TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.7, July 201
4, pp
. 5387 ~ 53
9
1
DOI: 10.115
9
1
/telkomni
ka.
v
12i7.388
7
5387
Re
cei
v
ed
Jul
y
13, 201
3; Revi
sed Fe
bru
a
ry 1
5
, 2014;
Acce
pted Ma
rch 9, 2
014
Study on Mahalanobis Discriminant Analysis of EEG
Data
Yuan Shi*, Li
nlin Yu, Fang Qin
Dali
an Institute
of Science a
n
d
T
e
chnolo
g
y
BinGan
g St.99
9
-26, Da L
i
a
n
, Chin
a
*Corres
p
o
n
id
n
g
author, e-ma
i
l
: 2008
80
41@
q
q
.com
A
b
st
r
a
ct
Objective
in t
h
is p
a
p
e
r, w
e
have
do
ne
Maha
lan
o
b
i
s
Discri
m
i
nant
a
nalysis
to EE
G data of
exper
iment
obj
ects w
h
ich ar
e
record
ed
i
m
p
e
rson
ally c
o
me up
w
i
th a r
e
l
a
tively
accur
a
te
metho
d
us
e
d
i
n
feature extr
acti
on a
nd c
l
assifi
cation
dec
isio
n
s
.
Methods In
accord
ance
w
i
th the stre
ngth
of
wave, the
hea
d electr
ode
s are divi
ded i
n
to four speci
e
s. In use
of part of 21 electro
des
EEG data of 63 peo
pl
e, w
e
have
don
e Ma
hal
ano
bis D
i
sc
rimina
nt an
aly
s
is to EEG dat
a of six ob
ject
s. Results in
u
s
e of part of E
E
G
data of
63
peo
ple, w
e
h
a
ve
d
one M
a
h
a
la
no
bis Discr
i
m
in
an
t analys
is, the
electro
de cl
ass
i
ficatio
n
acc
u
ra
cy
rates is 64.4
%
. Concl
u
sio
n
s
Mahal
ano
bis
Discrimin
ant
has hi
gher pr
edicti
on accur
a
cy, EEG featur
e
s
(ma
i
nly
w
ave) e
x
tract more
ac
curate. Ma
ha
la
nob
is D
i
scri
m
i
nant w
o
uld
b
e
better a
p
p
lie
d t
o
the
featur
e
extraction a
nd
classificati
on d
e
cisio
n
s of EEG data.
Ke
y
w
ords
:
el
e
c
troence
p
h
a
lo
gra
m
, Maha
lan
obis d
i
scri
m
i
n
a
n
t,
rhyth
m
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
The pu
rpo
s
e
of routine b
r
a
i
n wave insp
ection i
s
to evaluate whet
her the b
r
ain
wave is
norm
a
l or n
o
t
and provid
e
help to diag
nose the br
ai
n diso
rd
ers
whi
c
h is
also
kno
w
n a
s
b
r
ain
wave inte
rp
retation. The
traditional
brain wave int
e
rp
retation i
s
reali
z
ed th
rough
rea
d
ing
the
multi-chan
nel
electro
e
n
c
ep
halog
ram on
the record
ing
paper by experts, which is to unde
rsta
nd
and
eval
uate electroen
ce
p
halog
ram (EE
G
) with
the
m
e
thod of vi
su
al inspe
c
tion.
The e
s
sen
c
e
of
this method
based on ex
pertise i
s
that experts
utilize experi
ence to wi
pe out the di
sturbance
and a
r
tifact of
sign
als,
con
duct featu
r
e
extraction
to the EEG a
c
co
rding to
the freque
ncy, ra
n
ge,
pha
se po
sitio
n
and othe
r i
n
formatio
n, and ca
rry
out
the categ
o
ry
descri
p
tion fo
r the extracte
d
feature
s
with
the re
co
gni
ze
d expe
rien
ce
to analy
z
e
a
nd evalu
a
te t
he EEG [1].
Up to
no
w, this
method i
s
wi
dely appli
ed
to the cli
n
ic.
The visual in
spe
c
tion, to
some
extent, can
catch t
h
e
patholo
g
ical
waveform o
r
even
confi
r
m the p
o
siti
o
n
of the
brai
n focus.
Ho
wever,
due
to the
stron
g
no
n-st
ationary a
n
d
nonlin
ear
chara
c
te
ri
sti
c
s of EEG, wi
th the additi
on of the g
r
eat
depe
nden
ce
of visual
i
n
sp
ectio
n
o
n
kno
w
ledg
e
-
level a
nd
experie
nce
of EEG an
alysis
person
nel, the new meth
o
d
must be ex
plore
d
to reali
z
e the b
r
ea
kthrou
gh of EEG re
sea
r
ch [2].
Mahala
nobi
s Discrimina
n
t analysi
s
h
a
s
be
en intro
duced into t
he re
se
arch
of EEG,
whi
c
h
will acti
vely prom
ote
the extraction and cl
as
sification of EEG
data to
assi
st the inspection
and qua
ntitative analysis
of EEG and provide
the
effective analysis me
an
s for the EEG
examination.
2. Objects and
Metho
d
s
2.1. Object o
f
Stud
y
We ta
ke
28
men a
nd
35
wome
n a
s
th
e re
se
arch
o
b
ject
s, who
s
e
age
is ra
ngin
g
from
20
to 60, and th
e avera
ge a
g
e
is 3
6
.7. All the su
bje
c
ts
are enjoying
good health without seri
o
u
s
nerve
system
dise
ases
an
d histo
r
y of ta
king
psy
c
hotropic
dru
g
s, a
nd they
are selecte
d
from t
h
e
norm
a
l pop
ulation.
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TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5387 – 53
91
5388
2.2. Build th
e Selection
of Mathema
t
ical Modelling EEG Data
The
sampli
ng
freque
ncy
of experim
ent re
cording
of EEG is 1
0
0
H
z
which i
s
re
cord
ing 21
electrode
d
a
ta a
c
cording
to the
lea
d
lo
cation
in
inte
rnation
a
l 1
0
-20
system:
C3, CZ,
C4,
F
P
1,
FPZ, FP2, F7, F8, FZ, F3, F4, O1, OZ, O2, P3,
PZ,
P4, T5, T6, T3, T4.. A bloc
k
(indic
a
ting a
sho
r
t time period
)
of EEG
data is acqui
red at
every turn, and the
numbe
r of sa
mpling poi
nts for
each bl
ock i
s
512
with
the
recording
time of
5.1
2
s.
T
he el
ectroen
cephal
ogram
of no
rmal
pe
ople
is mai
n
ly in
rhythm, the st
rength
s
of
wa
ve ap
pea
r i
n
the
occiput
, and th
en
weakenin
g
grad
ually fro
m
back to front. Cla
ssify
the 21 con
ductin
g
elect
r
ode
s into 4
catego
rie
s
in
accordan
ce
with the
inten
s
ity differen
c
es
of t
he
rhythm in va
riou
s part
s
of th
e
head,
whi
c
h i
s
,
former hea
d electrode, sid
e
head el
e
c
trode, central
electrode, o
c
ci
put ele
c
trod
e. The spe
c
ific
cla
ssifi
cation
situation i
s
as follows:
(1) T
he first category: ce
ntral electrode
(C3, CZ, C4)
(2) T
he seco
nd cate
gory: forme
r
hea
d e
l
ectro
de (FP
1
, FPZ, FP2, F
7
, F8, FZ, F3, F4)
(3) T
he third
categ
o
ry: occiput electr
ode (O1, OZ, O2,
P3, PZ, P4,
T5, T6)
(4) T
he forth
categ
o
ry: sid
e
head el
ectrode (T
3, T4)
2.3. The Co
mputer Proc
essing of EE
G Da
ta
The ele
c
troe
nce
phal
ogra
m
dedicated
toolbox
EEG Toolbox i
s
de
signe
d with the
MATLAB pro
g
rammi
ng l
a
ngua
ge i
n
o
r
de
r to fa
cili
tate analy
z
in
g the
origi
n
al data
of t
h
e
electroen
ce
p
halog
ram. In EEG Toolbox
, after the
original data wa
s introd
uced,
it was saved
in
the matrix, a
nd lin
e rep
r
e
s
ent
s the
timi
ng of
exper
i
m
ent
recordi
ng (that
i
s
sa
mpling point
) while
colum
n
indi
cates the el
ectrode. All the
data of
every subje
c
t we
re introd
uced
before
analy
s
is
and the ele
c
t
r
oen
ce
phal
og
ram shoul
d b
e
sho
w
n intu
i
t
ively, and a block of EEG
data sh
ould
be
displ
a
yed on
each pag
e [3].
The
4 p
opula
t
ion Mah
a
lan
obis di
stan
ce
discrimina
n
ce cl
assifie
s
th
e sample
dat
a into
4
categ
o
rie
s
b
a
se
d on the
electrode
cla
ssifi
cation
m
e
thod introdu
ced a
bove. F
i
rstly, put the 21
electrode E
E
G data which
will bui
ld the math
ematical m
o
dels into th
e four matri
x
es
on the ba
sis
of classification. Put the cu
rrent blo
ck
of EEG data into the Matrix
X, which i
s
5
12×21 matrix
. The elect
r
o
de cla
s
sificati
on re
sult
s are pre
d
icte
d with Mahalan
o
b
is
distan
ce di
scriminan
ce an
d
expresse
d b
y
putting them into vector.
Whe
n
the M
ahala
nobi
s di
stan
ce di
scri
minan
ce
i
s
a
dopted, the
d
i
scrimin
a
ting
data will
be cla
s
sified
into the nea
rest cat
ego
ry based on t
h
e
distan
ce le
n
g
th of popul
a
t
ion cent
re fro
m
the disting
u
ishing EEG dat
a. The Mahal
anobi
s di
stan
ce
an
alysi
s
proce
dure in the resea
r
ch is
on
the basi
s
of multi-cha
n
n
e
l EEG data desig
n.
Firstly, the mathematical model, nam
ely,
discrimi
nation
functio
n
,
sho
u
ld b
e
b
u
ilt, then
predi
ct
the
categ
o
ry
of EEG d
a
ta
according
to t
h
e
discrimi
nation
rules. The
Mahala
nobi
s distan
ce
di
scrimin
a
n
c
e coul
d be explaine
d by the
followin
g
mathematical formula:
(1)
(2)
(3)
Formul
a
(1-3
) is the M
a
h
a
lano
bis
dist
ance
di
scrimi
nan
ce fun
c
ti
on, and
4
p
opulatio
n
Mahala
nobi
s
distan
ce
discriminan
ce
will build 4 di
scri
minan
ce fun
c
tions. Sub
s
titute an un
kn
o
w
n
cla
ssifie
d
EE
G data
X into
the fou
r
M
a
h
a
lano
bis dist
ance di
scrimi
nation fu
nctio
n
s, a
nd
acqui
re
the
minimum Mahala
nobi
s distan
ce
a
nd discri
mi
nate it to the correspondi
ng totali
ty.
Each
blo
c
k o
f
EEG data
can b
e
p
r
e
d
ict
ed a
nd
cla
s
si
fied by the
M
ahala
nobi
s
di
stan
ce
discrimi
nation
function
and
the pre
d
icated cl
assifica
t
i
on re
sult
s a
s
well a
s
a
c
t
u
al cla
s
sif
i
cat
i
ons
can b
e
intuitively displayed
in the Mahala
nobi
s di
sta
n
ce discrimi
nan
ce predi
catin
g
result cha
r
t.
(
1
,
2
..
.4
)
i
Xi
2
()
*
j
dX
A
B
()
'
1
1
()
j
n
j
i
i
j
AX
X
n
()
(
)
()
()
'
'
1
1
[(
)
(
)
]
n
j
jj
jj
ii
j
j
B
XX
X
X
A
nn
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Study on Ma
halan
obis
Discrim
i
nant Ana
l
ysi
s of EEG Data (Yu
an Shi)
5389
3. EEG Data
Analy
s
is Results fr
om Mahalanobis
Dista
n
ce
Dis
c
riminance
Cla
ssify the
21 co
ndu
ctin
g elect
r
od
es
into
four categori
e
s
acco
rding to the i
n
tensity
differen
c
e
s
of
wave
on
various pa
rts of
the he
ad, a
n
d
forecast
21
ele
c
tro
des
cl
assificatio
n
con
d
ition
s
of
six subje
c
ts i
n
the
cu
rrent
bloc
k
with M
a
halan
obis di
stance
di
scrimi
nan
ce:
C3,
CZ
,
C4, FP1,
FP
Z, FP2, F7,
F8, FZ, F
3
,
F4, O1,
OZ,
O2, P3, PZ,
P4, T5, T6,
T3, T4.
Draw the
Mahala
nobi
s distan
ce
di
scrimina
nce predicating re
sult chart an
d
2D pie ch
art
of Mahalano
bis
distan
ce di
scrimination a
c
cura
cy rate wit
h
Mahala
nobi
s dista
n
ce discrimi
nan
ce p
r
oce
dure [4].
Mahala
nobi
s dista
n
ce di
scrimi
nant
an
alysis
proced
ure
ca
n fo
re
ca
st an
d
cla
ssify the
EEG data of
all blo
c
ks fo
r vario
u
s
su
b
j
ects.
Due
to
the sp
ace constraint
s,
o
n
ly
t
he f
o
re
c
a
st
results of the EEG data in six blocks for thr
ee subject
s
are gi
ven in
detail, and the whole
situation can be
refle
c
ted by
sho
w
ing o
n
ly classification re
sults
of two blocks for ea
ch
subj
ect,
and the fore
cast cla
s
sificat
i
on re
sults in
other bl
o
c
ks
are si
milar to
these. Analyze the predi
cat
ed
results
of one
subj
ect in
de
tail. We nu
mb
er the
6
subje
c
ts fo
r the
sa
ke of
conve
n
i
ent de
scriptio
n:
1, 2, 3, 4, 5,
6. First co
nd
uct the Mahal
anobi
s
di
stan
ce di
scrimin
a
n
t analysi
s
for the 12th blo
c
k
of EEG data of Subject 1. The figure of EEG is sho
w
n in Figure 1.
Note 1):
The ho
rizontal ordinate is
frequenc
y (Unit:
Hz),
w
h
ile the ve
rtical
coordinate is voltage (Unit:µV), and the
electrode parts h
a
ve been marke
d
on the left side of the data.
Figure 1. EEG Data of the
Twelfth Block of in Subject 1
Note 1):
The top
left corner is the
predicating results of
the first–categor
y
electrode; t
he top right cor
n
er is the
predicating results of the second–categor
y
electrod
e; the le
ft bottom
is the predicating results of the t
h
ird–categor
y
electrode; and th
e bottom right co
rner is the pr
edi
cating results of the forth–catego
r
y
electrode. 2)
：
Th
e horizontal
ordinate is the na
mes of various kinds
of electrodes and the catego
r
y
is listed
on the vertical coordinate. 3): re
d*
represents the
predicated classif
i
c
a
tion si
tuation, blue O
indicates th
e actual
category
situation. * and O
w
ill coincide
w
h
en the p
r
edicated classif
i
cation
is consis
tent w
i
th
the actual classif
i
cation. 4)
：
first–categor
y
electrod
e (C3, C
Z
, C4
),
second–categor
y electrode (F
Z, F
3
, F4, FP1,
FPZ,
FP2, F7,
F8), t
h
ir
d–categor
y (P3,
PZ, P4, O1
, OZ,
O2, T
5
, T6
),
forth–catego
r
y
electrode (
T
3, T4
).
Figure 2. Mahalan
obis
Distance Predi
ca
ting Re
su
lts o
f
the Twelfth Block in Su
bj
ect 1
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5387 – 53
91
5390
Carry out the Mahala
nob
is distan
ce
discrimi
nant analysi
s
for
the 6 subje
c
ts, and
rand
omly extract 1
0
blo
c
ks of EEG
data for eve
r
y subj
ect to
predi
ct cla
s
sificatio
n
. The
Mahala
nobi
s
distan
ce p
r
ed
icating results is sho
w
n b
y
Figure 2. T
he avera
ge a
c
cura
cy rate
is
64.4% (sho
wn in Table
1). On the
whol
e,
the fore
ca
st re
sul
t
s of Mahal
anobi
s di
sta
n
ce
discrimi
nan
ce
are bette
r; the extractio
n
o
f
the
EEG characteri
stics (mainly
wave) is relatively
accurate. The
pre
d
icating
result
s can
ref
l
ect the
i
n
ten
s
ity differen
c
es of
wave
in variou
s p
a
rts
of the h
ead.
To
some
exte
nt, the o
c
currence ra
te o
r
amount
of
wa
ve
, namely, t
he q
uantity o
f
wave
record
e
d
in the EEG within a certai
n peri
od of time, has h
uge
differen
c
e
s
in individual
s.
The
fo
re
ca
st results
are
in
fluenced by su
ch si
tuatio
ns
wh
ere
wa
ve
con
s
tantl
y
appe
ars i
n
some
pe
ople
and
sp
ora
d
ically in oth
e
r
p
eople,
or
wh
e
n
othe
r frequ
ency
wave
s
a
ppea
r. Th
e m
i
s-
discrimi
nan
ce
can al
so be
cau
s
e
d
by the amplitude
modulatio
n a
nd right
-an
d
-l
eft difference.
Table 1. The
Average Accura
cy Rate of
Mahal
an
obi
s Distan
ce
Discrimi
nan
ce Predicating EEG
Cla
ssif
i
cat
i
on
Subject
1 2 3 4 5 6
Average
Accuracy
Rate
Accur
a
cy
Rate
66.7
％
63.2
％
64.2
％
63.5
％
65.4
％
63.1
％
64.4
％
4. Conclusio
n
Becau
s
e Eu
clide
an di
sta
n
ce i
s
oversimp
lified, a
nd the ab
solute dista
n
c
e an
d
Che
b
ysh
e
vy distan
ce
can not
com
p
letely expr
ess the
cha
r
acte
ri
stic dif
f
eren
ce
s of
the
multidimen
sio
nal data in the high
-dim
e
n
sio
nal
spa
c
e, therefore, we u
s
ually a
nalyze the E
E
G
data
with Ma
halan
obis di
stance
discrim
inan
ce in
ex
p
e
rime
nts.
Cla
ssify 2
1
cond
ucting
ele
c
tro
de
into four cate
gorie
s
acco
rding to th
e i
n
tensity
differences of the
wave
in eve
r
y pa
rt, build
Mahala
nobi
s distan
ce di
scrimi
nan
ce
mathemati
c
al
model
with 21 brain ele
c
trod
e data,
and
con
d
u
c
t the Mahala
nobi
s
distan
ce di
scrimina
n
t anal
ysis to the E
E
G data of 6
normal
su
bj
ects.
The predi
cati
ng cla
s
sificati
on accu
ra
cy rate is 6
4
.4%
.
On the who
l
e, the predi
cating re
sult
s of
Mahala
nobi
s distan
ce di
scrimi
nan
ce i
s
better,
the extraction
of EEG c
hara
c
teri
stics (m
a
i
nly
wave
) is mo
re a
c
curate,
a
nd the
predi
cating results
can
refle
c
t th
e inten
s
ity differen
c
e
s
of
wave
on the variou
s pa
rts
of the head. The expe
rim
ent indicates
that Mahalan
obis di
stan
ce
discrimi
nation
ca
n p
r
efera
b
ly extract t
he EEG
ch
a
r
acte
ri
stics of
normal p
e
o
p
le an
d
can
be
applie
d to the classification
deci
s
ion of EEG data.
The EEG of
norm
a
l pe
o
p
le presents
rhythm an
d
wave
is th
e majo
r EEG
cha
r
a
c
teri
stic of normal p
e
ople. The p
r
e
d
icatin
g
cla
ssification resul
t
s of different
blocks
are
n
o
t
compl
e
tely e
quivalent,
whi
c
h
refle
c
ts th
at the EEG
is a n
o
n
-
statio
nary
ran
dom
sign
al a
nd
wave
is
co
nsta
ntly cha
ngin
g
. Th
e amplitu
de
modulatio
n p
henom
eno
n, l
e
ft-and
-rig
h
t
differen
c
e
an
d
individual
differen
c
e
s
i
n
su
bject
s
will ex
ert an
influe
n
c
e
on p
r
e
d
ica
t
ing cl
assifica
tion of EEG d
a
ta
and ca
use
t
he
mi
s-discri
minan
ce. We
an
alyze
the rea
s
on
s for
mi
s-discri
minan
ce of the
electrode
s a
s
follows:
(1) When
th
e Mah
a
lan
o
b
is
dista
n
ce
cla
s
sificatio
n
di
scrimina
nce
is ado
p
t
ed, the
discrimi
nating
data
will
be
cla
ssifie
d
into
the
nea
re
st
categ
o
ry
ba
sed o
n
th
e di
stance
len
g
th
of
each po
pulati
on
cente
r
fro
m
the di
sting
u
ishi
ng EEG
data [5]. It is i
m
possibl
e to
get infinite E
E
G
data sa
mple
s, so the lim
ited sam
p
le
s with ce
ntra
li
zed trainin
g
are u
s
e
d
to estimate eve
r
y
popul
ation center. The
waveforms,
amplitude
s
a
nd pha
se p
o
sition
s of the normal p
eople
colle
cted
in t
he exp
e
rim
e
n
t
are
differe
nt in the
EEG
data, which
may lead
to t
he in
accu
ra
cy of
predic
a
ting c
l
ass
i
fic
a
tion.
(2)
Wh
en Ma
halan
obis
distance
discri
m
i
nation i
s
ado
pted to an
alyze the EEG
data of
norm
a
l pe
op
le, wh
ere
mis-discri
min
a
tion exis
t
s
.
The
prin
ci
ple of M
a
h
a
lano
bis
dist
ance
discrimi
nan
ce
is to cla
ssify
the discrimi
nating sampl
e
s to the ne
are
s
t cate
gory [6].
If the two
kind
s
of the
sample
s a
r
e
o
v
erlapp
ed
an
d the
discr
imi
nating
sa
mpl
e
s
are ju
st in
the
overla
pp
ed
area, the
sa
mples
will probably be
cla
ssifie
d
wrongl
y. We take th
e two pop
ulat
ions for
exam
ple
in order to gi
ve a bette
r e
x
planation. S
uppo
se th
at the sampl
e
x i
s
on
e-dimen
s
ion vari
able,
G1
and G2 a
r
e t
w
o po
pulatio
ns, and Fig
u
re 3 is the
dist
ribution
situat
ion of the two
populatio
ns.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Study on Ma
halan
obis
Discrim
i
nant Ana
l
ysi
s of EEG Data (Yu
an Shi)
5391
Figure 3. Dist
ribution
Diag
ram of Two P
opulatio
ns
For in
stan
ce,
if x belong
s to Populatio
n
G1, but it
falls on the left si
de of
, in acco
rdan
ce to th
e
rule
s, x is classified to G2; similarly, the poi
nt in G2 ca
n be classified to G1 wrongly
with
Mahala
nobi
s
distan
ce
discrimina
n
ce. T
he e
r
ror
pro
b
ability is
sho
w
n i
n
the
sh
ado
w a
r
ea
of
the
diagram. If th
e two popul
ations a
r
e nea
r to each othe
r, the rate of mis-discri
min
a
tion must score
high [7].
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