Correlating EEG Signals and Electrode Locations by Means of

Multidimensional Scaling

Luc

ıa Rodr

ıguez-Giraldo and Juan P. Ugarte

Grupo de Investigaci

on en Modelamiento y Simulaci

on Computacional - GIMSC, Universidad de San Buenaventura,

Keywords:

Multichannel EEG, Dimensional Reduction, Procrustes Algorithm.

Abstract:

The adoption of physiological data, such as electroencephalograms (EEG), is undergoing a growing interest in

addressing the characterization of human emotions. However, the setup of recording electrodes that allows a

proper study of emotions remains to be determined. This work proposes a method for processing multichannel

EEG signals by means of multidimensional scaling (MDS), looking for patterns related to the electrodes spatial

setup. We analyze the SEED-IV database consisting of 1080 trials, each one having 62 simultaneous EEG

recorded during four different emotions induction. A low dimensional representation of each set of 62 EEG

signals is obtained through the MDS algorithm. The resulting MDS maps evinced a pattern of points that

is correlated with the recording electrodes sites in 68% of the trials from SEED-IV database. Among these

trials, those recorded during the neutral emotion induction are slightly prevalent than the remaining emotions.

Furthermore, it was determined that the electrodes spatial distribution can be successfully recovered through

the MDS analysis with an EEG minimum duration of 45 s. These results suggest that the proposed analysis

based on the MDS algorithm shed some light upon the information content of simultaneous EEG signals and

its correlation with the underlying cerebral structures.

1 INTRODUCTION

Emotions are biological states that are reﬂected in

neuropsychological changes and affect human behav-

ior. Distinct mental illnesses and neuropsychiatric

disorders, such as depression and autism, are related

to emotional states (Jia et al., 2020).

The adoption of physiological electroencephalo-

grams (EEG) has recently received special attention

for tackling the study of emotions. The EEG sig-

nals represent the dynamics of voltage potential, orig-

inated from the electrical activity of neurons. Cur-

rent technology enables the simultaneous recording

of multiple EEG by deploying a set of electrodes on

the scalp with high temporal resolution (Doma and

Pirouz, 2020). The spatial distribution of the record-

ing sites obeys to correlations with underlying cere-

bral structures. Accordingly, electrodes placement

is deﬁned by standards, such as the 10-20 or 10-10

systems, looking for consistency across multicentric

experiments. The resulting spatial resolution can be

deﬁned in terms of the number of electrodes of the

recording setup. In the case of emotions assessment,

https://orcid.org/0000-0001-8008-3528

establishing the EEG recording sites that provide rel-

evant information remains as an open question. In

addition, the number of electrodes used for effec-

tive characterization of human emotions varies among

studies. A recent review article found that, in the last

12 years, more than the 60% of the reviewed papers

processed 32 or more simultaneous EEG signals, al-

though the trend aims to reduce the number of record-

ing electrodes (Rahman et al., 2021). On this regard,

traditional EEG processing schemes secure a ﬁxed set

of recording sites for all assessed subjects. However,

the complexity of the human brain behavior and in-

ter subject variability often leads to variations in the

subset of electrodes that provide useful information

(Gannouni et al., 2021; Ozel and Akan, 2021). For

instance, an initial step for addressing this problem

would be evaluating the correlation of the recorded

EEG and the underlying brain region.

Bearing these ideas in mind, this paper proposes

a strategy for processing multichannel EEG signals

by means of multidimensional scaling (MDS). The

MDS algorithm reduces the dimensionality of a set

of objects by preserving the distances between pair of

objects. Thus, the MDS analysis is used to obtain a

Rodríguez-Giraldo, L. and Ugarte, J.

Correlating EEG Signals and Electrode Locations by Means of Multidimensional Scaling.

DOI: 10.5220/0011750200003414

In Proceedings of the 16th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2023) - Volume 4: BIOSIGNALS, pages 309-316

ISBN: 978-989-758-631-6; ISSN: 2184-4305

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

309

low dimensionally representation of the set of simul-

taneously recorded EEG signals. For this purpose, the

SEED-IV database of multichannel EEG signals cap-

tured during emotions induction is used. The MDS

maps are analyzed looking for patterns related to the

electrodes spatial setup. In this line of thought, this

paper is organized as follows. Section 2 describes the

SEED-IV database, the preprocessing stage and the

mathematical tools. Section 3 presents and discusses

the MDS results. Finally, the conclusions of the work

are summarized in section 4.

2 METHODOLOGY

2.1 SEED-IV Database

The SEED-IV (Zheng et al., 2019) is a subset of the

SEED database that includes EEG signals from a to-

tal of 15 healthy, right-handed participants, aged 20

to 24 years. The signals were recorded during a trial

where a subject watched a ﬁlm clip with high emo-

tional content. The clips were chosen in order to ob-

tain 4 target emotion categories: happy, sad, fear and

neutral emotions. A total of 72 ﬁlm clips were split

into 3 different sessions. Each session consisted of 24

trials (6 per emotion) and each session was performed

on a different day. Each subject was evaluated in all 3

sessions and a total of 1080 recordings were obtained.

The ESI NeuroScan system was used to capture sig-

nals from 62 channels. The raw EEG data signals in

the database have a sampling frequency of 200 Hz and

varying recording duration. The database characteris-

tics are shown in Table 1.

Table 1: Characteristics of SEED-IV dataset.

No. of participants 15

Gender Female (8), Male (7)

Age range 20 - 24 years

Device ESI NeuroScan system

Sample rate 200 Hz

Acquisition method

International 10-10 system,

62 channels

Target emotions Happy, sad, fear and neutral

No. of sessions 3

No. of trials per session 24

No. of trials per emotion 270

No. of records 1080

Signals duration range 43 - 260 s

The 62 simultaneously recorded channels are spa-

tially arranged according to the international 10-10

system as depicted in Figure 1. The lobes underly-

ing the electrodes are FP (Frontopolar), AF (Anterior

Frontal), F (Frontal), FC (Frontal Central), C (Cen-

tral), CP (Central Parietal), P (Parietal), PO (Parietal

Occipital), O (Occipital), T (Temporal) and Z (Mid-

line). Odd and even numbers refer to the left and right

hemisphere, respectively. A color code was deﬁned to

distinguish between recording electrodes by the un-

derlying lobes, namely, {FP+AF, F, FC, C, CP, P, PO,

CB+O, FT+T+TP, midline}.

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Figure 1: Electrode placement according to international

10-10 system.

2.2 Preprocessing and Mathematical

Tools

Let x

′

i,c

[n] be a discrete EEG raw signal, where

i = 1, . . . ,1080 corresponds to the i-th trial of the

database, c = 1, . . . , 62 represents the c-th channel per

trial and n = 1, . . . , N stands for the discrete samples

of the signal x

′

i,c

. The raw EEG data are normalized

using the following equation:

i,c

[n] =

′

i,c

[n] − µ

i,c

, (1)

where x

i,c

[n] is the normalized signal, µ

i,c

and σ

i,c

are

the arithmetic mean and standard deviation of x

i,c

[n],

respectively. The i-th trial can be represented by a

62 × N dimensional matrix, where N is the number of

samples of x

i,c

2.2.1 Multidimensional Scaling (MDS)

The MDS technique is used as an exploratory data

analysis by mapping objects from a high dimensional

space, in this case, signals, into a low dimensional

space while preserving the distances between all pairs

of objects (Torgerson, 1952). The MDS algorithm

estimates the coordinates of a M-dimensional space

so that, the distances between pair of objects remain

equal to those distances measured at a N-dimensional

space, where M < N. Thus, for the i-th trial, a 62-

square symmetric matrix D

, p, q ∈ {1, 2, ..., 62}

BIOSIGNALS 2023 - 16th International Conference on Bio-inspired Systems and Signal Processing

310

is calculated, whose elements correspond to the dis-

tances between x

i,p

and x

i,q

. The matrix D

is used

as input to the stress function S (Xu et al., 2004), de-

ﬁned as follows:

S =

∑



− D



∑





, p ̸= q , (2)

where

are the predicted Euclidean distances

between the pair of low dimensional objects ˆx

i,p

[m]

and ˆx

i,q

[m], m = 1, . . . , M. The coordinates of ˆx

i,c

[m]

are estimated so that S is minimized. Here, M = 2 or

M = 3 can be used in order to visualize the data in

two- or three-dimensional charts.

In this work, D

corresponds to the Jaccard

distance (Cha, 2007) deﬁned by the following

expression:

∑

n=1

i,p

[n] − x

i,q

[n])

∑

n=1

i,p

[n]

∑

n=1

i,q

[n]

−

∑

n=1

i,p

[n]x

i,q

[n]

(3)

The MDS analysis allows visualizing the EEG record-

ings captured during a single trial through two or

three-dimensional maps. The interpretation of such

charts is based on the emerging patterns determined

by the relative distance between points.

2.2.2 Procrustes Method

The Procrustes method adjusts an object, deﬁned by a

set of Cartesian coordinates, to a reference object by

applying linear transformations, such as rotation, re-

ﬂection, translation and scaling (Kendall, 1989). The

Procrustes distance d ∈ [0, 1] is a measure of dissimi-

larity between the adjusted objects by quantifying the

degree of ﬁt. This method is useful for ﬁnding pat-

terns in a group of objects that have similar d (Warheit

et al., 1992).

3 RESULTS AND DISCUSSION

The signal x

i,c

[n] corresponding to the trials i =

1, . . . , 1080 are processed by the MDS technique us-

ing the Jaccard distance D

to generate the distance

matrix D

. Figure 2 shows the MDS map corre-

sponding to a representative trial. Each point stands

for a low dimensional depiction of a single-channel

EEG recording. In Figure 2A, colors were assigned

to each point following the color code presented in

Figure 1. It can be veriﬁed that the points distribu-

tion agrees with the electrodes placement. Figure 2B

depicts the same set of points from Figure 2A but, in

this case, different colors distinguish the brain hemi-

spheres and the midline. Since neighboring channels

record activity from a common brain region, the cor-

responding EEG signals have high similarities (i.e.,

low values of D

) at a global level. Still, the magni-

tude of D

of neighboring signals is high enough to

keep dissimilarities at a local level.

The rest of the trials are processed using the

MDS analysis and then superimposed through the

Procrustes algorithm. The quality of the Procrustes

result can be assessed by means of the Procrustes dis-

tance d. The low the value of d, the better the align-

ment between the sets of points. Figure 3 shows the

values of d sorted in increasing order and the cor-

responding histogram chart. It can be veriﬁed that

approximately 80% of the trials result in values of

d < 0.5, which indicates that a signiﬁcant portion of

trials generates an MDS pattern that agrees with the

electrodes spatial distribution. However, it was ob-

served that the range 0.45 < d < 0.5 corresponds to

MDS maps, where some electrodes, such as temporal

and midline electrodes, have a signiﬁcant deviation

from their true spatial location. Thus, the criterion

: d ≤ 0.45 is adopted as a proper Procrustes out-

come.

Figure 4A shows the Procrustes superimposed tri-

als of the ﬁrst session that meet the C

criterion.

The chart allows identifying clusters composed by

electrode locations that capture information from the

same brain lobe in each hemisphere. Moreover, Fig-

ure 4B evinces that the hemispheres are separated by a

dividing line composed by the midline electrodes. On

the other hand, Figures 4C and 4D depict the charts of

the trials that do not meet C

(i.e., d > 0.45), in which,

the patterns of electrodes placement and hemispheres

and midline are lost. Figure 5 illustrates the MDS

maps from a representative trial from the set having

d > 0.45. It is evident that the resulting patterns do

not match the spatial distribution of electrodes, nor

the hemispheres and midline. Additional numerical

experiments on the trials not meeting C

using differ-

ent distances, evinced no correlations between the re-

sulting MDS loci and the electrodes placement. From

Figure 4B, it is noteworthy that, the clusters represent-

ing the left and right hemispheres (denoted by colors

orange and blue, respectively) are intermingled with

points from the opposite hemisphere. A second cri-

terion, C

, is deviced with the purpose of ﬁltering the

trials that generate such artifact. The centroids of the

clusters, related to the temporal lobes, are calculated

Correlating EEG Signals and Electrode Locations by Means of Multidimensional Scaling

311

Figure 2: MDS maps of a representative trial. The charts A and B use different colors for distinguishing among electrodes

placement and left and right hemispheres, respectively.

Figure 3: A. Procrustes distance d vs Trials of all dataset, sorted in increasing order. B. Histogram of Procrustes distance d

for the entire dataset.

using the k-means algorithm. The clusters of the tem-

poral lobes are set as the reference since their record-

ing positions are far from the midline. The two re-

sulting centroids are considered representatives of the

left and right hemispheres. The trials having inter-

mingled hemispheres have at least one point whose

distance to the centroid of the belonging hemisphere

is larger than the distance to the other centroid. Such

trials are discarded.

Figures 6A and 6B portray the superimposed

MDS maps applying the C

criterion. Figures 6C and

6D depict the trials ﬁltered by C

. Both criteria are

applied to the data from the two remaining sessions,

obtaining similar MDS maps to those described for

session 1. For the sake of parsimony, these maps are

not included.

Figure 7A, left and middle, depicts the super-

imposed MDS maps of the full database by means

of Procrustes and then processed through the ﬁlter-

ing criteria C

and C

. It can be observed that the

electrodes spatial distribution agrees with the MDS

emerging clusters. Figure 7A right, shows the MDS

maps by adopting a color code that corresponds

to the sets {FP+AF, F+FC, C+CP, P+PO, O+CB,

midline,temporals}. One can observe that the clus-

ters agree with the spatial distribution of the 10-20

electrode placing system.

The charts shown in Figure 7B enclose the trials

ﬁltered by the C

criterion. Despite this, the clus-

ter patterning that agrees with the electrodes spatial

distribution and hemispheres is discernible. Figure

8A illustrates the histogram of the number of chan-

nels per trial ﬁltered by the C

criterion among the

entire database. From a total of 135 discarded trials,

51% (69 trials) contains a single channel identiﬁed by

, whereas ≈ 90% (121 trials) contains between 1

and 3 channels identiﬁed by C

. Additionally, Fig-

ure 8B shows the recurrence of channels detected by

. It can be seen that parietal occipital and occipital

channels are the most recurrent, whereas the frontal,

frontal central and central electrodes are the less re-

current in failing the C

criterion. The remaining

channels present an intermediate low degree of recur-

rence. These results suggest that criterion C

is able

to identify EEG signals whose MDS mapping does

not match with the underlying recording site. How-

ever, such mismatch does not imply that the spatial

pattern of the remaining signals is not correlated with

the corresponding recording sites, as one can observe

in Figure 7B. This behavior may be related to spe-

ciﬁc conditions of the corresponding recording sites.

For example, the electrodes positions CB1 and CB2,

BIOSIGNALS 2023 - 16th International Conference on Bio-inspired Systems and Signal Processing

312

A B

Figure 4: Procrustes superimposed MDS maps corresponding to all trials of session 1 from the SEED-IV database. The charts

A and B depict the maps that met the C

criterion. The charts C and D show the maps ﬁltered by C

. Different colors are used

for distinguishing among electrodes placement and left and right hemispheres.

Figure 5: MDS maps of a representative trial from the set having d > 0.45. The charts A and B use different colors for

distinguishing among electrodes placement and left and right hemispheres, respectively.

which are among the most recurrent channels accord-

ing to Figure 8B, are usually discarded in EEG studies

due to the brain’s electrical activity is not accurately

reﬂected. On the other hand, criterion C

is sensitive

to the trials not preserving the electrodes placement

patterns. Thus, C

provides a global assessment of the

MDS map quality, whereas C

evaluates local spatial

behavior. Figure 8C summarizes the results of apply-

ing the criteria C

and C

. Neutral emotion has the

lowest number of trials (22.6%) ﬁltered by C

. Re-

garding the C

criterion, the number of ﬁltered trials

is similar for all 4 emotions, emphasizing that, neu-

tral emotion again has the lowest number of trials dis-

carded.

As a complementary experiment, the effect of the

EEG signals duration on the MDS outcome is as-

sessed. First, the EEG recordings of the trial used as

the Procrustes reference are analyzed. These signals

Correlating EEG Signals and Electrode Locations by Means of Multidimensional Scaling

313

A B

Figure 6: Procrustes superimposed MDS maps corresponding to all trials of session 1 from the SEED-IV database. The charts

A and B depict the maps that met the C

criterion. The charts C and D show the maps ﬁltered by C

. Different colors are used

for distinguishing among electrodes placement and left and right hemispheres.

Figure 7: Procrustes superimposed MDS maps corresponding to all trials of the SEED-IV database. The chart A depicts

the maps that met the C

and C

criteria. The chart C shows the maps ﬁltered by C

and C

. Different colors are used for

distinguishing among electrodes placement, left and right hemispheres, and brain regions.

have a duration of 177 s, which is a value close to the

mode of signals durations of the entire dataset. Sev-

eral numerical tests evinced that the duration of the

EEG signals can be reduced up to 45 s without affect-

ing the MDS outcome. This result can be seen in Fig-

ures 9A and 9B, in which, the MDS maps obtained

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314

Figure 8: A. Histogram of the number of channels per trial ﬁltered by C

criterion. B. Number of points per channel not

meeting C

criterion. C. Number of trials ﬁltered and not ﬁltered by C

and C

criteria according to the evoked emotions.

Figure 9: Charts A and B depict the MDS maps of the trial used as the Procrustes reference with a sample reduction from

177 s to 45 s. Different colors distinguish among electrodes placement (A) and left and right hemispheres (B). In chart C, N

represents the percentage of trials not ﬁltered by C

after each duration reduction with respect to the case with no reduction.

In chart D, N

represents the percentage of trials not ﬁltered by C

and C

after each duration reduction with respect to the

case with no reduction.

from signals with durations of 45, 55, 65, . . . , 175s,

are superimposed by means of Procrustes. One can

observe a good alignment of the individual MDS

maps, which supports the robustness of the proposed

method to variations in the durations of the EEG

recordings.

The signals duration reduction was performed on

the entire database. Since the recording duration of

the database is not uniform, the trials were sorted ac-

cording to their duration from largest (≈ 275 s) to

shortest (≈ 40 s). The test values are from 225 s to

75 s in reducing steps of 50 s, and from 75 s to 5s

in reducing steps of 10 s. Each duration test value is

applied to all trials that have a correspondingly larger

duration and, thus, can be reduced to such duration.

We use the number of trials resulting from ﬁltering

criteria C

and C

as a ﬁgure-of-merit. Figure 9C de-

picts the percentage of trials not ﬁltered by C

after

each duration reduction with respect to the case with

no reduction (N

). It can be seen that the EEG dura-

tion can be reduced up to 45 s without affecting the

MDS outcome regarding the C

criterion. Similarly,

Figure 9D shows the scenario after applying C

and

in which the shorter duration without affecting the

MDS outcome is 65 s. According to Figure 8B, the

most recurrent channels being detected by the C

cri-

terion are located near the midline (i.e., PO4, CB1,

CB2, O2). Thus, it is expected that variations of the

duration of the corresponding EEG recordings gener-

ate displacements of its representation in the MDS lo-

cus (as it can be observed in Figure 9). Therefore, the

MDS outcome is less robust to EEG duration reduc-

tions when assessing the criterion C

(up to ≈ 65 s),

compared with criterion C

(up to ≈ 45 s). However,

Correlating EEG Signals and Electrode Locations by Means of Multidimensional Scaling

315

such differences are not signiﬁcant if we consider that

the trials not meeting the C

criterion present a clus-

tering behavior that is correlated with the electrodes

placement. Moreover, the fact of a better robustness

of the MDS outcome against signals reduction when

assessing the C

criterion, conﬁrms the effectiveness

of the proposed method in establishing correlations

between the EEG recordings and the electrodes spa-

tial distribution.

4 CONCLUSIONS

In this work, the raw multichannel EEG recordings

from the SEED-IV database were analyzed using the

MDS technique combined with the Procrustes algo-

rithm. To the best of our knowledge, this is the ﬁrst

work establishing a direct link between EEG record-

ings and recording electrodes position.

Regarding multichannel EEG studies, an issue

that remains unsolved is related to determining the

number of electrodes and the recording sites that pro-

vides relevant information on emotions. It is a com-

mon practice deﬁning a ﬁxed set of electrodes sites

on the scalp for studying a given population. Re-

cent investigations pose a subject-speciﬁc setup of

EEG recording sites (Gannouni et al., 2021; Ozel

and Akan, 2021). Our results suggest that the EEG

time series from most of the SEED-IV trials con-

tain information of their underlying recording locus,

so that the electrodes spatial distribution can be re-

covered. This outcome may support the importance

of deﬁning a set of EEG recording sites speciﬁc to

each subject. Moreover, the proposed methodology

sheds some light upon the information content of si-

multaneous EEG signals and its correlation with the

underlying cerebral structures. We did not focus on

the 32% trials of the database from which the elec-

trodes position cannot be recovered by means of the

MDS analysis. Our next research work will aim to

unveil the causes and implications of such outcome.

Although we did not observe a clear correlation be-

tween proper Procrustes alignment and evoked emo-

tions, the recordings obtained during neutral emotion

induction show a slightly superior alignment capacity

with regard to remaining emotions. Further studies

are needed to assess the signiﬁcance of such differ-

entiated behavior. Additionally, we analyzed multiple

EEG recordings corresponding to 15 subjects (72 tri-

als per subject), which may generate a self-bias due to

similar cognitive patterns of the same subject. There-

fore, the proposed methodology requires further vali-

dation with a larger population.

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