On Membe Labelling in Social Ne wo ks
Ra ael Co chuelo(B), An onia M. Reina Quin e o, and Pa icia Jim´enez
ETSI In o m´a ica, A da. Reina Me cedes s/n, E-41012 Se illa, Spain
{co chu, einaqu,pa iciajimenez}@us.es
Abs ac . So wa e agen s a e inc easingly used o sea ch o expe s, ecommend
esou ces, assess opinions, and o he simila asks in he con ex o social ne wo ks,
which equi es o ha e accu a e in o ma ion ha desc ibes he ea u es o he membe s
o he ne wo k. Un o u-na ely, many membe p ofiles a e incomple e, which has
mo i a ed many au ho s o wo k on au oma ic membe labelling, ha is, on echniques
ha can in e he null ea u es o a membe om his o he neighbou -hood. Cu en
p oposals a e based on local o global app oaches; he o me compu e p edic o s om
local neighbou hoods, whe eas he la - e analyse social ne wo ks as a whole. Thei
main p oblem is ha hey end o be inefficien and hei effec i eness deg ades
significan ly as he pe cen age o null labels inc eases. In his pape , we p esen Ka z,
which is a no el hyb id p oposal o sol e he membe labelling p oblem using neu al
ne wo ks. Ou expe imen s p o e ha i ou pe o ms o he p o-posals in he li e a u e
in e ms o bo h effec i eness and efficiency.
Keywo ds: Social ne wo ks · Membe labelling · Hyb id app oach · Neu al
ne wo ks
1 In oduc ion
On-line social media ha e sp ou ed ou du ing he las decade. They ha e pa ed
he way o on-line social ne wo ks whose membe s ypically in e ac o sha e o
o e ie e in o ma ion om one ano he . Ne e be o e has i been easie o find
in o ma ion abou indi iduals, hei demog aphics, hei likes, hei dislikes, he
ac i i ies in which hey engage, hei opinions, hei hough s, and so on. And
some hing ha is e en mo e impo an : hei ela ionships.
So wa e agen s a e being used in asks such as sea ching o expe s ega d-
ing a gi en opic, ecommending esou ces (pos s, ideos, music, and he like),
assessing opinions, a ge ing ad e isemen s, sociological s udies, and so on. Fo
hese agen s o succeed in p oducing accu a e in o ma ion, i is e y impo -
an ha he in o ma ion in a membe ’s p ofile be as comple e as possible.
Un o una ely, i is no uncommon ha many membe s do no comple e hei
p ofiles [11], which makes i e y difficul o so wa e agen s o wo k well.
Many au ho s ha e paid a en ion o a p oblem ha is commonly e e ed o
as membe labelling (aka. membe classifica ion, node classifica ion, link-based
classifica ion, o collec i e classifica ion). Simply pu , he idea is o in e he
ea u es o a membe o a social ne wo k as accu a ely as possible using solely
he ea u es a ailable om membe s wi h whom he o she has a ela ionship [1].
This has p o en o wo k well because social ne wo ks ha e a p ope y ha is
known as homophily [19], acco ding o which membe s who ha e simila ea-
u es end o ha e s onge ela ionships han membe s ha ha e e y dissimi-
la ea u es. The cu en p oposals in he li e a u e a e based on local o global
me hods. The o me lea n a p edic o om he ea u es o he membe s o a
social ne wo k, including some neighbou s; he la e ackle he p oblem om a
global pe spec i e and a emp o analyse social ne wo ks as a whole. The main
p oblem wi h cu en p oposals is ha hey ha e p o en o be inefficien and
ineffec i e as he size o a social ne wo k o he numbe o null ea u es inc eases.
This mo i a ed us o wo k on Ka z, which is a no el hyb id p oposal o sol e
he membe labelling p oblem. I is based on neu al ne wo ks, which a e used o
in e a p edic o o each membe ea u e using he in o ma ion p o ided by an
unbounded neighbou hood. I s a s analysing each membe ’s p ofile in isola ion,
and hen explo es his o he neighbou hood sea ching o he ela ionships and
ea u es ha con ibu e he mos o p oducing a be e p edic o . I is no a local
me hod since i explo es an unbounded con ex and selec s he mos in e es ing
ea u es and neighbou s o lea n a p edic o ; nei he is i a global me hod because
i does no a emp o analyse social ne wo ks as a whole; ha is he eason why
we e e o Ka z as a hyb id p oposal. Ou expe imen s on qui e a la ge eal-
wo ld social ne wo k p o e ha i ou pe o ms o he p oposals in he li e a u e
in e ms o bo h effec i eness and efficiency.
The es o he pape is o ganised as ollows: Sec ion 2desc ibes ou p oposal;
Sec ion 3 epo s on he esul s o ou expe imen s; Sec ion 4su eys he ela ed
wo k and compa es i o ou s; finally, Sec ion 5p esen s ou conclusions.
2 Ou P oposal
Ka z wo ks on a social ne wo k ha is ep esen ed as a g aph in which a node
ep esen s all o he ea u es o a membe p ofile and an edge ep esen s a ela-
ionship o ano he membe . I analyses he ne wo k and e u ns a map in which
each ea u e is associa ed wi h a se o neu al ne wo ks ha can be used o label a
new membe ega ding ha ea u e. No e ha each ea u e is p edic ed by means
o a se o neu al ne wo ks ha a e lea n om diffe en pa i ions o he social
ne wo k; he goal, which has been confi med empi ically, is o dec ease he e o
a e by using an ensamble-p edic o app oach ins ead o he single-p edic o
app oach ha is common in he li e a u e. In he ollowing subsec ions, we fi s
p esen he main p ocedu e o Ka z and hen an ancilla y p ocedu e ha is used
o ex end a neu al ne wo k o he mos app op ia e neighbou hood.
Main P ocedu e: Figu e 1shows he main p ocedu e o Ka z. I wo ks on a
g aph (N,E) ha ep esen s a social ne wo k. Nis a collec ion o ec o s o
he o m (m, 1, 2,..., n), whe e mis he unique iden ifie o a membe o he
social ne wo k and ia e he alues o i s ea u es (i=1...n); ea u es can be
1: Ka z(N,E)
2: m=∅
3: o each ea u e used in Ndo
4: ns =∅
5: epea β imes
6: = selec nodes in Nwi h a alue o
7: s = c ea e a aining se wi h γ| | nodes om
8: s = s
9: n=null
10: do
11: (n, s, s)=expandNeu alNe wo k(n, s, s,N,E)
12: exi when n=n
13: (n, s, s)=(n, s, s)
14: end
15: w=1/e o (n, s)
16: ns =ns ∪{(n,w)}
17: end
18: m=m∪{( ,ns)}
19: end
20: e u n m
Fig. 1. Main p ocedu e o Ka z
ei he nume ic (e.g., age, sala y, o opinion pola i y abou a opic) o ca ego ical
(e.g., na ionali y, gende , o dislikes). Eis a collec ion o ec o s o he o m
(m1,m2,k,w), whe e m1and m2a e he iden ifie s o wo membe s o he social
ne wo k, kdeno es a kind o ela ionship be ween hem, and wis he weigh o
ha ela ionship. The ela ionships include any kind o in e ac ion be ween any
wo membe s o a social ne wo k (e.g., eplies o pos s, pos o wa ds, iendship
eques s, message exchanges, and so on). Thus, he weigh o edge (m1,m2,k,w)
is compu ed as he numbe o ac ual in e ac ions o ype k ha ha e occu ed
be ween membe s m1and m2.
The esul o he main p ocedu e is compu ed in a iable m, which is a map
ha associa es e e y ea u e in he social ne wo k wi h a collec ion o uples
o he o m (n,w), whe e nis a neu al ne wo k, which ac s as a eg esso o a
classifie o he co esponding ea u e, and wis i s weigh , which is he in e se o
he e o a e; ha is, he smalle he e o a e, he mo e impo an he neu al
ne wo k and he la ge he e o a e, he less impo an he neu al ne wo k. Ka z
e u ns β ules o e e y ea u e, whe e βis a use -p o ided pa ame e . To label a
new membe ega ding a gi en ea u e, he neu al ne wo ks a e applied one a e
he o he . In he case o nume ic ea u es, he alues p edic ed by each ule a e
weigh ed acco ding o hei no malised e o a e and hen a e aged; in he case
o ca ego ic ea u es, he esul s a e weigh ed acco ding o he no malised e o
a e and he mos o ed one is e u ned.
The main p ocedu e basically i e a es o e he se o ea u es in he social
ne wo k; in each i e a ion, i epea s he ollowing p ocedu e β imes: i fi s
selec s he subse o nodes ha ha e a alue o he ea u e being analysed and
hen spli s i in o a aining se and a alida ion se . The size o he aining se
is con olled by means o γ, which is a use -p o ided pa ame e ; he emaining
1: expandNeu alNe wo k(n, s, s,N,E)
2: i n=null hen
3: n= lea n ne wo k om s
4: else
5: c= expand he neighbou hood o s and s using (N,E)
6: o each (u, )in cdo
7: n= lea n a ne wo k om u
8: s=u
9: s=
10: i e o (n, s)<e o (n, s) hen
11: (n, s, s)=(n, s, s)
12: end
13: end
14: end
15: e u n (n, s, s)
Fig. 2. P ocedu e o expand a neu al ne wo k
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Fig. 3. Exce p o an expanded aining se
nodes a e used o alida ion pu poses. I hen ini ialises a neu al ne wo k n
o a null ne wo k ha does no hing, and hen epea edly expands i un il no
u he expansion is possible. Expanding a neu al ne wo k consis s o ex ending
i o some neighbou s as long as his helps o educe he e o a e. We p o ide
addi ional de ails in he ollowing subsec ion.
Expanding Neu al Ne wo ks: Figu e 2shows he p ocedu e o expand a
neu al ne wo k. I wo ks on a neu al ne wo k n, a aining se s, a alida ion
se s, and a social ne wo k (N,E); i e u ns a new neu al ne wo k, he aining
se om which i was lea n , and he alida ion se on which i was alida ed.
The p ocedu e fi s checks i he inpu neu al ne wo k is null, in which case i
simply lea ns a neu al ne wo k om he aining se and e u ns i . O he wise,
i fi s expands he neighbou hood o he aining and he alida ion se s using
he in o ma ion p o ided by he social ne wo k. Expanding he neighbou hood
o a da ase means ha i s ec o s a e expanded wi h addi ional componen s
ha ep esen he ea u es o a kind o neighbou . Fo ins ance, Figu e 3shows
Table 1. Expe imen al esul s
ŐĞ EĂƚŝŽŶ
Nulli .
ETETETETET
Nulli .
ETETETETET
5.00% 5.55 7.01 9.70 12.39 8.85 6.75 5.00% 19.12 5.56 19.77 5.60 3.44 11.77 7.94 13.51 5.40 4.10
10.00% 9.39 8.22 14.30 12.74 12.55 6.69 10.00% 26.85 6.79 21.28 6.95 6.81 12.27 8.33 15.06 9.09 3.76
15.00% 16.45 9.18 10.70 15.60 10.88 4.36 15.00% 27.55 7.33 22.01 7.83 9.00 12.64 14.96 18.77 13.55 3.74
20.00% 6.49 10.61 11.16 16.30 11.75 4.71 20.00% 22.76 9.04 22.75 6.96 10.33 15.55 8.94 20.13 17.36 3.23
25.00% 20.43 11.37 20.00 14.55 18.83 4.70 25.00% 34.96 7.25 23.56 7.39 19.24 16.57 8.59 20.62 25.13 4.40
30.00% 24.08 10.94 31.86 16.23 15.62 4.68 30.00% 48.85 7.99 24.25 7.27 7.88 12.54 17.79 22.72 12.34 5.07
35.00% 35.55 13.56 21.17 15.63 10.59 5.05 35.00% 23.34 8.59 25.05 8.13 22.35 13.76 35.32 26.06 20.84 4.76
40.00% 23.39 12.46 15.31 17.88 17.86 4.66 40.00% 22.85 7.19 35.82 8.14 24.67 16.75 27.80 23.97 20.46 2.44
45.00% 50.13 12.92 36.26 21.65 13.18 6.38 45.00% 54.20 7.53 26.50 8.65 19.85 16.79 19.85 23.39 21.07 3.33
50.00% 40.23 15.81 17.44 20.75 10.48 5.59 50.00% 49.13 7.86 44.71 10.52 52.53 17.77 17.79 27.51 44.04 3.57
Mean 23.17 11.21 18.79 16.37 13.06 5.36 Mean 29.96 7.51 25.57 7.74 17.61 14.64 16.73 21.17 17.93 3.84
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Nulli .
ETETETETET
Nulli .
ETETETETET
5.00% 5.40 6.35 10.25 6.54 5.62 5.40 9.73 4.65 8.01 4.08 5.00% 21.75 5.50 16.52 7.54 4.06 5.81 9.85 4.55 6.46 5.41
10.00% 5.72 9.33 13.54 6.90 14.50 5.61 16.40 4.86 12.73 4.14 10.00% 23.86 6.59 18.81 9.03 11.93 5.69 15.55 4.98 5.48 4.04
15.00% 6.52 10.71 22.70 6.04 12.84 6.42 11.45 5.97 11.17 4.44 15.00% 27.77 7.92 19.95 9.47 10.85 5.89 10.73 5.32 8.01 5.27
20.00% 14.85 12.21 26.83 6.96 24.15 6.08 17.67 6.67 15.25 4.76 20.00% 30.22 8.19 21.11 7.34 11.14 6.30 8.69 5.33 7.12 5.24
25.00% 15.29 13.68 31.03 7.16 5.59 7.49 23.57 5.72 17.17 3.22 25.00% 35.98 9.64 22.26 7.92 8.18 6.55 22.06 5.59 21.34 5.30
30.00% 7.71 15.19 20.18 8.41 35.44 5.93 32.64 6.49 10.59 4.14 30.00% 24.09 9.59 23.47 9.40 25.70 6.88 19.83 5.69 28.90 2.09
35.00% 25.13 16.59 21.76 9.59 6.35 4.73 23.68 6.95 16.38 3.55 35.00% 40.91 11.79 24.63 8.97 14.68 7.94 35.23 6.84 28.30 2.07
40.00% 18.76 18.08 23.57 7.91 20.12 3.62 24.36 7.03 14.36 4.06 40.00% 53.60 9.75 25.74 9.76 21.84 9.44 24.57 7.36 25.61 1.57
45.00% 13.36 19.68 29.06 7.91 27.63 3.21 14.86 5.82 13.36 4.09 45.00% 30.26 7.60 30.94 9.48 30.13 9.62 31.53 8.74 29.31 2.28
50.00% 28.18 20.87 26.63 9.50 27.29 2.88 42.70 6.43 15.29 3.83 50.00% 32.96 7.78 28.06 11.67 21.03 12.00 19.98 10.05 32.13 2.29
Mean 12.09 14.27 22.16 7.69 17.95 5.14 21.71 6.06 13.43 4.03 Mean 32.14 8.43 22.75 9.06 15.95 7.61 19.80 6.44 17.27 3.56
'ƌŽƵƉ >ŝŬŝƐ
Nulli .
ETETETETET
Nulli .
ETETETETET
5.00% 14.36 5.01 18.56 6.07 8.53 9.52 9.17 4.13 8.33 5.40 5.00% 19.49 5.49 13.50 7.91 10.34 5.19 15.19 10.84 10.75 6.26
10.00% 23.36 9.27 23.09 9.35 14.53 9.32 13.18 9.30 11.34 5.06 10.00% 24.50 9.33 20.25 9.28 18.35 9.26 20.20 9.31 13.75 5.62
15.00% 27.86 10.79 25.28 10.75 17.54 10.82 15.18 10.74 12.83 3.85 15.00% 27.00 10.78 21.12 10.80 17.84 10.83 22.70 10.83 15.25 9.25
20.00% 32.36 12.26 27.57 12.30 20.53 12.23 17.17 12.27 14.33 4.26 20.00% 29.49 12.18 21.95 12.17 20.34 12.25 25.20 12.20 16.75 7.68
25.00% 36.86 13.84 29.75 13.64 23.53 13.76 19.17 13.82 15.84 4.19 25.00% 31.99 13.62 22.85 13.69 22.85 13.74 27.70 13.75 18.25 6.99
30.00% 41.36 15.22 32.08 15.31 26.53 15.22 21.18 15.13 17.33 5.77 30.00% 34.49 15.10 23.63 15.12 25.35 15.06 30.19 15.14 19.75 9.72
35.00% 45.86 16.70 34.43 16.54 29.53 16.56 23.17 16.60 18.84 5.14 35.00% 37.00 16.73 24.50 16.64 27.84 16.63 32.70 16.51 21.25 9.48
40.00% 50.36 18.02 36.70 18.25 32.53 18.33 25.18 18.06 20.33 2.97 40.00% 39.50 17.95 25.42 18.02 30.35 18.12 35.20 18.09 22.76 16.02
45.00% 54.86 19.72 38.72 19.74 35.53 19.76 27.18 19.64 21.83 3.82 45.00% 42.00 19.64 32.22 19.50 32.85 19.51 37.69 19.46 24.26 19.39
50.00% 59.36 21.27 45.05 21.01 38.53 21.32 29.17 21.35 23.33 3.41 50.00% 44.50 21.34 37.04 20.85 35.35 20.91 40.19 21.19 25.75 13.73
Mean 38.66 14.21 30.72 14.29 24.73 14.68 19.98 14.10 16.43 4.39 Mean 33.00 14.22 22.65 14.40 24.15 14.15 28.70 14.73 18.85 10.41
Ka zLGNJ MP B
NJ LG MP B Ka z
NJ LG MP B Ka z
NJ LG MP B Ka z
NJ LG MP B
NJ LG MP B
Ka z
Ka z
an exce p o an ini ial aining se on he le ; on he igh , ha aining se has
been expanded wi h he ea u es o he neighbou s ega ding he ‘sends-message’
ela ionship; no e ha he weigh o he ela ionship is added as an addi ional
ea u e o he ec o .
Then, he p ocedu e i e a es h ough he se o expansions o he aining se
and lea ns a new neu al ne wo k om each one. I e u ns he expanded neu al
ne wo k ha achie es he smalles e o a e oge he wi h he aining se om
which i was lea n and alida ion se on which he e o a e was compu ed.
3 Expe imen al Resul s
We conduc ed a se ies o expe imen s o analyse how Ka z pe o ms in p ac ice.
The expe imen s we e ca ied ou using a Ja a 1.7 implemen a ion ha was un

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Fig. 4. G aphic summa y
on a ou - h eaded In el Co e i7 compu e ha an a 2.93 GHz, had 16 GiB
o RAM, Windows 7 P o 64-bi , O acle’s Ja a De elopmen Ki 1.7.902, and
Weka 3.6.8.
We implemen ed he gene al amewo k by Ne ille and Jensen [17](NJ)
and hen he specific p oposals by Lu and Ge oo [12] (LG), Macskassy and
P o os [13] (MP), and Bhaga e al. [3] (B). Rega ding he p e ious p oposals,
we conside ed ha a labelling was es able when no mo e han 5% o he ea u es
changed in an i e a ion o he me hod. Rega ding Ka z, we expe imen ed wi h
se e al combina ions o pa ame e s and kinds o neu al ne wo ks. We ound ou
ha he ollowing alues o he pa ame e s wo k qui e well: β= 10, ha is, 10
neu al ne wo ks lea n o each ea u e, and γ=0.25, ha is, 25% o he nodes
a ailable in he social ne wo k a e used o aining pu poses and he emaining
o alida ion pu poses. Rega ding he lea ning echnique, we ound ou ha
RBFN ne wo ks [4] a e he bes pe o ming in his con ex .
The expe imen s we e pe o med on a da ase ha consis ed in a dump o
ou uni e si y social ne wo k. This ne wo k has 56,431 membe s, each o which
is cha ac e ised by a p ofile ha includes he ollowing ea u es: age (a na u-
al alue), gende (male, emale), g oup (s uden , lec u e , s aff), na ionali y
(Spanish, F ench, I alian, and so on), school (Compu e -Science, Ma hema -
ics, Physics, Philology, and so on), likes, and dislikes; o he ea u es like name,
add ess, na ional id o passpo we e disca ded o keep he da a anonymous;
nei he was i e y in e es ing o a emp o p edic hem. The likes and dislikes
a e se s o key wo ds ha a e selec ed by he membe s om a lis ha is com-
pu ed au oma ically om he messages pos by he membe s o he ne wo k; o
deal wi h hem in ou expe imen s, we selec ed he op 50 key wo ds and c ea ed
bina y ea u es o he o m likes Xo dislikes Y, whe e Xo Y ep esen s key wo ds.
The ela ionships be ween he membe s o he ne wo k a e he ollowing: pos s-
o-wall, eplies- o-pos , o wa ds-pos , sends-message, ollows-membe , eques s-
iendship. This da ase was pa icula ly use ul because almos e e y p ofile has
accu a e ea u es ha a e se au oma ically using he s uden s’ egis a ion da a
o he lec u e s’ and s aff’s wo k con ac s, and he likes and dislikes a e also
selec ed om se s o p e-compu ed key wo ds. Tha is, we had qui e a la ge
co ec ly labelled da ase on which could conduc qui e a p ecise alida ion.
To e alua e ou p oposal and compa e i o o he s, we c ea ed se e al da ase s
om he p e ious one. They we e e sions o he o iginal da ase in which we
nullified he ea u es o 5% up o 50% nodes ha we e chosen andomly. This
helped us o e alua e how ou p oposal wo ks and compa e i o o he s in e ms
o e o a e (E) and p ocessing ime (T). The e o a e was compu ed as he
pe cen age o w ong p edic ions; in he case o nume ic ea u es a ±10% ole ance
h eshold was es ablished o conside a p edic ion w ong. The p ocessing ime
was measu ed in CPU plus IO hou s, since hese imings a e a mo e eliable
and s able han use imes.
Table 1shows ou esul s and Figu e 4summa ises hem using a couple o
cha s. (The columns ha co espond o p oposals NJ and LG ega ding ea-
u e ‘age’ a e emp y because hese me hods canno be applied o nume ic ea-
u es.) Rega ding effec i eness, he fi s conclusion is ha he e o a e inc eases
s eadily as he pe cen age o nullifica ion inc eases, bu Ka z keeps he smalles
global mean in he majo i y o cases, whe e global mean e e s o he compu ed
mean o each ea u e o a gi en nullifica ion pe cen age, c . he uppe pa
o Figu e 4. To compa e he esul s mo e p ecisely, we ha e compu ed he en-
dency lines o each p oposal acco ding o he pe cen age o nullifica ion, which
is deno ed as N:
P oposal E o a e endency R2
NJ 2.78N+14.72 0.99
LG 1.88N+15.17 0.93
MP 2.99N+4.16 0.95
B2.15N+9.17 0.88
Ka z 1.69N+7.37 0.92
No e ha he R2coefficien is e y good in e e y case, which means ha
he e is a clea linea endency in he esul s. The smalles slope co esponds
o Ka z, which means ha i is he p oposal whose e o a e inc eases a he
lowes pace as he pe cen age o nullifica ion inc eases; i is ollowed by LG, bu
no e ha he e o a e o his p oposal is oughly double as Ka z’s.
Rega ding efficiency, he fi s conclusion is ha Ka z seems o ha e a
beha iou ha is e y s able, whe eas he o he p oposals seem o equi e mo e
p ocessing ime as he pe cen age o nullifica ion inc eases. To confi m his idea,
we ha e also compu ed he endency lines o each p oposal, namely:
P oposal P ocessing ime endency R2
NJ 1.04N+5.62 0.98
LG 0.66N+6.08 0.98
MP 0.78N+6.93 0.97
B1.00N+7.63 0.98
Ka z 0.08N+4.81 0.95
No e ha he R2coefficien is again e y good in e e y case. The smalles
slope co esponds again o Ka z, which means ha i is he p oposal whose p o-
cessing ime inc eases a a lowe pace as he pe cen age o nullifica ion inc eases.
No e ha i is e y close o 0.00, which means ha he p ocessing ime emains
almos cons an ; he eason is ha he size o he aining se s dec ease as he
pe cen age o nullifica ion inc eases, which makes lea ning neu al ne wo ks eas-
ie ; un o una ely, as he pe cen age o nullifica ion inc eases, he numbe o
neighbou s ha mus be explo ed o keep as a low e o a e as possible inc eases.
Ka z is ollowed by he o he p oposals, which equi e conside ably mo e p o-
cessing ime since hey ha e o i e a e un il he labelling is s able enough, which
is mo e and mo e difficul as he pe cen age o nullifica ion inc eases.
4 Rela ed Wo k
The e a e wo mains eam app oaches o he membe labelling p oblem [9],
namely: local and global me hods. They bo h wo k on a g aph-based ep e-
sen a ion o he social ne wo k being analysed, whe e he nodes s o e membe
ea u es and he edges keep ack o hei in e ac ions, bu diffe in ha he
o me ocus on lea ning local p edic o s om e e y membe and his o he local
neighbou hood, whe eas he la e analyse he social ne wo k as a whole.
Below, we epo on bo h app oaches and discuss on how ou p oposal
imp o es on hem om a concep ual poin o iew.
Local Me hods: These me hods can be u he classified in o ins an ia ions o
he I e a i e Classifica ion Algo i hm by Ne ille and Jensen [17] o ins an ia ions
o he Gibbs Sampling Algo i hm by Geman and Geman [8].
The me hods ha a e based on he I e a i e Classifica ion Algo i hm [17]
ans o m a social ne wo k in o a da ase o ec o s, each o which p o ides he
ea u es o a membe ’s p ofile plus some agg ega ed ea u es ha co espond o
he membe s in his o he neighbou hood. They analyse each ea u e in isola ion
as ollows: hey fi s lea n a local p edic o om he membe s whose p ofiles
p o ide a non-null alue o ha ea u e. (In o mally, his is commonly e e ed
o as “ he membe is labelled”.) The p edic o is ei he a eg esso o a classifie
depending on whe he he ea u e being analysed is nume ic o ca ego ical. I is
hen used o compu e he label o he unlabelled membe s, as long as hey ha e
a leas a labelled neighbou . No e ha labelling a membe will likely change
he alues o he agg ega ed ea u es in he neighbou hood, so he labelling p o-
cess needs o be epea ed i e a i ely un il he labels do no change d ama ically
o do no change a all. The p e ious idea has been ins an ia ed many imes
in he li e a u e, he diffe ence being he kind o p edic o used: Ne ille and
Jensen [17] used Nai e-Bayes p edic o s, Lu and Ge oo [12] used logis ic eg es-
sion, Macskassy and P o os [13] used a o ing app oach, and Bhaga e al. [3]
and McDowell e al. [16]usedk-nea es neighbou s. Recen ly, Ca al epe e al. [6]
ha e used diffe en ypes o p edic o s o membe ea u es and neighbou hood
ea u es, which a e hen combined o p oduce an ensamble p edic o .
The me hods ha a e based on he Gibbs Sampling Algo i hm [8]wo kin
ou phases, namely: boo s apping, bu n-in, collec ing, and labelling. In he
boo s apping phase, hey lea n a p edic o in a way ha is e y simila o
he me hods ha a e based on he I e a i e Classifica ion Algo i hm, and hen
use i o label he unlabelled membe s. Then, he bu n-in phase is epea ed a
numbe o imes; in each epe i ion, he membe s ha we e ini ially unlabelled
a e andomly o de ed and hen new labels a e compu ed using a p edic o , which
can be he same ha was used in he boo s apping phase o a new one [14]. In
he sample collec ion phase, he p ocess is epea ed a p e-defined numbe o imes
and he coun o labels assigned o each membe is compu ed. Finally, in he
labelling phase, he membe s ha we e ini ially unlabelled a e assigned he mos
likely label acco ding o he coun s ha we e compu ed in he p e ious phase.
Bo h McDowell e al. [15] and Macskassy and P o os [14] ha e ins an ia ed his
idea; he o me used Nai e-Bayes and k-nea es neighbou s and he la e used
diffe en combina ions o p edic o s.
Global Me hods: The mos common me hods in his ca ego y a e based on
andom walks and op imisa ion.
A andom walk on a g aph is a e y special case o a Ma ko chain. The co e
idea was in oduced by Zhu e al. [23]: hey ely on a ansi ion ma ix P ha
encodes he p obabili y ha a andom walk p oceeds be ween any wo membe s
o a social ne wo k using hei ela ionships. Gi en an unlabelled membe , he
me hod assigns i he mos common label ou o he membe s ha can be eached
om i using andom walks. Tha is, i equi es o compu e an app oxima ion