symme y
S
S
A icle
Design o an Unsupe ised Machine Lea ning-Based
Mo ie Recommende Sys em
Debby Cin ia Ganesha Pu i 1,* , Jenq-Shiou Leu 1and Pa el Seda 2,3
1Depa men o Elec onic and Compu e Enginee ing, Na ional Taiwan Uni e si y o Science and
Technology, Taipei Ci y 106, Taiwan; [email p o ec ed]
2Depa men o Telecommunica ions, B no Uni e si y o Technology, Technicka 12, 61600 B no,
Czech Republic; xsedap01@ u b .cz
3Ins i u e o Compu e Science, Masa yk Uni e si y, Bo anica 554/68A, 602 00 B no, Czech Republic
*Co espondence: [email p o ec ed]
Recei ed: 25 Decembe 2019; Accep ed: 13 Janua y 2020; Published: 21 Janua y 2020


Abs ac :
This esea ch aims o de e mine he simila i ies in g oups o people o build a ilm
ecommende sys em o use s. Use s o en ha e di icul y in inding sui able mo ies due o he
inc easing amoun o mo ie in o ma ion. The ecommende sys em is e y use ul o helping
cus ome s choose a p e e ed mo ie wi h he exis ing ea u es. In his s udy, he ecommende sys em
de elopmen is es ablished by using se e al algo i hms o ob ain g oupings, such as he
K
-Means
algo i hm, bi ch algo i hm, mini-ba ch
K
-Means algo i hm, mean-shi algo i hm, a ini y p opaga ion
algo i hm, agglome a i e clus e ing algo i hm, and spec al clus e ing algo i hm. We p opose
me hods op imizing
K
so ha each clus e may no signi ican ly inc ease a iance. We a e limi ed o
using g oupings based on Gen e and Tags o mo ies. This esea ch can disco e be e me hods o
e alua ing clus e ing algo i hms. To e i y he quali y o he ecommende sys em, we adop ed he
mean squa e e o (MSE), such as he Dunn Ma ix and Clus e Validi y Indices, and social ne wo k
analysis (SNA), such as Deg ee Cen ali y, Closeness Cen ali y, and Be weenness Cen ali y. We also
used a e age simila i y, compu a ional ime, associa ion ule wi h Ap io i algo i hm, and clus e ing
pe o mance e alua ion as e alua ion measu es o compa e me hod pe o mance o ecommende
sys ems using Silhoue e Coe icien , Calinski-Ha abaz Index, and Da ies–Bouldin Index.
Keywo ds:
a ini y p opaga ion; agglome a i e spec al clus e ing; associa ion ule wi h Ap io i
algo i hm; a e age simila i y; bi ch; clus e ing pe o mance e alua ion; compu a ional ime;
Dunn Ma ix; mean-shi ; mean squa ed e o ; mini-ba ch
K
-Means; ecommenda ions sys em;
K-Means; social ne wo k analysis
1. In oduc ion
The explosion o in o ma ion on he in e ne is de eloping ollowing he apid ad ancemen o
in e ne echnology. The ecommende sys em is a simple mechanism o help use s ind he igh
in o ma ion based on he wishes o in e ne use s by e e ing o he p e e ence pa e ns in he da ase .
The pu pose o he ecommende sys em is o au oma ically gene a e p oposed i ems (web pages, news,
DVDs, music, mo ies, books, CDs) o use s based on his o ical p e e ences and sa e ime sea ching
o hem online by ex ac ing wo hwhile da a. Some websi es using he ecommende sys em me hod
include yahoo.com,ebay.com, and amazon.com [
1
–
6
]. A mo ie ecommende is an applica ion mos
widely used o help cus ome s selec ilms om a la ge capaci y ilm lib a y. This algo i hm can ank
i ems and show use s high-le el i ems and good con en o p o ide a mo ie ecommended based on
cus ome simila i y. Cus ome simila i y means collec ing ilm a ings gi en by indi iduals based on
Symme y 2020,12, 185; doi:10.3390/sym12020185 www.mdpi.com/jou nal/symme y
Symme y 2020,12, 185 2 o 27
gen e o ags and hen ecommending ilms ha p omise o a ge cus ome s based on indi iduals
wi h iden ic as es and p e e ences.
T adi ional ecommende sys ems always su e om se e al inhe en limi s, such as poo
scalabili y and da a spa si y [
7
]. Se e al wo ks ha e e ol ed a model-based app oach o o e come
his p oblem and p o ide he bene i s o he e ec i eness o he exis ing ecommende sys em. In he
li e a u e, many model-based ecommende sys ems we e de eloped by pa i ioning algo i hms,
such as K-Means, and sel -o ganizing maps (SOM) [8–12].
O he me hods ha can be used in he ecommende sys em include he cla i ica ion me hod,
associa ion ules, and da a g ouping. The pu pose o g ouping is o sepa a e use s in o di e en
g oups o o m neighbo s who a e “like-minded” (closes ) subs i u es o sea ching he en i e use
space o inc ease sys em scalabili y [
13
]. In essence, making high-quali y ilm ecommenda ions wi h
good g oupings emains a challenge and explo ing hose ollowing e icien g ouping me hods is an
impo an issue in he ecommended sys em si ua ion. A e y use ul ea u e in he ecommende
sys em becomes he abili y o guess use p e e ences and needs in analyzing use beha io o o he
use beha io s o p oduce a pe sonalized ecommende [14].
To o e come he challenges men ioned abo e, se e al me hods a e used o classi y pe o mance o
he mo ie ecommende sys em, such as
K
-Means algo i hm [
15
–
17
], bi ch algo i hm [
18
], mini-ba ch
K
-Means algo i hm [
19
], mean-shi algo i hm [
20
], a ini y p opaga ion algo i hm [
21
], agglome a i e
clus e ing algo i hm [
22
], and spec al clus e ing algo i hm [
23
]. In his a icle,
we de elop
a g ouping
ha can be op imized wi h se e al algo i hms, hen ob ain he bes algo i hm in g ouping use
simila i ies based on gen e, ags, and a ings on mo ies wi h he Mo ieLens da ase . Then, he
p oposed scheme op imizes
K
o each clus e so ha i can signi ican ly educe a iance. To be e
unde s and his me hod, when we alk abou a iance, we a e e e ing o mis akes. One way o
calcula e his e o is by ex ac ing he cen oids o each g oup and hen squa ing his alue o emo e
nega i e e ms. Then, all o hese alues a e added o ob ain o al e o . To e i y he quali y o he
ecommende sys em, we use mean squa ed e o (MSE), Dunn Ma ix as Clus e Validi y, and social
ne wo k analysis (SNA). I also uses a e age simila i y, compu a ional ime, ules o associa ion wi h
Ap io i algo i hms, and pe o mance e alua ion g ouping as e alua ion measu es o compa e he
pe o mance o ecommende sys ems.
1.1. P io Rela ed Wo ks
Zan Wang, X. Y. (2014) p esen ed esea ch on an imp o ed collabo a i e mo ie ecommende
sys em o de elop CF-based app oaches o hyb id models o p o ide mo ie ecommenda ions
ha combine dimensional educ ion echniques wi h exis ing clus e ing algo i hms. In a spa se
da a en i onmen , “like-minded” selec ion based on he gene al anking is a unc ion o p oducing
high-quali y ecommended ilms. Based on he Mo ieLens da a se , an expe imen al e alua ion
app oach can p o e ha i is capable o p oducing high p edic i e accu acy and mo e eliable
ilm ecommenda ions o exis ing use p e e ences compa ed o exis ing CF-based clus e ing [
13
].
This s udy also applies he clus e ing me hod o ind he nea es clus e and ecommends a lis o
mo ies based on simila i ies among use s. Ou ecommende sys em da ase e e s o his esea ch
by using Mo ieLens da ase o es ablish he expe imen s, including 100,000 a ings by 943 use s on
1682 mo ies, wi h a disc e e scale o 1–5. Each use has a ed a leas 20 mo ies. Then, he da ase
was andomly spli in o aining and es da a a an 80% o 20% a io. Md. Tayeb Himel, M. N. (2017)
esea ched he weigh based mo ie ecommende sys em using
K
-Means algo i hm [
14
]. This esea ch
uses he
K
-Means algo i hm and explains he esul s. This esea ch mo i a es us o use o he me hods
as a compa ison o iden i y he algo i hm wi h be e pe o mance.
1.2. P oblem Fo mula ion
In o ma ion o e load is a p oblem in in o ma ion e ie al, and he ecommenda ion sys em is
one o he main echniques o deal wi h p oblems by ad ising use s wi h app op ia e and ele an
Symme y 2020,12, 185 3 o 27
i ems. A p esen , se e al ecommenda ion sys ems ha e been de eloped o qui e di e en domains;
howe e , his is no app op ia e enough o mee use in o ma ion needs. The e o e, a high-quali y
ecommenda ion sys em needs o be buil . When designing hese ecommenda ions an app op ia e
me hod is needed. This pape in es iga es se e al app op ia e clus e ing me hods o esea ch
in de eloping high-quali y ecommenda ion sys ems wi h a p oposed algo i hm ha de e mines
simila i ies o de ine a people g oup o build a mo ie ecommende sys em o use s. Nex , expe imen s
a e conduc ed o make pe o mance compa isons wi h e alua ion c i e ia on se e al clus e ing
algo i hms using he
K
-Means algo i hm, bi ch algo i hm, mini-ba ch
K
-Means algo i hm, mean-shi
algo i hm, a ini y p opaga ion algo i hm, agglome a i e clus e ing algo i hm, and spec al clus e ing
algo i hm. The bes me hods a e iden i ied o se e as a ounda ion o imp o e and analyze his mo ie
ecommende sys em.
1.3. Main Con ibu ions
This s udy in es iga es se e al app op ia e clus e ing me hods o de elop high-quali y
ecommende sys ems wi h a p oposed algo i hm o inding he simila i ies wi hin g oups o
people. Nex , we conduc expe imen s o make compa isons on se e al clus e ing algo i hms
including
K
-Means algo i hm, bi ch algo i hm, mini-ba ch
K
-Means algo i hm, mean-shi algo i hm,
a ini y p opaga ion algo i hm, agglome a i e clus e ing algo i hm, and spec al clus e ing algo i hm.
A e ha , we ind he bes me hod om hem as a ounda ion o imp o e and analyze his mo ie
ecommende sys em. We limi o using h ee ags and h ee gen es because o analyze pe o mance
and ge good isualiza ion, he mos s able esul s a e h ee ags and h ee gen es, be o e we ha e
ied mo e han h ee bu he isualiza ion esul s ob ained a e no so good wi h some o he me hods
used in his s udy. We s a losing he abili y o isualize co ec ly when analyzing h ee o mo e
dimensions. Then we limi i by using a o i e gen es and ags and mo e de ails on he algo i hm
compa ison. The main con ibu ions o his s udy a e as ollows:
•
Pe o mance compa ison o se e al clus e ing me hods o gene a e a mo ie ecommende sys em.
•
To op imize he
K
alue in
K
-Means, mini-ba ch
K
-Means, bi ch, and agglome a i e
clus e ing algo i hms.
•
To e i y he quali y o he ecommende sys em, we employed social ne wo k analysis (SNA).
We also used he a e age simila i y o compa e pe o mance me hods and associa ion ules wi h
he Ap io i algo i hm o ecommende sys ems.
The emainde o his pape is o ganized as ollows. In Sec ion 2, we p esen an o e iew o he
ecommende sys em and e iew he clus e ing algo i hm and sys em design o he ecommende
sys em. We de ail he algo i hm design o he
K
-Means algo i hm, bi ch algo i hm, mini-ba ch
K
-Means
algo i hm, mean-shi algo i hm, a ini y p opaga ion algo i hm, agglome a i e clus e ing algo i hm,
and spec al clus e ing algo i hm. Addi ionally, we p oposed a me hod o op imize
K
in some o he
me hods. This session also explains he e alua ion c i e ia. The expe imen s, da ase explana ion,
and esul s a e illus a ed in Sec ion 3. E alua ion esul s o algo i hms ia a ious es cases and
discussions a e shown in Sec ion 4. Finally, Sec ion 5concludes his wo k.
2. Recommende Sys ems
2.1. O e iew
A ecommende sys em is a simple algo i hm o p o ide he mos ele an in o ma ion o use s
o ind pa e ns in he da ase . This algo i hm a es he i em and indica es he use who is a ed high.
I a emp s o ecommend i ems ha bes sui cus ome needs (in he o m o p oduc s o se ices).
A e y use ul ea u e in a ecommende sys em is he abili y o guess he p e e ences and use needs in
analyzing use beha io o o he use beha io o gene a e a pe sonalized ecommende [
14
]. The chie
pu pose o ou sys em is o iden i y mo ies based on use s’ iewing his o ies and a ings p o ided in
Symme y 2020,12, 185 4 o 27
he Mo ieLens sys em and da ase s [
24
] and o use a speci ic algo i hm o p edic mo ies. The esul s
a e e u ned o he use as a ecommende i em wi h he pa ame e s o he use . The illus a ion o
he ecommende sys em is p esen ed in Figu e 1, which explains simila i ies wi hin people o build a
mo ie ecommenda ion sys em o use s.
Use 1 Use 2
A
B
B
A
C
Simila
Recommend
Figu e 1. Simila i ies wi hin people o build a mo ie ecommenda ion sys em o use s.
Figu e 1shows how wo use s ha e a simila in e es in i ems A and B. When his occu s,
he simila i y index o bo h use s will be calcula ed. Fu he mo e, he sys em can ecommend i ems C
o o he use s because he sys em can de ec ha bo h use s ha e simila i ies in e ms o he i ems.
2.2. Sys em Design
In his ecommende sys em,
K
-Means algo i hm, bi ch algo i hm, mini-ba ch
K
-Means algo i hm,
mean-shi algo i hm, a ini y p opaga ion algo i hm, agglome a i e clus e ing algo i hm, and spec al
clus e ing algo i hm a e used o de e mine he bes pe o ming algo i hms in mo ie ecommenda ions
based on op imized
K
alues. A e applying se e al algo i hms, all spaces a e sea ched o ob ain he
use nea es neighbo in he same clus e and Top-
N
Lis o ecommende mo ies. Figu e 2shows an
o e iew o he low o se en exis ing algo i hms.
Symme y 2020,12, 185 5 o 27
S a
Selec Da ase
Usedda ase byeachuse a g a ing
wi h a o i egen e/ a o i e ags
Plo  heeach alueo Kwi h he
Silhoue eSco ea  ha  alue
Clus e ingda ase wi h7me hods
(K-Means,bi ch,mini-ba ch
K-Means,mean-shi ,a ini y
p opaga ion,
agglome a i eclus e ing,and
spec alclus e ing)
End
Clus e  heuse s a emo ies
Find henea es nodewi hEuclidean
Dis ance
Top-Nlis o  ecommenda ionmo ie
o simila i yuse
Meansqua ede o ,
socialne wo kanalysis,
DunnMa ix,A e ageSimila i y,
Compu a ionalTime,Associa ion
Rulewi hAp io iAlgo i hm,
Clus e ingPe o manceE alua ion
Algo i hmcompa ison
 ope o manceanalysis
Figu e 2. Flowcha ha con igu es a ecommenda ion sys em o mo ies.
2.3. Clus e ing Algo i hm
Clus e ing is an analy ical me hod ha was used as ea ly as 1939 by T yon, R. C [
25
]. Clus e ing
was i s used in psychology and hen apidly expanded o o he ields. Since he explosion o he
amoun o in o ma ion a ailable on he in e ne , many e o s ha e been made o educe he p oblem
o in o ma ion o e load. This o e load can be esol ed by using a clus e ing me hod. Clus e ing is
a classi ica ion o he same objec s om di e en g oups wi h pa i ions using exis ing da a in o a
new g oup, and each g oup o da a is iden i ied wi h a ce ain deg ee o dis ance. In clus e analysis,
he e is also a con as be ween pa ame ic and nonpa ame ic app oaches [
26
]. Da a clus e ing is a
echnique commonly used in a ious ields, such as da a mining, pa e n ecogni ion, image analyze,
and a i icial in elligence. Da a clus e ing is employed o educe a la ge amoun o da a by p o iding
he ca ego ies o classi ying he da a ha ha e a high deg ee o simila i y.
2.3.1. K-Means Clus e ing Algo i hm and Op imize KNumbe Clus e
K
-Means clus e ing is a me hod ha au oma ically di ides da ase s in o
k
g oups [
27
]. Resul s
selec ed he ini ial cen al clus e
k
o be i e a i ely e ined by being assigned o he nea es cen al
clus e . Each cen e o he Cjclus e is upda ed o an a e age sample o i s cons i uen s.
K
-Means is used o g oup app oaches gi en i s simplici y, e iciency, and lexibili y in calcula ions
especially conside ing a la ge amoun o da a.
K
-Means calcula e he clus e cen e in assigning objec s
o he closes clus e based on dis ance. When he midpoin does no change, he clus e ing algo i hm
seeks con e gence. Howe e ,
K
-Means lacks he abili y o choose he igh ini ial seeds and could
cause classi ica ion inaccu acies. Selec ing a andom s a ing seed can p oduce a locally good solu ion
ha is qui e in e io o inding he di ec
K
alue. The a ious ini ial seeds ha un on he same da ase
migh deli e di e en pa i ion esul s. Gi en a se o objec s
(x1
,
x2
,
. . .
,
xn)
, whe e each objec is
an m-dimensional ec o , he
K
-Means algo i hm aims a sepa a ing hese objec s o o m
k
g oups
au oma ically. Algo i hm 1p o ides he K-Means p ocedu e.

Symme y 2020,12, 185 6 o 27
Algo i hm 1 K-Means algo i hm and op imize knumbe clus e
Inpu : Selec ing da ase and using da ase by each use a g a ing wi h a o i e gen e/ ags;
Ou pu : Finishing wi h elease Top-Nlis o ecommenda ion mo ie o simila i y use ;
1: unc ion K-MEANS()
2: Choosing kini ial clus e cen e s
3: Cj,j=1, 2, 3 . . . , k;
4: Each xiis assigned o i s closes clus e
5: cen e based on he dis ance me ic
6: J=∑k
j=1∑i∈C emp ||xi−Mj||2,
7: whe e Mjdeno es he mean o da a poin s
8: in C emp;
9: Choosing he igh Knumbe o Clus e s;
10: clus e ing he use ’s a e mo ies;
11: Finding he nea es node o sea ch simila i y wi h
12: use wi h Euclidean dis ance;
13: i he e is no change hen
14: The algo i hm has con e ged and clus e ing ask
15: is ended, also ecalcula e he Mo Kclus e s
16: as he new clus e cen e s and go o;
17: end i
18: end unc ion
Op imize KNumbe Clus e
To o e come he limi a ions abo e, we op imized
K
o choose he co ec numbe o
K
clus e s.
Choosing he bes numbe o
K
clus e s is he key poin o he
K
-Means algo i hm. To ind
K
,
we calcula e he clus e ing e o wi h mean squa ed e o (MSE) and silhoue e sco e. Fi s , we selec a
da ase and choose he ange o
k
alues o es . Then, we de ine he unc ion o calcula e he clus e ed
e o s and e o alues o all k alues. Finally, we plo each alue o
k
wi h he silhoue e sco e a ha
alue. A de ailed explana ion o mean squa ed e o (MSE) and silhoue e sco e is p o ided in [
28
,
29
].
(1) Silhoue e Sco e o de e mine he Knumbe clus e .
The silhoue e was i s in oduced by
Pe e J. Rousseeuw in [
30
] in 1986. This is a me hod o in e p e a ion and alida ion o clea da a
clus e s. This echnique p o ides a g aphical ep esen a ion o how well each objec i s inside he
g oup. The silhoue e alue o an a ibu e is gi en by he equa ion below:
Si=a(i)·b(i)
max {a(i),b(i)}, (1)
whe e
a(i)
is he a e age dissimila i y o da a poin
i
wi h o he da a wi hin he one clus e . He e,
b(i)
is he minimum a e age dissimila i y o da a poin
i
wi h any o he clus e in which
i
is no
inside membe a.
2.3.2. Bi ch Clus e ing Algo i hm
Balanced i e a i e educing and clus e ing using hie a chies (bi ch clus e ing) uses a hie a chical
da a s uc u e ha calls CF- ee o inc emen and dynamically clus e s da a poin s [
31
]. The bi ch
algo i hm uses an inpu se o da a poin s
N
, which is ep esen ed as a ec o o eal alue and he
desi ed numbe o clus e
K
. The i s phase builds a CF- ee om a da a poin . This can be de ined
wi h gi en a se o
N
d-dimensional da a poin s, and he clus e ing ea u e (CF) o he se is used o
es ablish he iple- CF = (N,LS,SS), whe e
Symme y 2020,12, 185 7 o 27
−→
LS =
N
∑
i=1
−→
xi, (2)
is he linea sum and
−→
SS =
N
∑
i=1
−−→
(xi)2, (3)
is he sum o he da a poin s.
Clus e ing ea u es a e o ganized on a CF- ee, a heigh -balanced ee wi hin wo pa ame e s,
including b anching ac o B and h eshold T. Each non-lea node con ains mos B en ies inside he
o m [
CFi
, child
i
], in which child
i
is one poin e o i s
i
he child node and
CFi
is he clus e ing ea u e
ep esen ing he associa ed subclus e .
2.3.3. Mini-Ba ch K-Means Clus e ing
The algo i hm Mini-ba ch
K
-Means was de eloped as a modi ica ion o he
K
-Means algo i hm.
I uses mini-ba ch o educe ime in e y complex and la ge-scale calcula ions o da ase s. The e o s
o op imize g ouping esul s could be used wi h his me hod. Mini-ba ch
K
-Means a e andomly used
as inpu , which is a subse o he en i e da ase . Mini-ba ch
K
-Means is as e han
K
-Means and is
usually used o la ge da ase s. Fo da ase
T={x
1,
x
2,
. . .
,
xn}
,
xi∈Rm·n
,
xi
ep esen s a ne wo k
eco d wi h an
n
-dimensional eal ec o . In addi ion,
m
indica es he numbe o eco ds inside he
da ase
T
. The objec i e o he clus e ing p oblem is o unco e he se
C
o clus e cen e s
c∈Rm·n
o minimize he da ase
T
o eco ds
c∈Rm·n
in unc ion [
32
]. In con as o
K
-Means, mini-ba ch
K
-Means andomly selec s a subse o eco ds om he da ase . Mini-ba ch
K
-Means g ea ly educes
he clus e ing ime and he con e gence ime. The sum o squa ed dis ances is compu ed in one clus e
as ollows:
min ∑
x∈T
|| (C,x)−x||2, (4)
whe e
(C
,
x)
e u ns he closes o clus e cen e
c∈C
o eco d
x
, and
|C|=K
and
K
is he numbe
o clus e s o ob ain.
2.3.4. Mean-Shi Clus e ing
The mean-shi algo i hm is p oposed as a me hod o clus e analysis [
33
]. Howe e , gi en ha
he mean-shi de e mines he g adien ascen , he con e gence o he p ocess needs e i ica ion
and i s ela ion wi h simila algo i hms needs cla i ica ion. The mean-shi algo i hm is pa o a
nonpa ame ic g ouping echnique ha does no equi e p io knowledge o he numbe o clus e s
and does no cons ain he shape o he clus e s. Mean-shi clus e ing is used o disco e blobs in
a smoo h densi y o samples, which wo ks by upda ing he candida es o cen oids o be he mean
poin s wi hin a gi en egion. These candida es a e hen il e ed in a pos p ocessing s age o elimina e
nea -duplica es o o m he inal se o cen oids. Gi en a candida e cen oid
xi
ollowed by i e a ion
,
he candida e is upda ed by he ollowing equa ion:
x +1
i=m(x
i), (5)
Symme y 2020,12, 185 8 o 27
whe e
N(xi)
is he neighbo hood o samples wi hin a gi en dis ance a ound
xi
and
m
is he mean-shi
ec o o each cen oid ha poin s agains a egion o he maximum inc ease in he densi y o poin s.
This is compu ed using he ollowing equa ion:
m(xi) = ∑xj∈N(xi)K(xj−xi)xj
∑xj∈N(xi)K(xj−xi). (6)
The algo i hm can au oma ically de e mine he numbe o clus e s, using bandwid h pa ame e s.
This in o ma ion can de e mine he size o he egion o sea ch h ough. This algo i hm is un eachable
because i equi es se e al close neighbo sea ches du ing i s execu ion.
2.3.5. A ini y P opaga ion Clus e ing
In he a ini y p opaga ion me hod all da a poin s a e conside ed as possible exempla s.
I exchanges eal- alues be ween exempla s un il high-quali y exempla s and co esponding clus e s
a e no p o ided. The pa icula messages a e u he upda ed based on a simple o mula ha
a iocina es a sum-p oduc . A any selec ed poin in ime, he magni ude in each message ep esen s
he cu en a ini y ha one poin has o choosing ano he da a poin as i s exempla , hence he name
“a ini y p opaga ion” [
34
]. The messages sen be ween poin s belong o one o he wo ca ego ies.
The accumula ed e idence
(i
,
k)
o sample
k
should be he exempla o sample
i
. In addi ion,
ega ding a ailabili y
a(i
,
k)
, he accumula ed indica es ha sample
i
should choose sample
k
o be an
exempla . The exempla chosen by samples is simila enough o many samples ha a e ep esen a i e
o hemsel es. The esponsibili y o a sample
k
o be he exempla o sample
i
is gi en by he
ollowing o mula:
(i,k)←s(i,k)−max[a(i,k0) + s(i,k0)∀k06=k]. (7)
The simila i y be ween samples
i
and
k
,
s(i
,
k)
is assessed. The a ailabili y o sample
k
o be an
exempla o sample iis gi en by he ollowing o mula:
a(i,k)←min[0, (k,k) + ∑
i0s, ,i0∈{i,k}
(i0,k)]. (8)
We de ine a clus e wi h upda e
(i
,
k)
and
a(i
,
k)
. All he alues o
and
a
we e se o ze o and
each i e a e is calcula ed un il con e gence is ound. To a oid nume ical oscilla ions, he i e a ion
p ocess equi es he damping ac o γas ollows:
+1(i,k) = λ· (i,k) + (1+λ)· +1(i,k), (9)
a +1(i,k) = λ·a (i,k) + (1+λ)·a +1(i,k). (10)
2.3.6. Agglome a i e Clus e ing
Agglome a i e clus e ing can scale la ge numbe s o samples when used oge he wi h he
connec i i y ma ix and all possible me ges a e conside ed a each s ep. Wa d’s me hod is one o he
agglome a i e clus e ing me hods based on a classical sum-o -squa es c i e ion, p oducing g oups
ha minimize wi hin-g oup dispe sion a each bina y usion. This me hod uses Euclidean dis ance as
he dis ance me ic.
||a−b||2= ∑
i
(ai−bi)2. (11)
Symme y 2020,12, 185 9 o 27
2.3.7. Spec al Clus e ing
Spec al clus e ing uses in o ma ion om he eigen alue (spec um) o a special ma ix ha will
be buil om a g aph o da a se . This ma ix will be buil and in e p e i s spec um using eigen ec o s
o assign da a o clus e s. An eigen ec o is an impo an objec o linea algeb a and helps illus a e he
dynamics o he sys em ep esen ed by he ma ix. Speci ic g ouping uses he concep o eigen alues
and eigen ec o s.
L=D−1/2 ·AD−1/2. (12)
I s closes clus e cen e is assigned based on he dis ance me ic. The a ini y ma ix is o med,
and he diagonal ma ix is de ined. The ma ix is o med and he no malized Laplacian ma ix and
eigen ec o s a e compu ed.
2.4. E alua ion C i e ia
We u ilized he aining da a o de elop he o line model, and he emaining da a a e used
o analyze and p o ide he mo ie ecommenda ion. To e i y he quali y o he ecommende
sys em, we employed he mean squa ed e o (MSE), social ne wo k analysis (SNA), Dunn Ma ix
as clus e alidi y indices, and e alua ion measu es wi h a e age simila i y, compu a ional ime,
associa ion ule wi h Ap io i algo i hm, and clus e ing pe o mance e alua ion. The ollowing is
e i ied and e alua ed.
2.4.1. Mean Squa ed E o
Mean squa ed e o (MSE) is used o acili a e aining and some o e all e o measu e is o en
used as a pe o mance me ic o an objec i e unc ion [35].
MSE =1
M·1
N
M
∑
m=1
N
∑
j=1dmj −ymj2, (13)
whe e
dmj
and
ymj
ep esen he desi ed ( a ge ) alue and ou pu a he
m
he node o he
j
he
aining pa e n espec i ely,
M
is he numbe o ou pu nodes, and
N
is he numbe o he aining
pa e ns. The pu pose o aining is o de ec he se o weigh s ha minimize he objec i e unc ion.
Mean squa ed e o (MSE) is e y cle e in p o iding in o ma ion abou his a i icially buil
model. By minimizing he mean squa ed e o (MSE) alue, he a ian model is minimized. This can
p o ide ela i ely consis en esul s as inpu da a compa ed o models wi h la ge a ian s (la ge mean
squa ed e o (MSE)).
2.4.2. Clus e ing Validi y Indices: Dunn Ma ix
The Dunn index (DI) is a me ic o e alua ing clus e ing algo i hms wi h in e nal e alua ion
schemes, wi h esul s being based on he clus e da a i sel . Dunn’s index is he a io o wi hin and
be ween clus e sepa a ion (Malay K. Pakhi a, S. B., 2004). Simila o all o he indices, he pu pose o
he Dunn index is o iden i y a se o compac clus e s wi h small a ian s be ween clus e membe s,
ha a e well sepa a ed, and wi hin which he a e age clus e di e s signi ican ly compa ed o he
clus e a ian s.
The highe he Dunn index alue is, he be e he g ouping. The numbe o clus e s maximizing
he Dunn index will be aken as he op imal numbe o clus e s
k
. I also has se e al sho comings.
As he numbe o clus e s and da a dimensionali y inc ease, he cos o compu ing also inc eases.
The Dunn index o cnumbe o clus e s is de ined as ollows:
Symme y 2020,12, 185 16 o 27
(a)
(b)
Figu e 8.
Visualiza ion o agglome a i e clus e ing algo i hm. Agglome a i e clus e ing gen e (
a
),
agglome a i e clus e ing ag (b).
To ob ain a mo e delimi ed subse o people o s udy, g ouping is pe o med o exclusi ely ob ain
a ings om hose who like ei he omance o science ic ion mo ies. X and Y-axes a e omance and
sci- i a ings, espec i ely. In addi ion, he size o he do ep esen s he a ings o he ad en u e
mo ies. The bigge he do , he highe he ad en u e a ing. The addi ion o he ad en u e gen e
signi ican ly al e s he clus e ing. The Top
N
-Mo ies lis s se e al clus e ing algo i hms wi h
K
-Means
gen e
n
clus e = 12,
K
-Means ag
n
clus e = 7, bi ch gen e
n
clus e = 12, bi ch ags
n
clus e = 12,
MiniBa ch-
K
-Means gen e
n
clus e = 12, MiniBa ch-
K
-Means ags
n
clus e s = 7, mean-shi gen e,
mean-shi ags, a ini y p opaga ion gen e, a ini y p opaga ion ags, agglome a i e clus e ing gen e
n
clus e = 12, agglome a i e clus e ing ag
n
clus e = 7, spec al clus e ing gen e, spec al clus e ing
ags a e epo ed below.
(a)
(b)
Figu e 9.
Visualiza ion o spec al clus e ing algo i hm. Spec al clus e ing gen e (
a
), spec al clus e ing
ag (b).

Symme y 2020,12, 185 17 o 27
Figu e 10. Example o isualiza ion Gen e K-Means o Top lis -No mo ies.
Conside ing a subse o use s and disco e ing wha hei a o i e gen e was, we de ine a
unc ion ha would calcula e each use ’s a e age a ing o all omance mo ies, science ic ion
mo ies, and ad en u e mo ies. To ob ain a mo e delimi ed subse o people o s udy, we biased ou
g ouping o exclusi ely ob ain a ings om hose use s who who like ei he omance o science ic ion
mo ies. We used he
x
and
y
-axes o he omance and sci- i a ings. In addi ion, he size o he do
ep esen s he a ings o he ad en u e mo ies ( he bigge he do , he highe he ad en u e a ing).
The addi ion o he ad en u e gen e signi ican ly a ec s he clus e s. The mo e da a added o ou
model, he mo e simila he p e e ences o each g oup a e. The inal e sion is Top lis o
N
o mo ies
(e.g., shown in Figu e 10). Addi ionally, we conside ed a subse o use s and disco e ed hei a o i e
ags. We de ined a unc ion ha calcula ed each use ’s a e age a ing o all unny ag mo ies, an asy
ag mo ies, and ma ia ag mo ies. To ob ain a mo e delimi ed subse o people o s udy, we biased ou
g ouping o exclusi ely ob ain a ings om hose use s who like ei he unny o an asy ags mo ies.
We also de e mined ha esul s ob ained be o e he compa ison algo i hm a e Top N mo ies o be
gi en o simila use s. The esul s o Top N mo ies be o e he compa ison algo i hm and Top N mo ies
o gi e o simila use s o in e es in a o i e gen e and ags a e p esen ed.
Op imize KNumbe Clus e
F om he esul s ob ained, we can choose he bes choices o he
K
alues. Choosing he igh
numbe o clus e s is one o he key poin s o he
K
-Means algo i hm. We also use mini-ba ch
K
-Means
algo i hm and bi ch algo i hm. We do no apply o mean-shi and a ini y p opaga ion because he
algo i hm au oma ically se s he numbe o clus e s. Inc easing he numbe o clus e s shows he
ange ha esul ed in he wo s clus e s based on he Silhoue e Sco e. Op imize K is ep esen ed by a
silhoue e sco e. The X-axis ep esen s he la ges sco e, so he g oup is mo e a ied o use and he Y
axis ep esen s he numbe o clus e s. This is so ha i can de e mine he igh numbe o clus e s o
be used in displaying isualiza ions. The esul s o op imize
K
in se e al clus e ing algo i hms a e
p esen ed in Figu e 11.
Symme y 2020,12, 185 18 o 27
Figu e 11. Example o isualiza ion op imiza ion o Kin K-Means gen e a ing.
4. E alua ion and Discussion
This sec ion con ains he e i ica ion and e alua ion esul s o he me hodology. The bes
pe o ming me hod is iden i ied, and a discussion is p esen ed.
4.1. E alua ion Resul
The e i ica ion and e alua ion esul s a e p esen ed below.
4.1.1. Mean Squa ed E o
Shown in Figu es 12 and 13, he mean squa ed e o (MSE) agglome a i e me hod se es as an
example among he se en clus e ing algo i hms.
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0 2 4 6 8 10 12
Mean Squa ed E o Sco e
Clus e
MSE Agglome a i e Clus e ing: Gen e
Mean Squa ed E o
Figu e 12. MSE agglome a i e clus e ing gen e.
Symme y 2020,12, 185 19 o 27
0
0.05
0.1
0.15
0.2
0.25
0 1 2 3 4 5 6 7
Mean Squa ed E o Sco e
Clus e
MSE Agglome a i e Clus e ing: Tags
Mean Squa ed E o
Figu e 13. MSE agglome a i e clus e ing ags.
4.1.2. Clus e Validi y Indices: Dunn Ma ix
The Dunn ma ix is used as a alidi y measu e o compa e pe o mance me hods o
ecommenda ion sys ems. The ollowing Dunn ma ix esul s a e shown in Table 1.
Table 1. Dunn Ma ix o se en clus e ing algo i hms.
Me hods Amoun o Clus e s Sco e
K-Means algo i hm: gen e a ing 3 0.41
K-Means algo i hm: ags a ing 3 0.41
bi ch algo i hm: gen e a ing 3 0.49
bi ch algo i hm: ags a ing 3 0.63
mini-ba ch K-Means algo i hm: gen e a ing 3 0.38
mini-ba ch K-Means algo i hm: ags a ing 3 0.37
mean-shi algo i hm: gen e a ing – 0.39
mean-shi algo i hm: ags a ing – 0.63
a ini y p opaga ion algo i hm: gen e a ing – 1.06
a ini y p opaga ion algo i hm: ags a ing – 0.47
agglome a i e clus e ing algo i hm: gen e a ing 3 0.43
agglome a i e clus e ing algo i hm: ags a ing 3 0.45
spec al clus e ing algo i hm: gen e a ing – 2.09
spec al clus e ing algo i hm: ags a ing – 4.60
4.1.3. A e age Simila i y
The a e age simila i y bi ch me hod example esul s om se en clus e ing algo i hms a e shown
in Table 2.
Symme y 2020,12, 185 20 o 27
Table 2. A e age simila i y o bi ch me hod.
Me hods Amoun A e age
o Clus e s Simila i y
bi ch algo i hm: gen e a ing
3 0.99
6 0.97
12 0.96
bi ch algo i hm: ags a ing
4 0.97
6 0.93
12 0.94
4.1.4. Social Ne wo k Analysis
Mean-shi esul s om se en clus e ing me hods o social ne wo k analysis (SNA) a e shown in
Table 3.
Table 3. Mean-shi social ne wo k analysis esul .
Me hods Clus e SNA
mean-shi algo i hm: gen e a ing Clus e : (0, 2, 1, 4)
Deg ee, densi y in clus e 0 ( he highes numbe
in esul ), compa e o sequence lis o he clus e
whe e he dis ance esul is 5831.49.
Closeness, he highes in clus e 0 o clus e 1 (bo h
clus e s ha e a high linkage ela ionship) whe e he
dis ance esul is 1.44.
Be weenness, he highes in clus e 0 ( i s ) o
clus e 2 (end), be ween 1 (clus e 0 is he mos
ha e a ela ionship whe e he clus e 1(be ween)
and 2 whe e he dis ance esul is 1.39.
mean-shi algo i hm: ags a ing Clus e : (3, 0, 1, 2)
Deg ee, he densi y in clus e 0 ( he highes numbe
in esul ), compa e o sequence lis o he clus e
whe e he dis ance esul is 148.11.
Closeness, he highes in clus e 0 o clus e 1 (bo h
clus e s ha e a high linkage ela ionship) whe e he
dis ance esul is 0.67.
Be weenness, he highes in clus e 3 ( i s ) o
clus e 1 (end), be ween 0 (clus e 3 is he mos
ha e a ela ionship wi h clus e 0 (be ween) and 1
whe e he dis ance esul is 3.12.
4.1.5. Associa ion Rule: Ap io i Algo i hm
The associa ion ule wi h Ap io i algo i hm is used as an e alua ion measu e o compa e he
me hod pe o mance o he ecommenda ion sys ems. An example o esul s o associa ion ules wi h
he Ap io i algo i hm om se en clus e ing algo i hms is shown in he ollowing sec ion.
Rule: 12 Ang y men (1957) -> Ad en u es o P iscilla, Queen o he Dese , The (1994)
Suppo : 0.25
Con idence: 1.0
Li : 4.0
========================================
Rule: 12 Ang y Men (1957) -> Ai plane! (1980)
Suppo : 0.25
Con idence 1.0
Li : 4.0
========================================
Rule: Amadeus (1984) -> 12 Ang y men (1957)
Symme y 2020,12, 185 21 o 27
Suppo : 0.25
Con idence: 1.0
Li : 4.0
========================================
Rule: Ame ican Beau y (1999) -> 12 Ang y Men (1957)
Suppo : 0.25
Con idence: 1.0
Li : 4.0
========================================
Rule: Aus in Powe s: In e na ional Man o Mys e y (1997) -> 12 Ang y Men (1957)
Suppo : 0.25
Con idence: 1.0
Li : 4.0
4.1.6. Compu a ional Time
The compu a ional ime is used as an e alua ion measu e o compa e pe o mance me hods o
ecommenda ion sys ems. Compu a ional ime esul s a e epo ed below (see Table 4).
Table 4. Compu a ional ime o se en clus e ing algo i hms.
Clus e ing Me hod Compu a ional Time [ms]
K-Means-gen e 31.16
K-Means- ags 14.43
bi ch-gen e 24.49
bi ch- ags 15.34
mini-ba ch K-Means me hod-gen e 23.82
mini-ba ch K-Means me hod- ags 15.79
mean-shi -gen e 13.75
mean-shi - ags 10.15
a ini y p opaga ion-gen e 20.04
a ini y p opaga ion- ags 8.53
agglome a i e clus e ing-gen e 32.00
agglome a i e clus e ing- ags 10.37
spec al clus e ing-gen e 15.55
spec al clus e ing- ags 6.22
4.1.7. Clus e ing Pe o mance E alua ion
Clus e ing pe o mance e alua ion (CPE) esul o
K
-Means and bi ch me hod examples om
se en clus e ing algo i hms a e epo ed below (see Table 5).

Symme y 2020,12, 185 22 o 27
Table 5. Clus e ing pe o mance e alua ion o K-Means me hod and bi ch me hod.
Me hods
Clus e ing
Sco ePe o mance
E alua ion
K-Means algo i hm: gen e a ing
Silhoue e Coe icien 0.29
Calinski Ha abaz Index 59.41
Da ies Bouldin Index 1.13
K-Means algo i hm: ags a ing
Silhoue e Coe icien 0.25
Calinski Ha abaz Index 7.47
Da ies Bouldin Index 0.86
bi ch algo i hm: gen e a ing
Silhoue e Coe icien 0.23
Calinski Ha abaz Index 39.03
Da ies Bouldin Index 1.24
bi ch algo i hm ags a ing
Silhoue e Coe icien 0.25
Calinski Ha abaz Index 5.73
Da ies Bouldin Index 1.16
4.2. Discussion
A de ailed explana ion o he abo e-men ioned expe imen s is discussed in he subsequen
sec ion. In gene al, o all o hese me hods, he highe he alue o he li , suppo , and con idence,
he be e he link is o he ecommende sys em. Fu he , he highe he Dunn index alue, he be e
he g ouping.
4.2.1. K-Means Pe o mance
Mo ie ecommende quali y is e alua ed wi h
K
-Means. MSE esul s om
K
-Means show
di e en esul s o gen e a ing and a ing ags. The a ing ag esul s a e ela i ely smalle wi h
a ing gen e sco es o 0–0.95 and a ing ags sco es o 0–0.28.
K
-Means has a Dunn Ma ix ha ends
o be e enly dis ibu ed o gen e and ags wi h alues o 0.41. The highe he Dunn index alue,
he be e he g ouping. The a e age simila i y in he gen e showed ha he alue inc eases as he
numbe o clus e s dec eases. The a e age simila i y in
K
-Means ags shows ha he high simila i y
alue depends on he numbe o clus e s. The associa ion ule wi h Ap io i algo i hm in
K
-Means
clus e ing app oach 13% suppo o he gen e and 25% o ags o cus ome s who choose mo ies A
and B. Suppo is an indica ion o how o en he i emse appea s in linkages. The con idence is 61% o
he gen e and 100% o ags o he cus ome s who choose mo ie A and mo ie B. Li ep esen s he
a io o 3.3 o gen e and 4.0 o ags o he obse ed suppo alue. This is a condi ional p obabili y.
Clus e ing pe o mance e alua ion showed ha he
K
-Means me hod showed good pe o mance wi h
he Calinski-Ha abaz Index wi h a sco e o 59.41.
4.2.2. Bi ch Pe o mance
To e alua e he mo ie ecommende quali y wi h bi ch, mean squa ed e o (MSE) esul s om
bi ch showed ela i ely small esul s wi h a a ing gen e sco e ange o 0–0.25 and ag sco es o 0–0.17.
Bi ch ag a ings ha e a Dunn Ma ix alue ha ends o be g ea e han 0.64. The a e age simila i y
in he bi ch gen e showed ha he alue inc eases, as he numbe o clus e s dec eases. The a e age
simila i y in bi ch ags e ealed ha he high simila i y alue depended on he numbe o clus e s.
The associa ion ule wi h Ap io i algo i hm in he bi ch clus e ing app oach p o ides 16% suppo o
gen e and 50% suppo o ags o cus ome s who choose mo ies A and B. Suppo is an indica ion
o how o en he i emse appea s in linkages. Con idence is 100% o he gen e and 50% o ags o
Symme y 2020,12, 185 23 o 27
he cus ome s who choose mo ie A and B. Li ep esen s he a io o 4.0 o gen e and 1.0 o ags
o he obse ed suppo alue. The pe o mance e alua ion showed ha his me hod p o ides good
pe o mance wi h a sco e o 1.24 on he Da ies–Bouldin Index.
4.2.3. Mini-Ba ch K-Means Pe o mance
To e alua e mo ie ecommende quali y wi h mini-ba ch
K
-Means, MSE esul s om mini-ba ch
K
-Means showed di e en esul s in gen e a ing and a ing ags. The a ing ag esul s we e ela i ely
smalle wi h a a ing gen e sco e ange o 0–0.69 and a ing ag sco es o 0–0.19. The mini-ba ch
K
-Means wi h gen e a ing has a Dunn Ma ix alue ha ends o be g ea e han 0.38. The a e age
simila i y in he mini-ba ch
K
-Means gen e showed ha he high simila i y alue depended on he
numbe o clus e s. The a e age simila i y in he mini-ba ch
K
-Means ags showed ha he high
simila i y alue depended on he numbe o clus e s. The associa ion ule wi h Ap io i algo i hm in
mini-ba ch
K
-Means clus e ing app oach p o ides 13% suppo o gen e and 14% suppo o ags o
cus ome s who choose mo ies A and B. Suppo is an indica ion o how o en he i emse appea s in
linkages. Con idence is 100% o he gen e and 100% o ags o he cus ome s who choose mo ie A
and mo ie B. Li ep esen s he a io o 3.75 o gen e and 7.0 o ags o he obse ed suppo alue.
The e alua ion showed ha he mini-ba ch
K
-Means me hod pe o ms well wi h Calinski-Ha abaz
Index wi h a sco e o 48.18.
4.2.4. Mean-Shi Pe o mance
To e alua e he mo ie ecommende quali y wi h he mean-shi , he MSE esul s om he
mean-shi showed ela i ely la ge esul s wi h a gen e a ing sco e ange o 0–1 and a ag sco e o
0–1. The mean-shi algo i hm wi h a ing ags has a Dunn Ma ix alue ha ends o be g ea e han
0.63. The a e age simila i y in he mean-shi gen e showed ha he alue inc eases as he numbe o
clus e s dec eases. The a e age simila i y in ags mean-shi showed ha he high simila i y alue
depended on he numbe o clus e s. The mean-shi in he gen e has he bes compu a ional ime a
13.75 ms. The associa ion ule wi h Ap io i algo i hm in mean-shi clus e ing app oach p o ides 12%
suppo o gen e and 9% o ags o cus ome s who choose mo ies A and B. Suppo is an indica ion
o how o en he i emse appea s in linkages. Con idence is 81% o he gen e and 100% o ags o he
cus ome s who choose mo ie A and mo ie B. Li ep esen s a a io o 3.06 o gen e and 5.5 o ags o
he obse ed suppo alue. The abo e-men ioned e alua ion depic s he a ini y p opaga ion me hod
o p o ide su icien pe o mance wi h Calinski-Ha abaz Index wi h a sco e o 20.14.
4.2.5. A ini y P opaga ion Pe o mance
To e alua e he quali y wi h a ini y p opaga ion mo ie, he esul s o he mean squa ed e o
(MSE) om a ini y p opaga ion showed di e en esul s o gen e a ing and a ing ags. The a ing
gen e esul s we e ela i ely smalle wi h a gen e a ing sco e ange o 0–0.17 and a a ing ag sco e o
0–0.89. The a ini y p opaga ion algo i hm wi h gen e a ing has a Dunn Ma ix which ends o be
highe a 1.06. The a e age simila i y in he a ini y p opaga ion gen e showed ha he high simila i y
alue depended on he numbe o clus e s. The a e age simila i y in a ini y p opaga ion ags showed
ha he high simila i y alue depended on he numbe o clus e s. The associa ion ule wi h Ap io i
algo i hm in a ini y p opaga ion clus e ing app oach p o ided 10.5% suppo o he gen e and 20%
suppo o ags o cus ome s who choose mo ies A and B. Suppo is an indica ion o how o en he
i emse appea s in linkages. He e, 66% con idence is no ed o he gen e and 100% o ags o he
cus ome s who choose mo ie A and mo ie B. Li ep esen s he a io o 4.22 o gen e and 5.0 o
ags o he obse ed suppo alue. Clus e ing pe o mance e alua ion also showed ha he a ini y
p opaga ion me hod showed good pe o mance wi h he Calinski-Ha abaz Index wi h a sco e o 53.49.
Symme y 2020,12, 185 24 o 27
4.2.6. Agglome a i e Clus e ing Pe o mance
Now we e alua e he mo ie ecommende quali y wi h agglome a i e clus e ing. MSE esul s
om agglome a i e clus e ing showed di e en esul s in gen e a ing and a ing ags. The a ing gen e
esul s we e ela i ely smalle wi h a ing gen es sco es o 0–0.06 and a ing ags sco es wi h 0–0.23.
Agglome a i e clus e ing algo i hms wi h a ing ags ha e Dunn Ma ix esul s ha end o be g ea e
han 0.45. The a e age simila i y in he agglome a i e clus e ing gen e showed ha he high simila i y
alue depended on he numbe o clus e s. The a e age simila i y in agglome a i e clus e ing ags
showed ha he high simila i y alue depended on he numbe o clus e s. The associa ion ule wi h
he Ap io i algo i hm in agglome a i e clus e ing app oach p o ides 22% suppo o he gen e and
16% o ags o cus ome s who choose mo ies A and B. Suppo is an indica ion o how o en he
i emse appea s in linkages. In addi ion, 22% con idence is no ed o he gen e and 16% o ags o
cus ome s who choose mo ie A and mo ie B. Li ep esen s a a io o 1.0 o gen e and 1.0 o ags
o he obse ed suppo alue. F om he pe o mance e alua ion, we see ha he agglome a i e
clus e ing me hod pe o ms well wi h he Calinski-Ha abaz Index wi h a sco e o 49.34.
4.2.7. Spec al Clus e ing Pe o mance
Now we e alua e he mo ie ecommende quali y wi h spec al clus e ing. Mean squa ed e o
(MSE) esul s om spec al clus e ing showed di e ences in gen e a ing and a ing ags. The a ing
ag esul s we e ela i ely smalle wi h a a ing gen e sco e ange o 0–0.62 and a ing ags sco es
o 0–0.17. Spec al clus e ing algo i hm wi h ag a ing has he bes Dunn Ma ix esul s a 4.61
and he bes spec al clus e ing algo i hm esul s wi h gen e a 2.09. The a e age simila i y in he
spec al clus e ing gen e showed ha he high simila i y alue depended on he numbe o clus e s.
The a e age simila i y in spec al clus e ing ags showed ha he high simila i y alue depended
on he numbe o clus e s. Spec al clus e ing in ags has he bes compu a ional ime a 6.22 ms.
The associa ion ule wi h Ap io i algo i hm in spec al clus e ing app oach p o ides 12% suppo o
he gen e and 33% suppo o ags o cus ome s who choose mo ies A and B. Suppo is an indica ion
o how o en he i emse appea s in linkages. Con idence is 75% o he gen e and 100% o ags o
he cus ome s who choose mo ie A and mo ie B. Li ep esen s he a io o 3.12 o gen e and 3.0
o ags o he obse ed suppo alues. Clus e ing pe o mance e alua ion showed ha he spec al
clus e ing me hod showed good pe o mance wi h he Calinski-Ha abaz Index wi h a sco e o 16.39.
5. Conclusions
In his s udy, se en clus e ings we e used o clus e pe o mance compa ison me hods o mo ie
ecommenda ion sys ems, such as he
K
-Means algo i hm, bi ch algo i hm, mini-ba ch
K
-Means
algo i hm, mean-shi algo i hm, a ini y p opaga ion algo i hm, agglome a i e clus e ing algo i hm,
and spec al clus e ing algo i hm. The de eloped op imized g oupings om se e al algo i hms we e
hen used o compa e he bes algo i hms wi h ega d o he simila i y g oupings o use s on mo ie
gen e, ags, and a ing using he Mo ieLens da ase . Then, op imizing
K
o each clus e did no
signi ican ly inc ease he a iance. To be e unde s and his me hod, a iance e e s o he e o .
One o he ways o calcula e his e o is o ex ac he cen oid o i s espec i e g oups. Then, his alue
is squa ed ( o emo e he nega i e e ms) and all hose alues a e added o ob ain he o al e o .
To e i y he quali y o he ecommende sys em, he mean squa ed e o (MSE), Dunn Ma ix as
clus e alidi y indices and social ne wo k analysis (SNA) we e used. In addi ion, a e age simila i y,
compu a ional ime, associa ion ule wi h Ap io i algo i hm and clus e ing pe o mance e alua ion
measu es we e used o compa e he me hods o pe o mance sys ems.
Using he Mo ieLens da ase , expe imen e alua ion o he se en clus e ing me hods e ealed
he ollowing:
1.
The bes mean squa ed e o (MSE) alue is p oduced by he bi ch me hod wi h a ela i ely small
squa ed e o sco e in he a ing gen e and a ing ags.
Symme y 2020,12, 185 25 o 27
2.
Spec al clus e ing algo i hm wi h ag a ing has he bes Dunn Ma ix esul s a 4.61 and he
spec al clus e ing algo i hm has he bes gen e esul s a 2.09. The highe he Dunn index alue
is, he be e he g ouping.
3.
The closes dis ance o he social ne wo k analysis (SNA) is he mean-shi me hod,
which indica es ha he dis ance be ween clus e s has a high linkage ela ionship in a iance.
4.
The bi ch me hod had a ela i ely high a e age simila ly o inc ease he numbe o clus e s,
which showed a good le el o simila i y in clus e ing.
5.
The bes compu a ional ime is indica ed by he mean-shi o gen e a 13.75 ms and spec al
clus e ing o ags a 6.22 ms.
6.
Visualiza ion o clus e ing and op imizing
k
o mo ie gen e in algo i hms is be e han mo ie
ags because ewe da a a e used o mo ie ags.
7.
Mini-ba ch
K
-Means clus e ing app oach is he bes app oach o he associa ion ule wi h
Ap io i algo i hm wi h a high sco e o suppo , 100% con idence, and 7.0 a io o li o
i em ecommenda ions.
8.
Clus e ing pe o mance e alua ion shows ha he
K
-Means me hod exhibi s good pe o mance
wi h he Calinski-Ha abaz Index wi h a sco e o 59.41, and he bi ch algo i hm wi h a sco e o
1.24, on he Da ies–Bouldin Index.
9. Bi ch is he bes me hod based on a compa ison o se e al pe o mance ma ices.
Au ho Con ibu ions:
W i ing—o iginal d a p epa a ion, D.C.G.P.; w i ing— e iew and edi ing, P.S.;
supe ision, J.-S.L. All au ho s ha e ead and ag eed o he published e sion o he manusc ip .
Funding: This esea ch ecei ed no ex e nal unding.
Acknowledgmen s:
This esea ch was suppo ed by he Minis y o Science and Technology (MOST) unde he
g an MOST-108-2221-E-011-061- and MIT Labo a o y, Na ional Taiwan Uni e si y o Science and Technology. 2.
Fo he esea ch, in as uc u e o he SIX Cen e was used.
Con lic s o In e es :
The au ho s decla e no con lic o in e es .The unde s had no ole in he design o he s udy;
in he collec ion, analyses, o in e p e a ion o da a; in he w i ing o he manusc ip , o in he decision o publish
he esul s.
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