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Epileptic Seizure Detection based on Wavelet Transform Statistics Map
and EMD Method for Hilbert-Huang Spectral
Analyzing in Gamma
Frequency Band of EEG Signals
Morteza Behnam(1) - Hossein Pourghassem(2)
(1) MSc Student - Department of Electrical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Isfahan, Iran
morteza.behnam@sel.iaun.ac.ir
(2) Associate Professor - Department of Electrical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Isfahan, Iran
h_pourghasem@iaun.ac.ir
Seizure detection using brain signal (EEG) analysis is the important clinical methods in drug therapy and the decisions before brain surgery. In this paper, after signal conditioning using suitable filtering, the Gamma frequency band has been extracted and the other brain rhythms, ambient noises and the other bio-signal are canceled. Then, the wavelet transform of brain signal and the map of wavelet transform in multi levels are computed. By dividing the color map to different epochs, the histogram of each sub-image is obtained and the statistics of it based on statistical momentums and Negentropy values are calculated. Statistical feature vector using Principle Component Analysis (PCA) is reduced to one dimension. By EMD algorithm and sifting procedure for analyzing the data by Intrinsic Mode Function (IMF) and computing the residues of brain signal using spectrum of Hilbert transform and Hilbert – Huang spectrum forming, one spatial feature based on the Euclidian distance for signal classification is obtained. By K-Nearest Neighbor (KNN) classifier and by considering the optimal neighbor parameter, EEG signals are classified in two classes, seizure and non-seizure signal, with the rate of accuracy 76.54% and with variance of error 0.3685 in the different tests.
Index Terms: Epilepsy, wavelet transform, hilbert-huang transform, brain rhythms, K-nearest neighbor (KNN). :+ @ A -g &-gt; O ,
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./ Y , .2 / .> +3 (D / O1( .
_( R 5( K G
15 K Zl G
) 29 (
Neg(y)=An(yGaussian)-An(y) (8)
G'
yGaussian
. R .8 L ( U1
yGaussian y
01 M+ 1 ( ' M1 / U1 ( (
]
24
[
GV ( 5( .Z1 N .
) 8 ./ ( i G' .2 / .> +3 . g( ( N/ 5( . C G (
G1 > t GZ / / U1 ./ M15 '
K Zl ( N/ O1( .
5( (
]
25
[
:
{ }
3 2 Kurt(y)248 1 y E 12
1 ) y (
ApNeg ≈ + ( 9)
Y0 ) 6 6 :(
EEG
( D1 + ( .H .8 L
Fig. (6): Original EEG signal with stochastic noise
Y0 ) 7 G+ + / R + :( 6 5( (
EEG
H 8
Fig. (7): The Gamma band of prototype filtered EEG signal
G'
y
./ G 8 R h+ ,( M+ 1 ( 2 O 6+ / F /
]
25
[
. (5( G - 1 + 6
EEG
( 5( 1 N/
ApNeg
I ( ( i G'
Y/ 4 .R`1 5( /3 G N+ UI / ./
./ ( 3 ( G _ 8 (
ApNeg=[w(0) w(1) w(2) w(3)]T
J1 +
. (
3 * 1 * 2 * I 0 M ! D% . 7H ,)! N %
PCA
G2E / Y HW 1 6E( 1 .H (
PCA
< GH I 5( ZI
( Y HW ./ /3
1 6E( .
PCA
O 6+ / ( (
-( ( ./ GZ W/ F / G
Y1 Z D' /
./ ./ GZ W/ ( ( M+ 1 ( ' M1 / M[ . + .
O1( 5( -GH, / 1 N/ 1 ( `1 M+ 1 ( ' M1 / ( `
./ GZ W/ „ D s C +( . +
… / `1 ( `1 ( N/ O1 ./ G 1 I / / z8 ( 6+ - 3
13
]
15
[
O .6 Z (D / G GI . 4
/ † 2 ( D/ ( G2E
5(
PCA
( (
-ApNeg
G 1 J ' ./ ( ( < O1( . 1
3 / ( ( . ( ( O1( / n †
G2E G Z + (
./ G Y , / / (DI( M[ . ( i / / + S
O1 ' ( ( (DI( S / -O 6+ / ( N/ 5( GH 8 O1 ./ X=, n +
]
15
[
(5( G 1 + (=E . U1 DF/ 6
./ Y,( / G' - GZ W/ /3 .R`1 G 3 5( (
GNZf ( / ( l 6
O1( / . + 2 (
) UI / G N+ /3 .R`1 ( .R`1 O1( -GE N/
SFWM
(
30
./ . / +
3 * 2 * " #$% O$' $ P ($) 1 ! %
5( Q C / .R`1 K ZH Y1 Z ) f
–
) T+(
HHT
(
31
(
./ ' (
SFWM
B C G /5 / .R`1 U1 ( l G
5( . + ) f *1( ( O1( . 8 R h+ k
HHT
5(
<
EMD
./ 2 ( .
Y0 ) 8 5 , UI / Y1 Z .0 \(5 / G N+ 5( . 1 + :( .& N/ /5
Fig. (8):The map of DWT in some levels in Time-Scale domain
Y0 ) 9 N J1 + :( N+
UI / Y1 Z .0 \(5 / G 4
JC
) 30 ( 3 * 2 * 1 * + ,$ $ P (Q % EMD 1 6E( EMD
6 G'
K G (
x
( J1 +
M+ ' 8 + + ( W/ Y/ G' . (c {1( d U1 G - +( ./ ( 0 -.H ( ( t ( l IMF G') G K ci(n)
(5( G
i=0,1,2,…,m
./ ( J1 + ( +
( N/ G O q
r(n)
( K Z W/ + / G' ./ G1D*
+
]
26
[
: ( ( i (=E
∑
= + = m 1 ii(n) r(n)
c ) n (
x (10)
( N/ G'
m
d ( ( O 6+ /
IMF
./ + / ( N/ .
r(n)
G2E / .H ( 6 Y1 5( . 6+ / N N, 3 . ,
./ d ( .
IMF
61 > Y' .R`1 o ( ( ( (
: . ( 1
/ '( ( 6 .Z +
DF/
/) 1D' / 6 2 5( Zl ( N/ (
( ( 1
. ,( U1 X4 i( }'( , 1 ( ( N/ 2
G+ + G' .1
/ 1 1D' / { .HW/
./ )1 ( 2 - +
] 26 27 [ . 3 * 2 * 2 * ,) R 7H ,)!
32
d ( Q( C ( I 6E b 1 6E( U1
IMF
„ ZHR ( (
.1t
( )
u
E n
. 1 > „ ZHR .HW/ 1D' / {
( )
l
E n
/ R + 6 .HW/ / {
x
./ *1( +
]
26
[
.
„ ZHR 1 N/ O 6+ / M[ _ + . 1 > .1t
m1(n)
: ( i GZ W/ 2 ) n ( E ) n ( E ) n (
m u l
1
+
= (11)
: ( ( i .H ( 6 5( ( N/ O1( X=, M[ ) n ( m ) n ( x ) n (
h1 = − 1 (12)
G'
h1
{1(
IMF
./ p ( ( ( 0 . 1 +
k
/53 5( GZ /
: ( ( i 1 + GZ W/
c1(n)=h1k(n)-m1(k-1)(n) (13)
+ / ( N/ G' K G
) n ( c ) n ( x ) n (
r1 = − 1
GZ W/
./ + / 1 N/ 1 6E( ( 0 (=E .
r1,r2,…,rk
K G d (
( 01
33
5( M> 1 6E( ( 0 1 + .
k
) GV ( -GZ / 13
(
G+ + UI / Y1 Z 5( . C ( l G G1D* 5( (
EMD
G
/3 ( i
] 27 [ . 3 * 2 * 4 * I HSA 34
$#8! # /
d ( GZ W/ 5( M>
IMF
d ( 5( ( DF/ 6 (5( G
-IMF
K G : ] T ) L ( IMF )... 1 ( IMF ) 0 ( IMF [ ) k (
IMF = (14)
./ G'
-L
./ .H ( 6 f ( N/
k
( 0 (
d ( ( O q
IMF
./ BC / ( GV ( 5( 2 ( . 1 +
ZH Y1 Z d ( _ (5( G G' K
./ GZ W/ . (c ( i ( ] 28 [ :
∑
= π∫ = L 1 j dk ) k ( IMF 2 i j H(k) a (n)eIMF (15)
dk k k ) k ( IMF / V . P 1 )) k ( IMF (
HT
∫
H+∞
∞
− − ′
′
π
= (16)
G'
P.V
O ^ GZ W/ O ( . ' GV ( .H ( S1( p ( N/ ./ .E( 6 +( L i( G G'
CPV 35 / + ./ + ] 28 [ . M[
Y1 Z ) f S1( p 5( . 1 / -K ZH Y1 Z ) f GZ W/ S ' . ( ( i K ZH
EMD
) K ZH Y1 Z ) f
HSA
(
Y HW Y1 Z v ,4V ( ( K ZH
–
./ T+( / +
]
29
[
.
Q( C (
))
k
(
IMF
(
HT
Q( C ( G + DF/ 6 5(
GNZf I 3 5( S / .R`1 . ( k B C
) f S1( p {H C/ / G GI
))
k
(
IMF
(
HT
5( +( ( N/
)Y0 10 H ) f C1 3 J1 + :( Z
K – 6 5( T+(
EEG
Fig. (10): The water-fall plotting for Hilbert-Huang spectral of EEG signals
3 xHV/ / 1D' / O . Hg( GH 8 GZ W/ 3 ./ G 5( +( J1 + 5( G+ + U1 . 13
))
k
(
IMF
(
HT
G K ) Y0 9 C1 3 J1 + U1 G' (36
(5( G 10 ( 0
GZ W/
IMF
./ C1 3 J1 + . ( /3 G
( N N, h+ / ( +
K G ( (D*/
3 /D J1 + 5( R HI ./ 2 ( G1 Y0 G
(=E .
./ G 8 1 3 G GH, / O1( G' 1 I .R`1 l U1
(=E . ( ) f 5( m i GVN+ O GH 8 ( l G .N N,
5( +( GZ W/
2 )) k ( IMF ( HT
K L C/ U1 € 8 3
D + xHV/ / '( o N+ -) f ( K G
./ 15 : +
(
HT(IMF(k)))
(x ,y,z )Max 1 1 1
2
) 31 (
(
HT(IMF(k)))
(x ,y ,z )Min 2 2 2
2
= (18) . Hg( GH 8 (=E 3
xHV/ / 1D' / o N+ O G
K / GZ W/ 15 .
:
) 19 (
2 2 1 2 2 1 2 2
1 x ) (y y ) (z z )
x ( ) Max , Min (
d = − + − + −
GNZf ( G' 1 I .R`1 O1( -GE N/ O1( 6
DF/
) .2 f GH 8 .R`1 8 R ( i ( g 2 ( /
DSF
(
37
/ +
./ .
4 * % H ! 7$T D C H
GNZf h / G 6
EEG
A ( ( &4' G
.R`1 5( -A
SFWM DSF
GE N/ O1( .8 /
./ 2 ( .R`1 O1( Q( C ( .
6 ./ 5(
GNZf 1 + - ( 61 > I / 6
5( 2 (
GNZf
K
U1 D+ ./ K G1 O1 . 1=>
4 * 1 * &) U FH ! # !
7H ,)! 0 PCA
N 5( M> -GE N/ O1( G\( ( 1 6E( G N+
Y1 Z
15 _( R -UI / .> +3 / GZ W/ 1 L
GZ W/ (D ( U1 ( l G .2 / d . R b (D /
( N/ ^ Y/ DF/ 6 (=E . ( 2 ( d15 5(
./ .2 / .> +3 ) f 5( .I( C ( .R`1 ^ X / G'
1 6E( 5( 2 ( . ( 6 UI /
PCA
( N/ ^ O1(
./ ( > 6+ 1 I / / z8 G ^ z8 O1( . '
`1 ( ^ -G1 > JN+ / /
./ 21( ( z8 '
]
15
[
N/ ^ . `1 (
( K g ‚ +( (D / D + … /
.R`1 6+ ) ( `1 ./ 1 I z8
. '
) Y0 11 G2E / ( N/ ( (5( G ( `1 1 N/ dg( 1 .H (
./ J1 + ( 61 > Y' .2 / .> +3 ( N/ ^ G _5t .
G' ( 'c
PC 1
- ( JC `1 ( N/ G o /
PC 2
G o /
-_ ^ JC `1 ( N/
PC 3
_ JC `1 ( N/ G o /
PC 4
.E D+ S G G' _ JC `1 ( N/ G o / D + ) Y0 11 ( J1 + ( . +(
./ `1 ( N/ G' + / ( Y1 Z G N+ 5( ( JC
/ 6 UI
EEG
G+ 6 1( (=E . ( ‚ +( ( N/ G ( (
./ ( 6 G'
( d A A ( (
. ' . R d15 ( ( i UI / Y1 Z .0 \(5 / G N+ 5( G2E / O1( I / ‚ +( (=E . X( W+( 1 5( J .H (
G2E / . ( - 3 … / `1 ( `1 ( N/ O1( s C +(
.R`1 ( g 6+ W ( JC 5( Q( C ( .2 / .> +3
G 8 R K G GNZf g 6+ .R`1 U1 /
./ ( g 2 ( . R
4 * 2 * ' KNN
< ./ ( ,( .E 6^ d O C G (
. /( > b O C /( > O C :5( Zl G' ( ( g l 1 6E(
KNN
d O /( > b O C < U1 ( l G
./ /( . ( .8 L 13 8 1 ( U1 ,( .E 6^ G 3 5( (
GNZf U1 ( l < . + 2 ( D +
KNN
U1 s C +(
/( >
K
GNZf 5( .Z1 N ( l G S / GW2 -O1D
.R`1 1( .R`1 ( D' / G ( ( t ( ' () .1
./ /53 ( 1 1 I G+ R G - 1 +
G' (
K
5( /
G+ + 1( Yi( .R`1 z8 I / + R ( g
]
30
[
.
&4' (
i
ω
.yR`1 ( O y (
x
GyV ( 5( 2 (
-: 15 . t ,(
n i i
K K ) x | (
P ω = (20)
) Y0 11 G2E / 1 N/ 5( S / J1 + :( 5( M> .H (
l(
PCA
..2 / .> +3 1 N/
Fig. (11): The sorted diagram for principle values after applying the PCA on the Negentropy values.
G'
Ki
G+ + ( &4'
i
_(
Kn
G+ + Y' ( I /
./ h+ / G , + GNZf Y l
-./ K => 1
]
30 31
[
.
Gl */ 5( 1 I G+ + ( ,( ( N/ O1( GZ W/ (=E ( ./ - /53 GNZf Y l (
Q( C ( 5( 2 (
6 ( G\( ( .R`1 6 A \4l ,
. ( _ *+( E 4 * 3 * ' H + ,$
%
GH• / GNZf ( . ( (
5( 2 (
KNN
s C +(
S /
K
./
]
31
[
G SI / G h / O1( ( . 5
( G' . '( G GI O q 1 6E( .01 D+ Y E G
.61 5( K 2 / 8 ( N/ ^ - + ( 61 01 G .R`1 1 N/ ( i( GNZf A1 +
3 5( 2 ( ./
) 32 (
) I 1 GNZf J1 /53 A1 + Y/ ( 6
DF/
./ GNZf W ( N/ & ( J1 /53 A1 + . (
( GNZf . ( / ^ O q J1 /53 ./
.
S G / O1( 6+
/ < 1=> ] W
(TP) 38
/
] W
(TN) 39
) + / < 1=>
-FP
(
40
+ /
(FN) 41
./ GNZf ( Y' W | + 5( 2 ( . (
. + .61 /( > ( g Vi . W / . ( i
4 * 3 * 1 * -?% H ! ! P> V $ 0 ,
GZ W/ Vi 5 SI / v R -Q 5 .61 /( > U1 s C +( GNZf K H l 1 6E( 5( 2 (
KNN
./ 5( 2 ( .
G1t U1 HI .ZLl G0Z U1 5( 2 ( O q - >
l g ( -„ Z+ E <5 /3 GNZf Vi G o /
I /
I ) 1 ./ <5( ( +
]
9
[
.ZLl G0Z <5 /3 5( M> .
) Y0 . W / 12
( Vi ( N/ 5( . + .E / ( l G (
.61 /( >
K
. /3 ( i G
( N/ n 5( u U1 h / G
K
W (D /
GNZf ./ -GH / ( + ( ) Y0 (
13 ) Y0 ( 17 ( ( GI
( G ) I I /
1 / G' V+ . + (
./ GNZf
-KNN
(5( G
K=5
GNZf O1 ( i
0H l W (D / 5379
/ 76 ./ + % G+ R G .
( G' (
.61 1 N/ 5( ' 1
5 0H l W ( N/
GNZf ./ J ' . 1
) Y0 12 . + . W / :( .61 /( > (5( G Vi
.)H C/
Fig. (12): Interpolated curve of error values for different neighborhood parameters.
) Y0 13 ( N/ :(
TP
)H C/ 1 N/ (5( G
K
.
Fig. (13): TP values for different K.
Y0 ) 14 ( N/ :(
TN
)H C/ 1 N/ (5( G
K
.
Fig. (14): TN values for different K
) Y0 15 ( N/ :(
FP
)H C/ 1 N/ (5( G
K
.
Fig. (15): FP values for different K.
) 33 (
Table (1): Performance of seizure and non-seizure signals classification.
) I 1 GNZf 0H l (D / :( 6
A A ( (
.
A0!0 D C % ' 0 L#? WV
KNN (%)
K TP
TN FP
FN . WV
. P>
A0!0 ?Q
1
3 11.0157 64.5207
17.5966 6.8670
75.5365 24.4635
A0!0 ?Q
2
5 11.0157 65.5222
17.5966 5.8655
76.5379 23.4621
A0!0 ?Q
3
7 9.8712 65.2361
18.7411 6.1516
75.1073 24.8927
A0!0 ?Q
4
9 9.1559 66.3805
19.4564 5.0072
75.5365 24.4635
A0!0 A , B H
A0!0 W -% ( Y'
( .l (
E G
Vi O 6+ /
+ ,$ 0! M %
12480 2040
10440 76.5379
24.3208
+ ,$ C %
6240 GN g 1020GN g
5220GN g
KG
Vi M+ 1 (
+ ,$ 0 %
100% 16.3%
83.7% 5
0.3685
) Y0 16 ( N/ :(
FN
)H C/ 1 N/ (5( G
K
.
Fig. (16): FN values for different K.
) Y0 17 G Y' W ( N/ :( )H C/ 1 N/ (5(
K
A B C G
1 6E( GH
KNN
.
Fig. (17): Total accuracy for different K in seizure detection by KNN algorithm.
4 * 3 * 2 * 3! 0
9 $#-42
.61 /( > ( /3 G A1 + G GI
K
/
-./ (5( G G'
5
K =
GNZf A1 + O1 6
./ G DF/ -GE N/ O1( G\( ( .R`1 I . 13
( l G .R`1 O1( . ( z8 U1 -.R`1 z8 G2E / .R`1 GW2 ) K L C/ GW2 l .N8( ( (
6 ./ W/
./ GZ +
]
30
[
O1( G' ( 'c G _5t .
J `> 70 ( % GNZf <5 /3 (
30 3 % h / G
. ( G 8 R h+ /53 Q 5
.R`1 X / 5( &4' U1
6
EEG
) Y0 I / T+ D/ g o N+ . ( 18
Q 5 -(
.R`1 ( GZ W/ 30
5( G+ + 6
EEG
.
GH 8 . Hg( G GW2 I / o N+ .R`1 o N+ ./ (5(
.R`1 ./ GZ W/ .61 /( > O 8 R h+ .
5
) GV ( I / ,( GZ W/ 20
.R`1 GW2 -( Y0 x V/
) 18 G , + ( ./
_( R 1 v ,4V ( ( Y0 O1( . .1 +
–
./ O H 1 R
]
30 31
[
6 &4' . A ( (
6 61 01 5( ' i T+ 5( 2 ( D + A
./ / . ( ( I G , + L 5 / G'
G / (
D/ g o Vi Y0
) 18 ( ./ .R`1 GW2 G
3
N G , + / , . (
1 I 6 U1
.R`1 Q( C ( ./ - 3 5( G\( (
O1( G' + . (
.R`1 G , + G^ ./ ( g (
L (=E . + R 1 I ( R
. ( _ *+( Y g .+ 3 G 6 U1 A I _ l
5 * Q$H ZV $
D E +3 6
EEG
B C /3 ' (D ( U1 ( l G
GI . ( .l A G
+ . + ' 8 I / 1
) 34 (
GH , M+ ' 8 > u 3 8 O q ./ -A
1 (
<5( > ( ( / R DF/ G /5 h+ /
A B C
( C ( . +( S / .R`1 Q
+ G' .1 GZ I _
6 O1( (=E . ( ( D\ , - J1 /53 /
J `> <4 ( .R`1 Q( C ( K 2
.H' 5( 8
6 .0 ( .0 / 1 G GI .8 f 5( . J > (
B C 1 6E( ' J > G /5 G\( ( A
. -.
.R`1 ( . Z W/ GZ / t .0 H' <5 ( .1
O 1 > G\( ( + . ( O1( h / 5( .R`1 /3 .R`1 .1
Y1 Z . Z/ /5
–
2 ( M+ ' 8 (
. G\( ( G N+
DF/ 1 ( UI / Y1 Z ./ / R
( .Z / / +(
6 I / O 0 o N+ J1 +
EEG
N .
.R`1 Q( C ( 5( /3
15 UI / G N+ 5( 1 L
./ i( O 0 o N+ d15 G /5 ( 2/ K l4f( . (=R
) Y0 18 .1 + _( R 1 :( –
H ( O 30 6 5( G+ + . DF/
Fig. (18): Voronoi-Tessellation diagram for 30 sample of EEG signals
< 5( 2 (
PCA
s C +( .R`1 /3 ‚ +( ./
+(
1 6E( 5( 2 ( . J1(D8( ( B C | + W
EMD
K ZH .2 f D E +3
–
. * < U1 ( l G T+3
./ -Y1 Z . Z/ GZ I +(
d ( . + ' 8 8 5( 61 (
+5 G\( ( (=E . / R 6 .R`1
SFWM DSF
6 5( Y/ ' .2 ( <4 -GE N/ O1( ( (
. .8 / E A Q( C ( 5( M>
.R`1 GNZf (
-( G\( ( J1 /53 GNZf U1
B C ( 1 <5 /3
G+ + GNZf 1 6E( 5( 1 I
K
U1 D+ G1 O1
GNZf 5( .Z1 N ( l G < O1( . ( 2 ( G O1D
f ( 2 ( H g - W/ .61 /( > U1 (5( GNZ
( ./ ( ( ( 5( +( 5( J .R q > '( .1 ^ .
.R`1 U 02 5( GE N/ O1( I / ( i .Z / 1=>
> .E -< O1( O 1 > . Z W/ G 1D 3 5
./ G I q ( 3 5( 2 ( s C +( . (=E . 1 +
G -S / .61 /( > GNZf O1
| + O1
./ G A ( ( 6 B C W 6+ U1 . 13
./ .H' .R`1 Q( C ( G' + ( G+ 6 1( ( 5( /3
5( ( 2/ K l4f( - / R . + ' 8 + Y1 Z . Z/ 6E( 6 8
EEG
GH , _ 6 ./ + A
O1( .
.R`1 GNZf 5( 2 ( /3
KNN
M+ 1 ( W
./ B C ( .l A .E Zg Y g Vi .
:W
1- Electroencephalogram 2- Epoch
3- Kurtosis 4- NegEntropy
5- Principle Component Analysis 6- Empirical Mode Decomposition 7- Intrinsic Mode Function 8- K-Nearest Neighbor 9- Seizure
10- Epilepsy
11- Evoke Related Potential 12- Generalizability 13- Offline 14- Online 15- Residue
16- Electrocardiogram 17- Electrooculogram 18- Band Pass Filter 19- Finite Impulse Response 20- Wide Sense Stationary 21- Mean - Ergodic
22- Map of Wavelet Transform 23- Modulus-Maximas 24- Daubechies 25- Cone of Influence 26- Sub-Gaussian 27- Platykurtic 28- Super-Gaussian 29- Leptokurtic
30- Statistical Feature of Wavelet Map 31- Hilbert – Huang Transform 32- Sifting Process
33- Monotonic
34- Hilbert Spectral Analysis 35- Cauchy Principal Value 36- Water-Fall
37- Distance Spectral Feature 38- True Positive
39- True Negative 40- False Positive 41- False Negative
) 35 ( References
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[9] E. Ubeyli, I. Guler, “Detection of electrocardiographic changes in partial epileptic patients using Lyapunov exponents with multilayer perceptron neural networks”, Engineering Applications of Artificial Intelligence, Vol. 17, No. 6, pp. 567-576, Sep. 2004.
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