances.

2.3 Local Detectors

We then construct two separate ensembles: in the ab-

sence of seizures we calculate sequence of PSD ma-

trices F

for i = 1,..., p where p is the total num-

ber of windows for the jth EEG channel and simi-

larly, when the seizure is present we calculate F

i = 1, ... ,q where q is the total number of windows

for the jth channel and particular seizure epoch. Note

that in the preliminary approach we will use a single

channel detection system using C3 channel based on

10 − 20 system labels.

For each ensemble we then calculate the centre of

the ensemble by using a Frechet mean given as the

point which minimizes the sum of the squared dis-

tances (Barbaresco, 2008):

S|H

= argmin

S∈M

∑

i=1

,F |H

) (6)

where d(.,.) denotes the metric being used respec-

tively. Therefore the above expression can be inter-

preted as a way of calculating an averaged sample psd

matrix using a sliding window where S

represents an

i − th PSD window. Then we calculate empirical pdf

by ﬁnding by modelling the pdf as a set of radial basis

functions using

S|H

as a centre i.e.

ˆp

(d|H

) =

∑

l=1

−kd−kS k

/β

(7)

where subscript i denotes hypothesis (seizure

present or no seizure) and subscript j denotes with re-

spect to which of the three aforementioned distances

was used. Note that we obtain 6 different empirical

pdfs using two hypotheses and three distances. The

unknown coefﬁcients α

and β

are obtained by ap-

plying least squares ﬁt on the empirical counts based

on the training set (expert annotations).

The local decisions u

, n = 1,2,3 can be expressed

(

0, the nth detector favours H

1, the nth detector favours H

(8)

where ”favours” should be interpreted in the fol-

lowing way. If the prior probabilities are know pick

i so that P(H

) ˆp

(d|H

) ≥ P(H

1−i

) ˆp

(d|H

1−i

) (i.e.

maximum a posteriori detector) and if they are be-

ing treated as equally likely then pick ˆp

(d|H

) ≥

ˆp

(d|H

1−i

) (i.e. maximum likelihood detector). In

the remainder of the paper we will be using MAP de-

tector as the patients admitted to NICU have sufﬁcient

number of seizure epochs.

2.4 Distributed Detection System

Each of the metric detectors presented in the previ-

ous section can be considered as a single channel i.e.

local detector. In order to improve the overall perfor-

mance of a single detectors we propose to combine

the existing single detectors and utilize their strengths

by extending previous results on blind multichannel

information fusion (Liu et al., 2007).

Figure 3 shows the structure of a typical parallel

distributed detection system with N detectors. The

local detectors transmit local decisions u

based on

a particular metric that they are using. Obviously in

BIOSIGNALS 2020 - 13th International Conference on Bio-inspired Systems and Signal Processing

344

Local

Detector LD

Local

Detector LD

Local

Detector LD

Phenomenon

Fusion

Center

Figure 3: Parallel Distributed Detection System.

our case there are three local detectors as we are us-

ing three different metrics. All the local decisions are

then sent to the fusion centre, where the global de-

cision u

is made based on a fusion rule in order to

minimize the overall probability of error. Additional

detectors can be added into the system whenever more

information is required to make ﬁnal decision.

The local decisions u

, n = 1,2 can be expressed

(

0, the nth detector favours H

1, the nth detector favours H

(9)

where ”favours” should be interpreted in the follow-

ing way: pick i so that ˆp

(d|H

) ≥ ˆp

(d|H

1−i

After receiving the local decisions, the fusion cen-

tre makes the global decision by applying an optimal

fusion rule in order to minimize the ﬁnal error prob-

ability. The authors provided the optimality criterion

for N local detectors in the sense of minimum error

probability in (Varshney, 1986). We recall it here for

the case of N = 3.

(

1, if w

∑

n=1

> 0

0, otherwise

(10)

where,

= log





(11)

and

(

log((1 − P

)/P

), if u

= 1

log(P

/(1 − P

)), if u

= 0

(12)

The probabilities of false alarm and missed detec-

tion of the nth local detector are denoted as P

and P

respectively. The optimal fusion rule tells us that the

global decision u

is determined by the a priori prob-

ability and the detector performances, i.e., P

, P

and

Figure 4: Scatter plot of detection performance using blind

method.

Figure 5: Scatter plot of detection performance using MAP

method.

Figure 6: Scatter plot of detection performance using ML

method.

. In our previous work we considered these prob-

abilities to be unknown (Mirjalily, 2003),(Liu et al.,

2007). In the current work we assume prior probabili-

ties P(H

) and P(H

) are unknown as they can change

Detecting Neonatal Seizures using Short Time Fourier Transform and Frechet Distance

345

signiﬁcantly with time and depend on the neonate’s

state but we assume that the anomalies are estimated

from the empirical pdf distributions given in 7.

In order to make the ﬁnal decision, we need to uti-

lize the information available to us: the local binary

decisions u

. Note that in the presence of the training

set (annotations) the initial guesses for unknown pa-

rameters can be obtained from the training set but they

are non-stationary and change with time. The details

of the implementation are given in our previous work,

(Liu et al., 2014), (Jeremic and Nikolic, 2019).

3 RESULTS

We evaluate the performance of the proposed algo-

rithms on the data set consisting of preterm infants

(GA less than 32 weeks) admitted to the Neonatal In-

tensive Care Unit at McMaster Hospital. Due to phys-

ical limitations we were able to obtain prior expect

knowledge on a very limited time length and limited

set of patients. We selected only patients with seizure

epochs and obtained expert annotations on a limited

length (2 hours per patient).

For illustrational purposes in Figures 4-6 , we plot

the detection performance as a scatter diagram of win-

dows selected from testing data. Note that in the pres-

ence of motion artifacts the actual performance will

actually vary signiﬁcantly. Furthermore because the

original system design was based on no-seizures the

system was calibrated so that the probability of false

alarm is controlled. Due to motion artifacts and re-

action to pain stimuli during medical procedures in

NICU it is quite likely that local detectors will iden-

tify these manifestation in EEG as false seizure. In

Table 1 we present the results of our previously pro-

posed blind system (Jeremic and Nikolic, 2019) with-

out any training in which the detector anomalies and

priors are estimated and the local detectors are based

on (Rankine et al., 2007), (Gotman, 1997) and (Celka

and Colditz, 2002). In Tables 2 and 3 we illustrate our

two proposed algorithms with average probability of

error averaged of 1000 randomized training set runs.

As expected the proposed system performs better due

to the fact that expert annotations are available.

For comparison purposes we also implemented a

support vector machine (SVM) classiﬁer which at-

tempts to ﬁnd an optimal hyperplane in the feature

(or reduced dimension) space which minimizes over-

all probability of classiﬁcation error. To this purpose

we use PSD images and reduce their dimensional-

ity using principal component analysis (PCA) as fea-

ture reduction preprocessing technique. The overall

average accuracy of SVM was 82% for seizure-free

Table 1: Average seizure detection performance - blind.

Fused

false seizures 0.14 0.15 0.16 0.11

missed seizures 0.17 0.14 0.16 0.15

Table 2: Average seizure detection performance - training

set maximum a posteriori.

Fused

false seizures 0.07 0.09 0.12 0.05

missed seizures 0.09 0.08 0.11 0.07

Table 3: Average seizure detection performance - training

set based maximum likelihood.

Fused

false seizures 0.09 0.11 0.15 0.09

missed seizures 0.11 0.10 0.14 0.12

epochs and 78% for seizure epochs. The number of

features selected was set to 20 in order to capture 85%

of the variance (arbitrarily set). Note that the number

of features can be selected optimally and it will be

addressed in future work.

4 CONCLUSIONS

Automatic systems for seizure detection have been

subject of considerable research interest in the past.

One of main advantages lies in the fact that expert

time is potentially required only during the training

session. Furthermore, for newborn patients admitted

to NICU such systems enable continuous monitoring

of seizure events and hence can provide better insight

into neurological development. In recent years signif-

icant effort has been placed on developing systems

that predict seizures in order to potentially counter

them with appropriately generated electrical stimuli.

To this purpose in this paper we examined possibility

of detecting seizures by measuring different distances

using STFT. To achieve this goal we deﬁne local de-

tectors using empirically determined parameters and

fuse their local decisions using our previously devel-

oped information fusion algorithm for seizure detec-

tion. We demonstrated the applicability of the pro-

posed algorithms using a real data set consisting of

multiple NICU patients and expert annotations.

Our results indicate that training techniques of-

fer better performance if adequate expert annotations

are available. An effort should be placed on ex-

amining possibility of using machine learning tech-

niques which would enable efﬁcient management of

resources. Due to patient-to-patient variability we

BIOSIGNALS 2020 - 13th International Conference on Bio-inspired Systems and Signal Processing

346

expect that certain semi-supervised approach will

have to be used in order to adjust parameters of

the detection system to a particular patient as num-

ber of seizures may be insufﬁcient in the beginning

stage immediately after admission to NICU. Nonethe-

less, we expect that semi-supervised machine learning

and/or deep learning techniques could provide ade-

quate seizure detection with acceptable error levels

once the feature reduction algorithm is optimally de-

signed.

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