TELKOMNI
KA
ISSN:
1693-6930
■
Modula
r
Network SOM (m
nSOM): A Ne
w Powe
rful T
ool …… (M.
Aziz Mu
slim
)
169
MODULAR NETWORK SOM (M
NSOM): A NEW
POWERFUL TOOL IN NEURAL NETWORKS
Muhammad Azi
z
Muslim
Electri
c
al Eng
i
neeri
ng Dep
a
rtment, Bra
w
ijaya University
Jl. MT Ha
ryo
no 167, Mala
ng 651
45, Ind
one
sia, Phon
e/fax: (0341)
5541
66
Email: muhazizm
@
gmail.
com
Abs
t
rak
Pada pa
per i
n
i dipe
rkenal
kan
su
atu arsitektu
r
ba
ru
dalam
jaring
a
n
syaraf tirua
n
, yan
g
dise
but seba
gai m
odula
r
netwo
rk SOM
(m
nSOM).
m
n
SOM
adal
ah
suatu gen
erali
s
a
s
i
da
ri Self
Orga
nizi
ng
M
aps (SO
M
) yang
dibe
ntuk den
gan
m
e
n
gganti
unit-u
n
it nod
e p
a
d
a
SOM
de
ng
an
m
odul-m
odul
fungsi. M
o
d
u
l fung
si ini
dapat b
e
ru
p
a
su
atu m
u
lti laye
r pe
rce
p
tron, recurren
t
neural n
e
two
r
k
atau
bah
kan SOM
itu
sen
d
iri. Ka
re
na m
e
m
iliki fleksibilita
s
ya
ng
sang
at tin
ggi,
m
a
ka m
n
SOM m
enjadi tool yan
g
sa
ng
at berm
anfaa
t dalam
bidang jaring
an syaraf tirua
n
.
Kata kunci
:
m
odul-m
odul fungsi, ge
neralisa
s
i da
ri SOM, m
n
SOM
A
b
st
r
a
ct
In this
pap
er, a ne
w
po
werful
m
e
tho
d
in
artificial
neu
ral networks, calle
d m
odular
netwo
rk SO
M (m
nSOM) is introd
uced.
m
n
SOM is
a gene
ralization of Self
Orga
nizi
ng M
aps
(SOM) fo
rm
ed by re
pla
c
in
g each ve
ctor unit of SO
M
with functio
n
m
odule. The m
odular fun
c
tion
coul
d be a m
u
lti laye
r pe
rceptron, a re
curre
n
t neu
ra
l netwo
rk o
r
eve
n
SOM itself. Ha
ving t
h
is
flexibility, m
n
SOM becom
es a
new powerful tool in ar
ti
ficial neural network.
Key
w
ords
: f
unctio
n
m
odules, gen
erali
z
ation of SOM, m
n
SOM
1. INTRO
DUCTIO
N
Artificial Neural Net
w
orks,
comm
only referred
a
s
“Ne
u
ral
Networks” i
s
o
ne of t
he majo
r
research areas i
n
artificial in
telligence. Using neural net
works,
sci
entist
s
try
to solve many
probl
em
s by
mimicking
le
arnin
g
m
e
ch
anism
of
h
u
m
an b
r
ai
n.G
enerally spea
king, th
ere
a
r
e two
major le
arni
n
g
strate
gie
s
of neural net
works. Fi
rst is su
pe
rvise
d
learni
ng. Mult
ilayer pe
rcept
ron
and
Radi
al
Basis Fun
c
ti
on a
r
e exam
ples
of famo
us n
e
u
r
al n
e
t
works archit
ecture
whi
c
h
are
trained in
supervi
sed
way. The later is un
s
u
p
e
rvise
d
lea
r
ning. The
most succe
s
sfu
l
unsupe
rvise
d
learne
d network i
s
Koho
ne
n m
odel of Self Organi
zin
g
Maps
(SO
M
) [1].
SOM ca
n onl
y deal with ve
ctori
z
ed
data.
To co
pe with
this difficulty, many modifi
cation
s
to
the stand
ard algo
rithm
have been
prop
osed
[1].
Most
of the
modification
is
by chang
ing
comp
etitive process o
r
ad
aptiv
e pro
c
e
s
s in the stan
dard SOM al
gorithm. In 2
003, Tokuna
ga
et.al. [2] prop
ose
d
a
gene
ralizatio
n of S
O
M alg
o
rithm
calle
d mo
dul
ar n
e
two
r
k SOM (m
nSOM
).
The idea i
s
q
u
ite simple: repla
c
e ea
ch
nodal u
n
it
in SOM by a function mo
dul
e. By choosin
g an
approp
riate f
unctio
n
mo
d
u
le a
c
cording
to the ta
sk,
the mnSOM
deal
s
with n
o
t merely vector
data but also deal
s with
function
s, systems
an
d manifold
s. By employing
a multi layer
percept
ron
(MLP) fo
r exa
m
ple, the
mn
SOM lea
r
n
s
i
nput-o
utput
relation
s a
s
a
set of fu
nctio
n
an
d
simultan
eou
sl
y generate
s
feature m
a
p
s
rep
r
e
s
entin
g the relatio
n
s.
This
pap
er
aims to int
r
od
u
c
e m
n
SOM a
nd di
scus
s it
s further ap
plication. The
re
st of this
pape
r is
org
a
n
ize
d
a
s
follo
ws. Se
ction II briefly
explai
ns a
r
chitectu
re and al
go
rithm of mnSO
M.
Suc
c
ess
f
ul applications
of mnSOM are given in
Sec
t
ion III. Finally Sec
t
ion IV c
o
nc
ludes
t
he
pape
r by discussion of futu
re re
se
arch di
rectio
n on mn
SOM.
2. THE
MN
SOM
mnSOM is a
n
extensio
n of SOM in which e
a
ch vector u
n
it is repla
c
ed by functio
n
module. Stud
ying the mn
SOM mean
s studying SO
M more d
e
e
p
ly. In this section the
o
re
tical
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ISSN: 1
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0
TELKOM
NIKA
Vol. 7, No. 3, Desem
b
e
r
2009 : 169
- 174
170
asp
e
ct of m
n
SOM will b
e
discu
s
sed
briefly,
starts from b
r
ief
explanation
on SOM theory
followe
d by discussio
n
on
mnSOM.
2.1. Self Organizing Map
s
[1]
The p
r
in
cipal
goal of
self
-o
rgani
zin
g
ma
ps i
s
to t
r
an
sform
an in
co
ming
sign
al p
a
ttern of
arbitrary dim
e
nsio
n into o
n
e
or t
w
o dim
e
nsio
nal di
scre
te map a
nd t
o
pe
rform thi
s
tra
n
sfo
r
mati
on
adaptively in a topologi
call
y ordered fashion, as
sho
w
n Fig. 1.
Fig.1 Kohon
e
n
model of SOM
There are two ways to train SOM, on-line lea
r
nin
g
and batch l
earni
ng. Fro
m
weight
adaptatio
n p
o
int of view,
on-lin
e lea
r
ni
ng al
ways
m
a
ke wei
ght
a
daptation on every
sin
g
le data
being
present
ed to t
he
net
work,
on th
e
other ha
nd
b
a
tch l
e
a
r
ning
SOM ma
ke
weight a
daptati
o
n
after all of data being p
r
e
s
e
n
ted to the ne
twork.
SOM algorith
m
con
s
ist
s
of 4 pro
c
e
s
ses [
1
]:
1. Evaluative
Proce
ss
After initializi
ng syna
ptic
weig
hts in th
e netwo
rk, fo
r each input
pattern, the n
euro
n
in th
e
netwo
rk
com
pute their respective value
s
of a discrimi
nant functio
n
.
2
2
1
k
i
k
i
w
x
E
for all
k
(
1
)
In this equati
on,
i
x
and
k
w
are in
put pattern a
nd syna
ptic weight, respe
c
tively
2. Comp
etitive
Process
Usi
ng th
e di
scrimin
ant fu
nction
in e
q
u
a
tion (1) a
s
the ba
si
s for com
petition
among
the
neuron
s, the particula
r neu
ron
with the large
s
t
value
of discrimin
a
n
t function i
s
decl
a
re
d a
s
winn
er
of the co
mpetitio
n. Usi
ng Eu
clide
an
cr
ite
r
ion,
the win
ner of
the competition
i
s
neuron which
gives minimu
m Euclide
an
distan
ce to th
e particula
r in
put pattern.
k
i
k
i
E
k
min
arg
*
(
2
)
3. Coo
perative
Process
Usi
ng the to
pologi
cal nei
ghbo
rho
od centere
d
at the win
n
ing
neuron,
a se
t of excited
neuron
s is de
termine
d
.
On-lin
e lea
r
ni
ng:
)
,
(
*
i
k
i
k
k
h
(
3
)
Batch lea
r
nin
g
:
'
*
'
*
)
,
(
)
,
(
i
i
i
k
i
k
k
h
k
k
h
(
4
)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOMNI
KA
ISSN:
1693-6930
■
Modula
r
Network SOM (m
nSOM): A Ne
w Powe
rful T
ool …… (M.
Aziz Mu
slim
)
171
usin
g Gau
s
si
an neig
hbo
rh
ood fun
c
tion :
2
*
2
*
2
)
,
(
exp
)
,
(
i
i
k
k
l
k
k
h
(
5
)
whe
r
e
)
,
(
*
2
i
k
k
l
is lateral distan
ce to
the winning
neuron. The
para
m
eter
i
s
the effective
width
of the t
opolo
g
ical
ne
ighbo
rho
od.
Usually
the
si
ze
of topol
ogi
cal
neig
hbo
rh
ood
sh
rin
k
s
with time. In t
h
is
case,
can be cho
s
en
in the form of:
)
/
exp(
).
(
)
(
min
max
min
t
t
(
6
)
whe
r
e
is
time c
o
ns
tant.
4. Adaptive
Pro
c
e
s
s
In adaptive process ea
ch
synapti
c
weig
ht of the network were u
p
dated usi
ng the followin
g
equatio
ns:
On-lin
e lea
r
ni
ng:
i
k
i
k
i
k
w
x
w
)
(
(
7
)
is learning
rat
e
para
m
eter,
and this p
a
ra
meter can be
decrea
s
in
g wi
th time such as
)
/
exp(
).
(
)
(
1
min
max
min
t
t
(
8
)
Batch lea
r
nin
g
:
i
i
k
i
k
x
w
(
9
)
whe
r
e
k
i
is normalize
d
neig
hborhoo
d fun
c
tion
state
d
in equatio
n 4.
2.2. Modular Net
w
o
r
k SO
M (mnSOM)
The mnS
O
M
con
s
i
s
t of a
n
array of fu
nction
modul
es o
n
a l
a
ttice. Type
of function
module i
s
d
e
termin
ed by d
e
sig
ner. F
o
r
dynamical
sy
stem, a recurrent ne
ural n
e
twork
(RNN) is a
good
can
d
ida
t
e [3]. An example of the
architectu
re
of mnSOM with RNN mod
u
les i
s
sho
w
n in
Fig. 2.
Fig 2. mnSO
M architectu
re [4]
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 1
693-693
0
TELKOM
NIKA
Vol. 7, No. 3, Desem
b
e
r
2009 : 169
- 174
172
A learni
ng
al
gorithm
of m
n
SOM i
s
si
mi
lar to th
at of the bat
ch l
earning SOM. It
con
s
i
s
ts
of four pro
c
e
s
ses [2][3]: evaluative, co
mpetitiv
e, cooperative and
adaptive
pro
c
e
s
ses. Let a
set
of input
-outp
u
t sig
nal
s
of
a dyna
mical
system
be
L
j
M
i
y
x
ij
ij
,
,
1
;
,
,
1
,
, where
M
and
L
are the
numbe
r of data cla
s
ses a
nd the numb
e
r
of each data
in each
cla
s
s, respe
c
tively.
1. Evaluative
proce
ss
Inputs
ij
x
are
entered to
all mod
u
le
s, and th
e
corre
s
p
ondin
g
output
s
)
(
~
k
ij
y
are
evaluated by:
2
1
)
(
)
(
~
1
L
j
ij
k
ij
k
i
y
y
L
E
(10
)
L
j
M
i
K
k
,
,
1
;
,
,
1
;
,
,
1
whe
r
e
k
sta
n
d
s for th
e mo
dule nu
mbe
r
,
K
stand
s for the numb
e
r
of module
s
,
i
st
and
s f
o
r
the numbe
r o
f
data classe
s, and
j
stand
s for the data
numbe
r in ea
ch cl
ass.
2. Comp
etitive
process
The mod
u
le
with the mini
mum
)
(
k
i
E
with res
p
ec
t to
k
is the win
ner fo
r data cla
s
s
i
.
)
(
*
min
arg
k
i
k
i
E
k
(11
)
3. Coo
perative
pro
c
e
s
s
Learning rate
s of the mod
u
les a
r
e dete
r
mine
d by the following n
o
rmali
z
e
d
nei
ghbo
rho
od
function:
T
t
t
v
k
r
t
v
k
r
t
M
i
i
i
k
i
,...,
1
;
)
);
,
(
(
)
);
,
(
(
)
(
1
'
*
*
)
(
(12)
)
(
2
exp
)
;
(
2
2
t
r
t
r
(13)
t
e
t
)
(
)
(
min
max
min
(14)
whe
r
e
)
,
(
2
1
k
k
r
stan
ds fo
r the
di
stan
ce b
e
twe
en mo
dule
1
k
a
nd mo
dule
2
k
,
t
is the
iteration num
ber in mnSO
M, T is t
he numbe
r of iterations in mnS
O
M,
min
is the minimum
neigh
borhoo
d
size,
max
is the
maximum n
e
i
ghbo
rho
od
si
ze, an
d
is
a neig
hbo
rho
od
decay
rate. mnSOM
term
inates whe
n
no
si
gnifi
ca
nt cha
nge i
s
o
b
se
rved in th
e re
sulting
map.
4. Adaptive
Pro
c
e
s
s
Suppo
se th
at RNN i
s
em
p
l
oyed a
s
fun
c
tion m
odule,
con
n
e
c
tion
weig
hts a
r
e
modified by
Backpropa
ga
tion Thro
ugh
Time (BPTT)
learni
ng a
s
follows,
M
i
k
k
i
k
i
k
E
t
1
)
(
)
(
)
(
)
(
)
(
w
w
(15)
whe
r
e
)
(
k
w
is
the con
n
e
c
tion weights
i
n
mod
u
le
k
.
Fi
g.
3 summ
ari
z
e
s
a
learning al
gorithm
of mnSOM.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOMNI
KA
ISSN:
1693-6930
■
Modula
r
Network SOM (m
nSOM): A Ne
w Powe
rful T
ool …… (M.
Aziz Mu
slim
)
173
3. SUCCESS
FUL APLI
CATIONS OF
MN
SOM
Since int
r
od
u
c
ed i
n
20
03,
mnSOM h
a
s
applie
d in
wi
de a
r
ea
s. To
kun
aga
et.al.[3] use
d
mnSOM
with
MLP mod
u
le
s to ge
nerate
map of
we
ath
e
r of
Japan
b
a
se
d o
n
mete
orolo
g
ical d
a
ta:
atmosp
he
ric
pre
s
sure, tem
peratu
r
e, h
u
m
idity and
su
nshi
ne h
ours.
Usi
ng the
re
sulting
map, t
hey
can p
r
edi
ct weather
cha
r
a
c
te
ristic
of unknown pla
c
e
s
.
Fig. 4 Control
l
er for AUV[9]
base
d
on
mnSOM.
Fig. 5 Face M
aps G
ene
rate
d by SOM
2
[11]
T. Minatohara et.al.[13] first appli
ed
mnSOM
in control with t
heir propo
sal
of Self
Orga
nizi
ng A
daptive Co
ntrolle
r (SOA
C) for cont
rolli
ng inverte
d
pend
ulum. O
ne year late
r,
S.Nishid
a
et.al. [9] propo
sed m
n
SOM t
o
contro
l their “Twi
n Burg
er” Auton
o
m
ous Unde
rwa
t
er
Vehicle
(A
UV
). Fig.4
depi
cts the
structu
r
e, a
nd F
a
ce
Map
s
Gen
e
rated by S
O
M
2
in Fig.5
sta
nd
for
Fo
rward Model Mod
u
les and
Controller Modul
es,
re
spe
c
tively. M. Aziz Mu
slim et.al. [4
-8]
prop
osed ta
sk
seg
m
entati
on in
mo
bile
ro
bot by
mn
SOM follo
we
d by a
g
r
ap
h
-
map
ap
pro
a
c
h.
Acco
rdi
ngly complex navig
ation task of mobile
robot
can b
e
simplif
ied to some e
x
tent.
S
pecial m
n
S
O
M cla
ss,
cal
l
ed S
O
M
n
, has bee
n pro
p
o
s
ed by T.Fu
ruka
wa [10]. Here, the
function m
o
dule is SOM itself. Thi
s
is fo
llowe
d by the
prop
osal of
S
e
lf Org
anizi
n
g
Hom
o
topy [11]
claime
d a
s
a
foundatio
n for brain-li
ke int
e
lligen
ce. Ap
plicatio
n of SOM
n
can
be f
ound in [1
2]. In
that paper, S
O
M
2
is used for face
re
cog
n
ition.
Initialization and Initial evaluative process
for t=1 to T
Competitive process (Eq.(11))
Cooperative process (Eqs.(12), (13) and (14))
for p=1 to P
for i=1 to M
for j
=1 to L
fo
r k=1 to K
BPTT lear
ning (Eq. (15))
en
d
end
end
end
end
Fig. 3 Summary of mnSO
M Trainin
g
Algorithm [4]
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 1
693-693
0
TELKOM
NIKA
Vol. 7, No. 3, Desem
b
e
r
2009 : 169
- 174
174
4. CON
C
L
U
D
I
NG REM
A
R
K
S
As a
gen
erali
z
ation
of SO
M, mnSOM i
nher
it
s all
of
advantag
eou
s a
nd di
sa
dvantage
ou
s
of SOM. In a
ddition it al
so
has
advanta
geou
s
ove
r
convention
a
l SOM, sin
c
e
m
n
SOM can d
eal
with un-ve
cto
r
ize
d
data.
Many fun
c
tio
n
mod
u
le
s h
a
ve be
en tri
ed
su
ccessfu
lly, such a
s
Elman n
e
two
r
ks, fully
con
n
e
c
ted RNN, MLP, Neural G
a
s an
d SOM it
self. Howeve
r, st
ill so many neural n
e
two
r
ks
architectu
re
remain
untou
ched, for exa
m
ple radial
b
a
si
s fun
c
tion
s family. It is a
l
so inte
re
stin
g to
inclu
de sto
c
h
a
stic p
r
o
c
e
ss
in the functio
n
module of
mnSOM.
Re
cent a
ppli
c
ation
of mn
SOM deal
s
with off-lin
e
data only. It is challe
ngin
g
to u
s
e
mnSOM in re
al-time. Altho
ugh
current v
e
rsi
on of mn
SOM algo
rith
m doe
s not p
r
ovide
with th
is
capability, we believe that
by
minor m
o
dification on the
st
andard algorithm,
m
n
SOM can
deal
with real
-time
data. As a relatively new
appro
a
ch, mnSOM still has ma
ny open que
stion
s
to
answe
r
an
d has wide app
lication
a
r
e
a
whi
c
h
is re
m
a
in untou
ch
e
d
. Hen
c
e, extensive
re
sea
r
ch
on mnSOM i
s
our co
mmon
task.
REFERE
NC
ES
[1].
T. Kohonen, “
Self-Or
g
anizing Maps
,” S
p
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95
[2].
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T. Furukawa
, and S. Ya
sui, ''
Modular
Net
w
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r
k
SO
M: Ex
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n of S
O
M
to th
e real
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OM) fo
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a
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Ishika
wa, and
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A Ne
w
Appro
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Segmenta
tio
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in Mobile Robo
ts by
mnSOM
," Proc. of 2006 I
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u
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b
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and Hiera
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iz
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k
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m
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t b
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i
th Spa
t
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Co
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r
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e
cture Note
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O
Ms"
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-
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a
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o
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k
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