TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 8, August 201
4, pp. 6324 ~ 6331
DOI: 10.115
9
1
/telkomni
ka.
v
12i8.461
7
6324
Re
cei
v
ed O
c
t
ober 3, 20
13;
Revi
se
d March 7, 201
4; Accepted Ap
ril 2, 2014
Cliques-based Data Smoothing Approach for Solving
Data-Sparsity in Collaborative Filtering
Yang Yujie*, Zhang Zhiju
n, Duan Xintao
Coll
eg
e of Co
mputer an
d Informatio
n
Engi
n
eeri
ng, Hen
an
Normal U
n
iv
ersit
y
,
Xi
n
x
i
ang, He
na
n, Chin
a, 453
0
0
7
*Corres
p
o
ndi
n
g
author, e-ma
i
l
:
y
u
j
i
e
y
a
n
g
y
u
j
i
e
@gma
il.com
A
b
st
r
a
ct
Coll
ab
orative
fi
lterin
g (CF
)
, as
a
pers
ona
li
z
e
d rec
o
mmen
di
ng tec
h
n
o
lo
gy, has
b
een
w
i
d
e
ly
us
e
d
in e-c
o
mmerc
e
an
d oth
e
r
ma
ny p
e
rson
a
l
i
z
e
d
reco
mm
end
er are
a
s.
How
e
ver, it s
u
ffers from s
o
me
prob
le
ms, suc
h
as
col
d
start
pr
o
b
le
m,
data
spars
i
ty a
nd
scala
bil
i
ty, w
h
ich re
duce
the
reco
mmend
ati
o
n
accuracy a
nd
user exp
e
ri
enc
e. T
h
is pap
er
ai
ms to so
lv
e the d
a
ta spars
i
ty in CF
. In the pa
per, cli
q
u
e
s-
base
d
data s
m
oothi
ng ap
pro
a
c
h is propos
ed
to alleviat
e th
e data spars
i
ty proble
m
. F
i
rst, users and ite
m
s
are div
i
d
ed i
n
to many cl
iqu
e
s
accordi
ng to
social
netw
o
rk analys
is (SN
A
) theory. T
h
e
n
, data s
m
oot
hin
g
proce
edi
ng is carried
o
u
t
to
fill
th
e missi
ng
ratings in
user-
i
tem ratin
g
mat
r
ix bas
ed
on t
he us
er a
nd
ite
m
cliqu
e
s. F
i
na
ll
y, the traditio
nal us
er-b
ase
d
ne
ar
est ne
i
ghb
or reco
mme
n
d
a
tion
al
g
o
rith
m is us
e
d
to
reco
mme
nd ite
m
s for
users.
T
he exp
e
ri
me
n
t
s show
that the pro
pos
ed
ap
proac
h
ca
n effectively
i
m
prov
e
the accuracy a
nd perfor
m
anc
e on spars
e
da
ta.
Ke
y
w
ords
: dat
a sparsity, coll
abor
ative f
ilteri
ng, cliq
ue, soci
al netw
o
rk an
al
ysis, data smo
o
thin
g
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
Colla
borative filtering
(CF) ca
n h
e
lp to
overco
me
"in
f
ormation
ov
erloa
d
" a
nd t
o
provide
person
a
lized
servi
c
e
s
in
social n
e
two
r
king we
b si
te.
Gene
rally sp
eaki
ng, coll
a
borative filteri
n
g
can b
e
cate
g
o
rized into m
e
mory-ba
s
ed
algorithm
an
d model
-ba
s
ed algo
rithm
[1]. The CF has
been a
pplie
d
in many areas
su
cce
ssf
ully, such as boo
k site
s, movie site
s and some
e-
comm
er
ce
si
t
e
s [
2
]
.
How
e
v
e
r,
t
he CF
also
suf
f
e
r
s
f
r
om a lot
of
issu
es,
su
ch a
s
c
o
ld s
t
art
probl
em, data
sparsity and
scalability [3].
This pape
r
a
i
ms
to solve the
data spa
r
sity
problem
. Data
spa
r
si
ty problem
will occu
r
whe
n
eithe
r
few rating
s are available fo
r the a
c
ti
ve user, o
r
for th
e target item
that predi
cti
o
n
refers
to, for the entire us
er-item
rating matrix
in
a
v
erage
[4]. The existin
g
solution
s of d
a
ta
spa
r
sity incl
ude dime
nsi
onality redu
ction te
chni
qu
e [5], data
smoothi
ng te
chni
que[6] a
n
d
asso
ciative retrieval techn
i
que [7] etc.
Paper
[8] p
r
o
posed a
novel goal
-ba
s
e
d
hybrid a
ppro
a
ch
to overcome
the cold
-st
a
rt p
r
oble
m
in e-l
ear
ning
intern
et. And it also h
e
l
ps to i
m
pro
v
e
colla
borative filtering usi
n
g
k-ne
are
s
t nei
ghbo
r as
nei
g
hborhoo
d
coll
aborative filte
r
ing
(NCF) an
d
conte
n
t-ba
se
d filtering a
s
content
-ba
s
ed coll
abo
rati
ve filtering (CBCF
)
. Pape
r [9] propo
se
d a
so
cial re
com
m
ende
r syste
m
that follows use
r
’
s
pref
eren
ce
s to provide re
com
m
endatio
n b
a
se
d
on the
simila
rity among
u
s
ers
parti
cipa
ting in t
he
social
network. And the ap
proa
ch
whi
c
h
it
prop
osed wa
s ba
sed o
n
integratio
n of major
cha
r
a
c
teristi
cs
of co
ntent-ba
s
e
d
and collab
o
ra
tive
filtering tech
n
i
que
s.
In this p
ape
r, cliqu
e
s-ba
sed d
a
ta smo
o
thing a
p
p
r
o
a
ch
is
propo
sed
to
solve
the data
sparsity probl
em in
collaborative filtering. Firstl
y, user
so
cial net
work a
nd ite
m
so
cial n
e
two
r
k
are
built. An
d then,
users and
item
s a
r
e
divided i
n
to ma
ny cli
q
u
e
s
re
sp
ective
ly acco
rding
to
social network
analysi
s
(SNA). In
order to fill the mi
ssi
ng
ra
tings,
data
smooth
ing operation is
carrie
d out
by usin
g th
ese
cliq
ue
s. Finally
, the
traditional
use
r
-ba
s
e n
eare
s
t nei
gh
bor
recomme
ndat
ion al
gorith
m
is u
s
e
d
to
re
commen
d
item
s fo
r u
s
e
r
s. T
he exp
e
rim
e
n
t
s indi
cate
th
at
this novel ap
proa
ch
can ef
fectively improve
the reco
mmend
ation
accuracy an
d
performan
ce
.
The rem
a
ind
e
r of this pap
er is o
r
ga
nize
d as follo
ws.
In sectio
n 2, we give a bri
e
f survey
of the related
wo
rk on
the
sol
u
tion of
d
a
ta s
parsity i
n
CF. S
e
ctio
n 3 d
e
scribe
s
the
propo
sed
algorith
m
in
detail. Sectio
n 4
presents
the experi
m
e
n
tal re
sults
a
nd an
alysis.
Finally, se
ctio
n 5
gives the con
c
lu
sion.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Cliqu
e
s-ba
se
d Data Sm
oothing App
r
oa
ch for Solvin
g Data-S
parsity in… (Yang Y
u
jie)
6325
2. Related
w
o
rk
Collaborative filtering recommends items to
u
s
e
r
s acco
rdi
ng t
o
thei
r p
r
efe
r
en
ce
s.
Therefore, a
history dat
ab
ase of u
s
e
r
s'
prefer
en
ce
s must be avail
able. Ho
weve
r, the databa
se
is alway
s
very spa
r
se. This lead
s to the reduction of re
comm
end
atio
n accuracy and
perfo
rman
ce.
Data
sparsi
ty is an
inev
itable p
r
obl
e
m
with all ki
nds
of CF
a
l
gorithm
s. Data
spa
r
sity in
clu
des t
w
o a
s
p
e
cts. O
n
the
one h
and,
t
he num
be
r
of use
r
ratin
g
is ve
ry sm
all
comp
ared to the num
ber
of items. On th
e other h
and,
the overlap
p
i
ng num
ber
of two user rating
is very fe
w. There a
r
e m
any re
sea
r
ch
ers who
h
a
ve
focu
sed
on t
he data
sp
arsity pro
b
lem
and
prop
osed so
me solutio
n
s.
Dimen
s
io
nalit
y reductio
n
tech
niqu
e, su
ch as p
r
in
cipl
e comp
one
nt analysis (P
CA) [10]
and
sing
ular value de
co
mpositio
n (S
VD) [11], i
s
comm
only u
s
ed to alleviat
e data
spa
r
sity.
Referen
c
e [5]
combi
ned th
e SVD and it
em-b
ased re
comm
end
er i
n
CF. It utilized the results of
SVD to fill th
e missin
g ratings an
d then
used the
tra
d
itional item
-based m
e
tho
d
to recomm
end.
This
combi
n
a
t
ion method
can in
crea
se
the accura
cy of system. Referen
c
e [1
2] investigate
d
a
hybrid re
co
m
m
endatio
n method whi
c
h
wa
s based
o
n
two-stage
data pro
c
e
s
si
ng-d
ealin
g wi
th
conte
n
t features
de
scribin
g
items an
d
handin
g
user be
havioral
data. This
hybrid meth
o
d
combi
ned
ra
ndom i
ndexin
g (RI) te
ch
ni
que
and SV
D to
pre
p
ro
cess the
cont
ent features.
The
experim
ents
improve
d
the
re
comm
end
ation a
c
cu
ra
cy with
out in
cre
a
si
ng th
e
com
putation
a
l
compl
e
x
i
t
y
.
Data sm
oothi
ng tech
niqu
e is the most u
s
ed me
th
od to solve the d
a
ta spa
r
sity p
r
oble
m
in CF. Va
rio
u
s
spa
r
sityme
asu
r
e
s
[13]
were u
s
e
d
to
enha
nce a
c
curacy
of CF
. These
spa
r
sity
measures we
re
com
puted
based
on l
o
cal an
d gl
obal
simila
rities.
T
hen, a
n
e
s
tim
a
ting p
a
ra
met
e
r
scheme fo
r weig
hting the
various
spa
r
sity meas
u
r
e
s
wa
s propo
sed. The exp
e
rime
ntal re
sults
demon
strated
that the p
r
o
posed
estim
a
te pa
ra
m
e
te
r outp
e
rfo
r
m
the
scheme
s
for which t
he
para
m
eter i
s
kept con
s
tant
on accuracy
of predi
ction rating
s.
Refe
rence
[14] pro
posed a pa
rtial
missi
ng data
predi
ction al
g
o
rithm, in whi
c
h the
inform
ation of both use
r
s a
nd ite
m
s wa
s take
n
into acc
o
unt. In this
algorithm, s
i
milarit
y
thre
s
h
o
l
d
fo
r
us
er
s
an
d ite
m
s
wa
s
se
t r
e
sp
ec
tive
ly, if
and o
n
ly if the interse
c
tion
of the nei
gh
bor
of us
er
a
nd the n
e
igh
bor
of item is not empty, the
missi
ng
data
will be
p
r
edi
cted. An it
erative pre
d
ictio
n
method [1
5]
wa
s p
r
op
ose
d
to alleviate
the
spa
r
sity probl
em in CF.Thi
s metho
d
clu
s
ters t
he u
s
e
r
and item re
spe
c
tively by using
spe
c
tral
clu
s
terin
g
al
g
o
rithm. Th
en,
the iterative
predi
ctio
n
techniqu
e is u
s
e
d
to convert
u
s
er-item
sp
arse
matrix to d
e
n
s
e
one
ba
se
d on
the expl
icit rati
n
g
s. M
o
reove
r
, clu
s
ter-ba
sed
sm
oothing
meth
od
[16], suppo
rt vector ma
ch
ine(SVM) [17
], BP neural
netwo
rks [18]
and ze
ro-su
m
reward a
n
d
puni
shme
nt
mech
ani
sm[1
9] are
also a
pplied to
sm
ooth the mi
ssing
ratin
g
s f
o
r the
sol
u
tio
n
of
data sp
arsity in CF.
With the
d
e
velopme
n
t of
social
net
work, so
cial
net
work a
nalysi
s
(SNA) [2
0] the
o
ry h
a
s
been
appli
ed to
re
comm
en
der syste
m
s. Referen
c
e
[2
1] pro
p
o
s
ed
to u
s
e
so
cial
netwo
rk to
so
lve
data sparsity probl
em in o
ne-cla
ss
CF.
It compa
r
ed so
cial
net
wo
rks belon
g
to spe
c
ific dom
ains
and the o
n
e
s
bel
ong to
more
gene
ri
c domain
s
in
terms
of their u
s
ability i
n
one
-cl
a
ss
CF
probl
em
s. Asso
ciative
retri
e
val techniq
u
e
was ap
p
lie
d to all
e
viate
the
spa
r
sity probl
em i
n
CF.
[22] gives a
social n
e
two
r
k rep
r
e
s
entati
on for
CF re
c
o
mmen
der
sy
st
em
s.
I
t
sho
w
s
som
e
of
t
h
e
advantag
es and re
sults
that
c
an b
e
obtaine
d ap
p
l
ying SNA.
Referen
c
e [2
3] gave a
b
ook
recomme
ndat
ion ba
sed o
n
web
so
cial
netwo
rk. It analyzed the
probl
em of trust in so
cial
netwo
rk
an
d prop
osed a
recom
m
en
der syste
m
mo
d
e
l ba
se
d on
social
net
work tru
s
t. Refe
re
nce
[24] pre
s
ent
ed a fra
m
e
w
ork of
re
co
mmend
atio
n
s
based on i
n
formatio
n n
e
twork a
naly
s
is.
Referen
c
e [2
5] propo
se
d a new weigh
t
ing me
thod
in netwo
rk-b
ase
d
re
com
m
endatio
n. This
method
pre
s
ents a
ne
w
expre
ssi
on
of initial re
so
urce di
stri
butio
n and
takes
into acco
unt
the
influen
ce of reso
urce a
s
so
ciated
with re
ceiver n
ode
s.
In this pap
er,
clique
s-ba
se
d data smoot
hing te
chniq
u
e
is p
r
op
ose
d
to solve th
e data
s
p
ars
i
ty problem in
CF. Firs
t, the s
i
milarity of
use
r
an
d item is co
mputed
re
sp
ectively and
the
use
r
a
nd ite
m
so
cial
net
works a
r
e
b
u
ilt ba
sed
t
h
e simil
a
rity.
Then, all
u
s
ers an
d item
s a
r
e
divided into
many cli
que
s acco
rdin
g to
SNA theo
ry.
The mi
ssing
ratings of testi
ng u
s
e
r
s will
be
predi
cted. T
h
i
s
predi
ction
will take i
n
to
account
both
user and item. The predi
ction values f
r
om
use
r
and ite
m
are wei
ght
ed togethe
r a
s
the smo
o
thi
ng value. Fin
a
lly, the traditional user-ba
s
e
nearest
neig
hbor re
co
m
m
endatio
n al
gorithm i
s
u
s
ed to
re
co
mmend ite
m
s for
user.
The
experim
ents demon
strat
e
that the prop
osed
algorithm
is effectively improvin
g th
e
recomme
ndat
ion accu
ra
cy.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 8, August 2014: 632
4 –
6331
6326
3. Cliques-b
ased Data Smoothing Al
gorithm
The a
ppli
c
ati
on of
so
cial n
e
twork
analy
s
is t
heo
ry in recom
m
en
der system
s i
s
b
e
comi
n
g
more
an
d m
o
re i
m
po
rtan
t. The pote
n
t
ial user
rel
a
tionship
ca
n be
mine
d
to re
co
mm
end
informatio
n o
r
item
s fo
r
use
r
s.
The
most
co
ntrib
u
tion of
this pap
er is p
e
rform
m
ing
data
smoothi
ng by
mean
s of
cli
que
s of u
s
er
and item
tog
e
ther. Th
e smoothing
rati
ng matrix i
s
u
s
ed
to the reco
mmend
ation.
This
re
com
m
endatio
n alg
o
rithm
ca
n i
m
prove
the
recomme
ndat
ion
perfo
rman
ce effectively.
3.1. Building Social Net
w
ork
A netwo
rk is com
p
o
s
ed
of node
s
an
d the re
latio
n
s a
m
on
g n
ode
s. Formal
ly, let us
con
s
id
er a n
e
t
work a
s
a g
r
aph
G=
(U
,E)
in
whi
c
h
U
re
pre
s
ent
s no
d
e
s an
d
E
re
prese
n
ts lin
ks. I
n
this pa
per, th
e users o
r
ite
m
s r
epresent
the nod
es
a
nd, the simi
l
a
rities
a
m
on
g use
r
s or
item
s
denote the rel
a
tions. We wi
ll build the user so
cial
n
e
twork a
nd item
so
cial net
work re
spe
c
tively.
In order to b
u
ild the
user
re
lation n
e
two
r
k,
firstly,
we n
eed com
pute the
si
milarity among
each pai
r u
s
e
r
s. A
s
sume t
hat
U=
{u
1
,u
2
,...,u
N
}
denote
s
t
he set of u
s
e
r
s,
P=
{p
1
,p
2
,...
,p
M
}
for the
set
of items,
an
d
R
as
a
n
N×
M
matrix of
ratings r
i,j
, with
i
∈
1,...,
N, j
∈
1,...,M
. The
r
e
are
many
algorith
m
s to
dete
r
mine
t
he
simila
rity among
u
s
e
r
s:
Pearson
'
s correl
ation coefficient, co
sine
simila
rity, and adju
s
ted
cosin
e
mea
s
u
r
e [26] a
nd
so o
n
. In the
pape
r, Pea
r
son'
s
co
rrelation
coeffici
ent is
use
d
. So, the similarity bet
wee
n
user
u
i
and
u
j
is
as
follows
:
,,
22
,,
[(
)
*
(
)
]
(,
)
()
*
(
)
uu
ij
uu
ij
ip
i
j
p
j
pP
P
ij
ip
i
j
p
j
pP
P
rr
r
r
si
m
u
u
rr
r
r
(
1
)
Whe
r
e
i
r
and
j
r
corre
s
p
ond
s
to the averag
e rating of u
s
er
u
i
a
nd
u
j
res
p
ec
tively.
i
u
P
denote
s
the item set of user
u
i
rating.
j
u
P
denote
s
the item set of user
u
j
rating. In prac
tice, becaus
e
the
amount of ite
m
s is ve
ry large, use
r
s ma
y only
rate few items. Th
e
numbe
r of o
v
erlappi
ng item
among
u
s
ers
may be ve
ry few. Thi
s
l
ead
s to th
e ina
ccurate
simila
rit
y
. For mo
re
a
c
cura
cy of th
e
s
i
milarity, a parameter
wh
ich
den
otes the ove
r
lap
p
in
g nu
mbe
r
of
rating
bet
wee
n
two
u
s
e
r
s
will be ad
ded
to adjust. So, the impr
ove
d
formula i
s
as
follows:
'
(,
)
,
(,
)
0,
ij
ij
si
m
u
u
T
sim
u
u
T
(
2
)
Whe
r
e
T
is a
threshold val
ue. The large
r
of the value
T
,the more ac
curac
y
of the s
i
milarity.
The buil
d
ing
of item netwo
rk i
s
a
s
sa
me
as
the u
s
e
r
netwo
rk. T
h
e
differen
c
e i
s
that the
similarity of item, rather than
the si
milarity of user,
will be
computed. For the same
reason, a
para
m
eter
which denotes the
overla
ppi
ng num
ber of
rating betwe
en two items
will be
added
to adjust. So, the improve
d
formula i
s
as
follows:
'
(,
)
,
(,
)
0,
ij
ij
s
im
p
p
T
sim
p
p
T
(3)
After comp
uting the simil
a
rity, the similarity
value n
eed
s bina
ry pro
c
e
ssi
ng in
orde
r to
building th
e social
netwo
rk. Con
s
id
erin
g
the cliq
ue
s di
vision (de
s
cri
b
ing n
e
xt section), the bin
a
r
y
threshold
req
u
ire
s
suita
b
le
in orde
r to obtain app
rop
r
i
a
te cliqu
e
s.
3.2. Cliques Div
i
sion
Acco
rdi
ng to
SNA theory, clique
s are some
sub
-
structures
of the netwo
rk. F
r
om the
view of soci
a
l
stru
cture, cl
ique fo
cu
se
s att
ention on
how
soli
dari
t
y and co
nne
ction of
so
ci
al
netwo
rk.
The
gen
eral
defi
n
ition of a
cli
que i
s
simply
a
sub
-
set of
node
s
whi
c
h
are
more
clo
s
ely
tied to each
other than th
ey are to nodes
which ar
e not part of the grou
p. More a
c
curatel
y
, it
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Cliqu
e
s-ba
se
d Data Sm
oothing App
r
oa
ch for Solvin
g Data-S
parsity in… (Yang Y
u
jie)
6327
insi
sts th
at every mem
ber
have a
dire
ct
tie with
e
a
ch
and eve
r
y oth
e
r m
e
mbe
r
. In ou
r a
pproa
ch,
the existing users and item
s will be divi
ded into many cliques respectively.
UCI
NET is a
kind of net
work an
alysi
s
softw
are. I
t
can make all kind
s of netwo
rk
analysi
s
,
su
ch a
s
net
wo
rk stru
ctu
r
e,
centrali
za
tion
and so
on. We
m
a
ke cli
que
s
divisi
on
by
mean
s of UCI
NET in this p
aper.
Comp
ared to
k-m
ean
s cl
u
s
ter al
go
rithm [16], cliqu
e
ha
s many
advantag
es.
On on
e
hand, k-me
a
n
s cl
uste
r divides the
simila
r us
ers into the same
clu
s
te
r, howeve
r
for
oneu
se
r,he/she is divid
ed
only one
clu
s
ter. Intuit
ively, each u
s
e
r
may have ma
ny intere
sts a
nd
they may join
a few
of com
m
unities. So,
the user
sh
ou
ld belo
ng to
several
clu
s
ters. Cliq
ue
s ca
n
avoid this ob
stacl
e
. On
ot
her
han
d, k-mean
s al
gorit
hm requi
re
s t
he
k
less
n
, whic
h
k
d
eno
tes
the numb
e
r o
f
cluste
rs,
n
i
s
the num
be
r of users. In fact, the clu
s
t
e
r num
be
r m
a
y be more than
that of the users.
Ho
wever, c
lique n
u
mb
er can mo
re t
han u
s
e
r
s.
Fi
nally, clique
can also prese
n
t
the user
rel
a
tion better.
It is not o
n
ly con
s
id
eri
ng the di
re
ct relation
ship
s, but al
so
the
transmissio
n relation
shi
p
s.
Sowe clu
s
te
r use
r
s
a
nd items by usin
g
cli
que theo
ry rather than
k-
mean
s clu
s
te
r algo
rithm.
3.3. Cliques-based
Data Smoothing
Becau
s
e
the
overla
ppin
g
numbe
r
of ra
ting items be
tween
u
s
ers
is
small
or
n
one, it
lead
s t
h
e
a
c
c
u
ra
cy
of
simil
a
rit
y
is
v
e
ry
l
o
w.
I
n
order t
o
en
han
ce
th
e a
c
curacy, it
is ne
ce
ssary
to
smooth the m
i
ssi
ng ratin
g
of user-item rating matrix.
In this pap
er,
the predi
ctive value of mi
ssi
ng
rating i
s
from two a
s
pe
cts: u
s
e
r
cliqu
e
s
and item cliq
ues. First, the clique’
s me
mbers of
use
r
and item are colle
cted re
spe
c
tively. Then,
the predictive rating
will be co
m
puted based on
user's
cliques and
item's cliques respectively.
Finally, the weighted value of the two predi
ctive ra
ting will be the
final predictiv
e
value of the
missi
ng ratin
g
. The weig
hted formul
a is
as follo
ws:
()
(
1
)
ij
mi
s
i
j
u
p
Sr
S
S
(4)
()
i
ku
i
ui
k
k
j
uC
Sw
r
(5)
()
j
kp
j
pj
k
i
k
pC
Sw
r
(6)
Whe
r
e
i
u
S
is the
predi
ctive val
ue
whi
c
h
rel
e
vant to the
cliqu
e
s of u
s
er
u
i
.
C
ui
rep
r
esents
the
cliqu
e
s
set
of
use
r
u
i
.
w
ik
is
the simila
rity betwe
en u
s
er
u
i
and
u
k
.
j
p
S
den
otes the p
r
edi
ctive value
according to the clique
s o
f
item
p
j
.C
pj
repre
s
e
n
ts th
e clique
s set of item
p
j
.
w
jk
is the similarity
betwe
en item
p
j
and
p
k
.
is a
significan
c
e
weig
hting factor.
S
mis
(r
ij
)
is
the final smo
o
thing value
of missin
g
rat
i
ng
r
ij
.
3.4. Prediction for Activ
e
User
After the missing
rating
s
are p
r
edi
cted
in the use
r
-item matrix, we can reco
mmend
items for th
e active users. In this pape
r, the traditional
use
r
-ba
s
ed
nearest n
e
ig
hbo
r
recomme
ndat
ion algo
rithm is adopte
d
. For the active
use
r
ui, the predi
ctive value of item pj can
be com
puted
as follo
ws:
1
1
()
(,
)
M
ik
k
j
k
ij
M
ik
k
wr
pr
e
u
p
w
(7)
Whe
r
e
M
is t
he numb
e
r of
neighbo
r of use
r
u
i
. The p
r
edi
ctive values are so
rted
accordi
ng to the
desce
nding. The
Top
N
items will be
sel
e
cted to the user
u
i
.
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ISSN: 23
02-4
046
TELKOM
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KA
Vol. 12, No. 8, August 2014: 632
4 –
6331
6328
The wh
ole st
ep of the pro
posed ap
pro
a
c
h is a
s
follo
ws:
(1)
Comp
utin
g the simila
ri
ties amon
g
use
r
s
and it
ems respe
c
tively acco
rdin
g to the
use
r-item
rati
ng matrix, th
en buil
d
ing
u
s
er rel
a
tion n
e
twork
and it
em rel
a
tion n
e
twork
ba
sed
on
thesesimilariti
es.
(2)
Dividing al
l users an
d items into ma
n
y
clique
s re
sp
ectively.
(3) Smo
o
thin
g the missing
rating acco
rd
ing to use
r
an
d item clique
s together.
(4) Finally, u
s
er-b
ased
ne
are
s
t nei
ghb
or
re
comm
en
dation i
s
use
d
to p
r
e
d
ict it
ems for
n
e
w
us
er
s
.
4. Experimental Re
sults
4.1. Data
se
t
The M
o
vieL
ens (
h
ttp://www.moviel
en
s.umn.ed
u)
dataset is u
s
ed
in thi
s
pape
r. In
MovieLen
s,
t
here
a
r
e
1
00,
000 rating
s with
943 pe
rso
n
s and 168
2 movies.
An
d each
p
e
rson
had
rated
at lea
s
t 20 m
o
vies.
The u
s
e
r
info
rmation i
n
cl
u
des
age,
sex
,
and o
c
cup
a
t
ion and
so o
n
.
The movie in
clud
es 1
9
types. The d
ensi
t
y of
the use
r
-item matrix is 6.3%.
First, the
dat
aset i
s
divid
e
d
into two p
a
rts, 20%
of all
person
s
are
selecte
d
to b
e
testing
set,
an
d
the
remai
n
ing
a
s
trainin
g
set. For mea
s
u
r
in
g
a
c
cura
cy, we co
ndu
cte
d
a 5-fold
cross
validation by
uniformly
cho
o
sin
g
differe
n
t
traini
ng a
n
d
test set
s
. In orde
r to b
e
tter evaluate th
e
perfo
rman
ce
of new
app
ro
ach,
we ta
ke
the testi
ng
u
s
ers from d
a
taset u
n
iforml
y. That is, the
degree
of all
use
r
s is firstl
y comp
uted a
nd
sorte
d
by
orde
r. Th
en, t
he te
sting
set
is
sele
cted
b
y
equal inte
rval
s. So, the te
sting set incl
ude
s all ki
nd
s of use
r
s. F
o
r the trainin
g
set, first, the
simila
rities a
m
ong ea
ch
pair u
s
e
r
s a
nd items
will
be com
pute
d
re
spe
c
tively acco
rdin
g
to
Equation (1), (2) and (3
).
In
order
to
im
prove
th
e a
c
cura
cy, in the
experim
ent, the pa
ram
e
ter
T
will be
set a
s
2 in E
quatio
n (2
)
and
5 i
n
Equatio
n (3
). Each u
s
e
r
s and
items re
pre
s
ent
s n
o
d
e
s,
and simil
a
ritie
s
form the rel
a
tions am
ong
the use
r
net
work an
d item netwo
rk
re
spe
c
tively.
4.2. Perform
a
nce Ev
aluation
In order to
estimate
the
pe
rform
a
n
c
e of the
p
r
o
posed
app
ro
ach, th
e p
r
e
c
isi
on
of
predi
ction i
s
measured wit
h
three different metrics.
Re
call: The recall sco
r
e is the average
propo
rtion o
f
items from test set that appe
ar
among
To
pN
of the
ran
k
e
d
list
from
th
e trai
ning
set [27]. Thi
s
m
easure
sho
u
ld be
a
s
high
a
s
possibl
e for
good
pe
rform
ance. Assum
e
N
is the
nu
mber of item
s
whi
c
h
are
i
n
the te
sting
set
and liked by
use
r
s,
n
i
s
th
e amou
nt of items which the
testin
g user likes
and
appe
ars in th
e
recomme
nde
d list. So, the
reca
ll is computed as follows:
n
Re
c
a
l
l
N
(8)
Preci
s
io
n: Th
e preci
s
io
n i
s
the p
r
op
ortio
n
of recomm
ende
d item
s t
hat the te
stin
g u
s
ers
actually liked
in the test
set [28]. This me
asure
is also a
s
high a
s
po
ssi
ble for g
ood
perfo
rman
ce.
The pre
c
i
s
io
n is co
mpute
d
as follo
ws:
n
P
r
eci
si
o
n
To
p
N
(9)
F-mea
s
u
r
e: It is al
so kno
w
n as th
e
F
1
m
easure,
whi
c
h com
b
ine
s
p
r
eci
s
io
n an
d recall int
o
a singl
e metric by taking t
he ha
rmoni
c
mean of
the
m
[28]. So, th
e F-me
asure
is com
puted
as
follows
:
1
(2
*
*
)
()
R
eca
l
l
P
r
eci
si
o
n
F
R
ec
a
l
l
P
r
eci
si
o
n
(10
)
4.3. Results and An
aly
s
is
For building
the user and item social net
work
respectively, first, utilizing
Pearson
correl
ation
coefficient
algorithm, each pair us
er's and each
pair item
's similarity will
be
comp
uted. T
hen, bi
nary
al
l simila
ritie
s
a
r
e
con
s
tructe
d a
s
follo
w:
we
set
a relat
i
on threshold
R
T
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Cliqu
e
s-ba
se
d Data Sm
oothing App
r
oa
ch for Solvin
g Data-S
parsity in… (Yang Y
u
jie)
6329
(it may be
different
as fo
r u
s
er an
d item
netwo
rk),
si
m
ilarity value
s
greate
r
o
r
e
q
ual than
are
set
1, that is, the
use
r
pai
r or item pair h
a
s li
nk, othe
rwi
s
e
0.
For conveni
ence, we u
s
e TCF as the
traditional user-ba
s
ed nea
re
st neigh
bo
r
recomme
ndat
ion al
gorith
m
and
the
pro
posed
algo
rithm is exp
r
e
s
s a
s
Cliqu
e
-
CF.
Figu
re
1,
Figure 2 an
d
Figure
3 gi
ves the com
pari
s
on
s of two alg
o
rithm
s
in re
call, p
r
eci
s
io
n an
d F-
measure with
differe
nt
Top
N
valu
es. In
t
hese figu
re
s,
the nu
mbe
r
o
f
neigh
bor
M
is selected
as
100. Th
e p
a
rameter
is
se
t 0
.
5
.
F
r
o
m
F
i
gu
r
e
1
,
we
c
a
n k
n
o
w
th
a
t
the
r
e
c
a
ll va
lu
e o
f
T
C
F
and
Cliqu
e
-CF i
s
grad
ually in
creasi
ng
with t
he in
crea
sing
of
To
pN
.
Howeve
r, the
perfo
rman
ce
of
Cliqu
e
-CF is
better than th
e TCF. Th
e recall of
C
liqu
e
-CF is la
rge
r
than TCF
co
nstantly. Furt
her,
with the
in
creasi
ng
of
To
pN
, the
g
ap i
s
b
e
comin
g
l
a
rge
r
. Fi
gure
2
depi
cts th
e comp
ari
s
o
n
in
pre
c
isi
on. T
h
e figure
sho
w
s that the
p
r
eci
s
io
n valu
e of b
o
th T
C
F an
d
Clique
-CF
is g
r
adu
ally
d
e
c
r
e
as
e
w
i
th
th
e inc
r
ea
sin
g
o
f
Top
N
.
Ho
weve
r, th
eperfo
rma
n
ce of
Cliqu
e
-CF i
s
better
than
TCF. The p
r
e
c
isi
on of Cliq
ue-CF is la
rg
er than T
C
F
alway
s
. But, it is different from Figu
re 1, the
gap bet
wee
n
Cliqu
e
-CF an
d TCF is b
e
coming smalle
r with the increasi
ng of
Top
N
.
Figure 1. The
Compa
r
i
s
on
of Recall bet
wee
n
TCF an
d Cliq
ue-CF with
Di
fferent
Top
N
Figure 2. The
Compa
r
i
s
on
of Preci
s
ion
betwe
en TCF
and Cliq
ue-CF with Differe
nt
TopN
Figure 3. The
Compa
r
i
s
on
of F-mea
s
u
r
e
bet
wee
n
TCF and Cliq
ue
-CF with
Different
TopN
Figure 3 de
scrib
e
s th
e ch
angin
g
of F-measur
e abo
ut Clique
-CF
and T
C
F with
different
TopN
. F
r
om t
he figure, we
can
see th
at the F-m
e
a
s
ure value of bot
h Cliqu
e
-CF
and T
C
F is al
so
grad
ually increa
sing
with
the increa
sing of
TopN
. As same Figure 1and
Figure 2, the
perfo
rman
ce
of Cliq
ue-CF
is b
e
tter tha
n
TCF.
Fr
o
m
t
he a
nalysi
s
,
we
ca
n
see
that the
pro
p
o
s
ed
algorith
m
is b
e
tter than the
traditional co
llaborativ
e filtering al
gorith
m
in recall, p
r
eci
s
io
n and
F-
Evaluation Warning : The document was created with Spire.PDF for Python.
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02-4
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TELKOM
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KA
Vol. 12, No. 8, August 2014: 632
4 –
6331
6330
measure.In the above, we set the nu
mber of
nei
g
hbor a
s
a
so
lid value. Figure 4 give
s the
perfo
rman
ce
of
Cliqu
e
-CF with
different neigh
bors
M
.
And the
Top
N
is
set
100. From Figu
re 4,
the perfo
rma
n
ce i
s
be
comi
ng better
with
the increasi
n
g of
M
. Furthe
r, the perfo
rm
ance increa
ses
fas
t
when
M
is less than 5
0
and then it become
s
sta
b
le with mo
re
M
.
Finally, in tim
e
pe
rform
a
n
c
e, the compu
t
ing
of si
milarities bet
wee
n
each p
a
ir
users an
d
each pai
r u
s
ers, th
e buil
d
ing of u
s
e
r
relation n
e
two
r
k
and item
relation n
e
two
r
k
and
dividi
ng
cliqu
e
s can b
e
implemente
d
in offline. So, its
speed is almo
st at the same level
comp
ared wit
h
the traditional
reco
mmen
d
e
r
system
s.
Figure 4. The
Performa
nce
of Clique
s-b
a
se
d Data
S
m
oothing Alg
o
rithm with
Di
fferent Neig
h
bor
M
5. Conclusio
n
This p
ape
r
prop
oses
a cliqu
e
s-ba
se
d data sm
oo
thing algo
rith
m to solve the data
spa
r
sity probl
em in coll
abo
rative filtering
.
Firs
t, the si
milaritie
s
of users a
nd item
s are com
put
ed
respe
c
tively and the u
s
e
r
so
cial net
wo
rk and item
social n
e
two
r
k can b
e
built. Then, all u
s
ers
and item
s a
r
e divided i
n
to many
cliqu
e
s a
c
cording
to so
cial n
e
t
work an
alysi
s
theo
ry. Th
e
missi
ng
rating of the user-item rating m
a
trix w
ill
be fi
lled according to the predi
ctive value from
use
r
cli
que
s
and item cli
q
ues. Fin
a
lly, we p
r
op
os
e
d
the tradition
al
use
r-b
ased
nearest n
e
igh
bor
recomme
ndat
ion alg
o
rith
m. The
exp
e
rime
ntal
re
sults sho
w
t
hat the
pro
posed
algo
ri
thm
perfo
rms b
e
tter than the traditional
co
lla
borative filteri
ng algo
rithm.
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