Heterogeneous Information Network Embedding for Meta Path based Proximity

1 MB·

by  Zhipeng Huang

Heterogeneous Information Network Embedding for
Meta Path based Proximity
Zhipeng Huang, Nikos Mamoulis
TheUniversityofHongKong
{zphuang, nikos}@cs.hku.hk
ABSTRACT
7 Anetworkembeddingisarepresentationofalargegraphinalow- v1 t1 v2 t2 v3
1 dimensional space, where vertices are modeled as vectors. The WWW Embed KDD Mining ICDM
0
objective of a good embedding is to preserve the proximity (i.e.,
2
similarity)betweenverticesintheoriginalgraph. Thisway, typ-

n ical search and mining methods (e.g., similarity search, kNN re- WWW15 KDD16 ICDM16
a trieval, classification, clustering) can be applied in the embedded
J spacewiththehelpofoff-the-shelfmultidimensionalindexingap- p1 p2 p3

9 proaches.Existingnetworkembeddingtechniquesfocusonhomo-
1 geneous networks, where all vertices are considered to belong to a a
1 2
a single class. Therefore, they are weak in supporting similarity

] measures for heterogeneous networks. In this paper, we present
AI aneffectiveheterogeneousnetworkembeddingapproachformeta Object Types: Author KDD15 Paper Embed Topic KDD Venue
pathbasedproximitymeasures. Wedefineanobjectivefunction, Edge Types: Write Publish Mention Cite
.
s whichaimsatminimizingthedistancebetweentwodistributions,
c onemodelingthemetapathbasedproximities,theothermodeling
[ Figure1:AnexampleofHIN
theproximitiesintheembeddedvectorspace. Wealsoinvestigate

1 theuseofnegativesamplingtoacceleratetheoptimizationprocess.
v As shown in our extensive experimental evaluation, our method
nalgraph. Searchandanalysiscanthenbeappliedontheembed-
1 createsembeddingsofhighqualityandhassuperiorperformance
dingwiththehelpofefficientalgorithmsandindexingapproaches
9 inseveraldataminingtaskscomparedtostate-of-the-artnetwork
forvectorspaces.
2 embeddingmethods.
Heterogeneousinformationnetworks(HINs),suchasDBLP[15],
5
YAGO[26],DBpedia[2]andFreebase[4],arenetworkswithnodes
0 Keywords
and edges that may belong to multiple types. These graph data
.
1 heterogeneous information network; meta path; network embed- sourcescontainavastnumberofinterrelatedfacts,andtheycanfa-
0 ding cilitatethediscoveryofinterestingknowledge[11,14,17,20].Fig-
7 ure1illustratesaHIN,whichdescribestherelationshipsbetween
1 1. INTRODUCTION objects(graphvertices)ofdifferenttypes(e.g.,author,paper,venue
v: Theavailabilityandgrowthoflargenetworks,suchassocialnet- andtopic).Forexample,JiaweiHan(a1)haswrittenaWWWpaper
Xi works,co-authornetworks,andknowledgebasegraphs,hasgiven (p1C),owmhpiacrhedmteonhtioomnsotgoepnieco“uEsmnbeetdw”o(rtk1s),.therelationshipsbetween
risetonumerousapplicationsthatsearchandanalyzeinformation
r objectsinaHINaremuchmorecomplex. Theproximityamong
a inthem. However,forverylargegraphs,commoninformationre- objectsinaHINisnotjustameasureofclosenessordistance,but
trievalandminingtaskssuchaslinkprediction,nodeclassification,
itisalsobasedonsemantics. Forexample,intheHINinFigure1,
clustering, and recommendation are time-consuming. This moti-
authora isclosetobotha andv , buttheserelationshipshave
vatedalotofinterest[6,22,31]inapproachesthatembedthenet- 1 2 1
different semantics. a is a co-author of a , while v is a venue
workintoalow-dimensionalspace,suchthattheoriginalvertices 2 1 1
wherea hasapaperpublished.
of the graph are represented as vectors. A good embedding pre- 1
Metapath[29]isarecentlyproposedproximitymodelinHINs.
servestheproximity(i.e.,similarity)betweenverticesintheorigi-
Ametapathisasequenceofobjecttypeswithedgetypesinbe-
tweenmodelingaparticularrelationship.Forexample,A→P →
V → P → Aisa metapath, whichstates thattwoauthors (A)
arerelatedbytheirpublicationsinthesamevenue(V). Basedon
metapaths, severalproximitymeasureshavebeenproposed. For
example,PathCount[29]countsthenumberofmetapathinstances
connectingthetwoobjects,whilePathConstrainedRandomWalk
(PCRW) [14] measures the probability that a random walk start-
ing from one object would reach the other via a meta path in-
ACMISBN978-1-4503-2138-9.
DOI:10.1145/1235 stance. These measures have been shown to have better perfor-
mancecomparedtoproximitymeasuresnotbasedonmetapaths, someexamplesasseeds. TheproblemoflinkpredictiononHINs
invariousimportanttasks,suchask-NNsearch[29],linkpredic- hasbeenextensivelystudied[27,28,35], duetoitsimportantap-
tion[27,28,35], recommendation[34], classification[12,13]and plications (e.g., in recommender systems). A related problem is
clustering[30]. entityrecommendationinHINs[34],whichtakesadvantageofthe
Although there are a few works on embedding HINs [7,21], different types of relationships in HINs to provide better recom-
none of them is designed for meta path based proximity in gen- mendations.
eralHINs. Tofillthisgap,inthispaper,weproposeHINE,which
learns a transformation of the objects (i.e., vertices) in a HIN to 2.2 MetaPathandProximityMeasures
a low-dimensional space, such that the meta path based proximi- Metapath[29]isageneralmodelfortheproximitybetweenob-
ties between objects are preserved. More specifically, we define jectsinaHIN.Severalmeasureshavebeenproposedfortheprox-
anappropriateobjectivefunctionthatpreservestherelativeprox- imitybetweenobjectsw.r.t. agivenmetapathP. PathCountmea-
imitybasedrankingstheverticesintheoriginalandtheembedded suresthenumberofmetapathinstancesconnectingthetwoobjects,
space. Asshownin[29],metapathswithtoolargelengthsarenot and PathSim is a normalized version of it [29]. Path constrained
very informative; therefore, we only consider meta paths up to a randomwalk(PCRW)wasfirstlyproposed[14]forthetaskofre-
given length threshold l. We also investigate the use of negative lationship retrieval over bibliographic networks. Later, [17] pro-
sampling[19]inordertoacceleratetheoptimizationprocess. posedanautomaticapproachtolearnthebestcombinationofmeta
WeconductextensiveexperimentsonfourrealHINdatasetsto paths and their corresponding weights based on PCRW. Finally,
compareourproposedHINEmethodwithstate-of-the-artnetwork HeteSim [25] is recently proposed as an extension of meta path
embeddingmethods(i.e.,LINE[31]andDeepWalk[22]),whichdo basedSimRank. Inthispaper,wefocusonthetwomostpopular
notconsidermetapathbasedproximity. Ourexperimentalresults proximitymeasures,i.e.,PathCountandPCRW.
show that our HINE method with PCRW as the meta path based
proximitymeasureoutperformsallalternativeapproachesinmost 2.3 NetworkEmbedding
ofthequalitativemeasuresused.
Networkembeddingaimsatlearninglow-dimensionalrepresen-
Thecontributionsofourpaperaresummarizedasfollows:
tationsfortheverticesofanetwork,suchthattheproximitiesamong
• This is the first work that studies the embedding of HINs them in the original space are preserved in the low-dimensional
forthepreservationofmetapathbasedproximities. Thisis space.Traditionaldimensionalityreductiontechniques[3,8,24,32]
animportantsubject,becausemetapathbasedproximityhas typicallyconstructtheaffinitygraphusingthefeaturevectorsofthe
beenprovedtobemoreeffectivethantraditionalstructured vertexes and then compute the eigenvectors of the affinity graph.
basedproximities. Graph factorization [1] finds a low-dimensional representation of
agraphthroughmatrixfactorization, afterrepresentingthegraph
• We define an objective function, which explicitly aims at asanadjacencymatrix. However, sincethesegeneraltechniques
minimizingthethedistancebetweentwoprobabilitydistri- arenotdesignedfornetworks,theydonotnecessarilypreservethe
butions, one modeling the meta path based proximities be- globalnetworkstructure,aspointedoutin[31].
tweentheobjects,theothermodelingtheproximitiesinthe Recently, DeepWalk [22] is proposed as a method for learn-
low-dimensionalspace. ing the latent representations of the nodes of a social network,
from truncated random walks in the network. DeepWalk com-
• Weinvestigatetheuseofnegativesamplingtoacceleratethe binesrandomwalkproximitywiththeSkipGrammodel[18],alan-
processofmodeloptimization. guagemodelthatmaximizestheco-occurrenceprobabilityamong
the words that appear within a window in a sentence. However,
• WeconductextensiveexperimentsonfourrealHINs,which
DeepWalkhascertainweaknesseswhenappliedtoourproblemset-
demonstratethatourHINEmethodisthemosteffectiveap-
tings.First,therandomwalkproximityitadoptsdoesnotconsider
proach for preserving the information of the original net-
the heterogeneity of a HIN. In this paper, we use PCRW, which
works;HINEoutperformsthestate-of-the-artembeddingmeth-
extendsrandomwalkbasedproximitytobeappliedforHINs.Sec-
odsinmanydataminingtasks,e.g.,classification,clustering
ond, aspointedoutin[31], DeepWalkcanonlypreservesecond-
andvisualization.
orderproximity,leadingtopoorperformanceinsometasks,suchas
linkrecoverandclassification,whichrequirefirst-orderproximity
The rest of this paper is organized as follows. Section 2 dis-
tobewell-preserved.
cussesrelatedwork.InSection3,weformallydefinetheproblem.
LINE[31]isarecentlyproposedembeddingapproachforlarge-
Section4describesourHINEmethod. InSection5,wereportour
scalenetworks. Althoughitusesanexplicitobjectivefunctionto
experimentalresults.Section6concludesthepaper.
preserve the network structure, its performance suffers from the
way it learns the vector representations. By design, LINE learns
2. RELATEDWORK
tworepresentationsseparately,onepreservingfirst-orderproximity
andtheotherpreservingsecond-orderproximity. Then,itdirectly
2.1 HeterogeneousInformationNetworks
concatenates the two vectors to form the final representation. In
TheheterogeneityofnodesandedgesinHINsbringchallenges, thispaper,weproposeanetworkembeddingmethod,whichdoes
but also opportunities to support important applications. Lately, not distinguish the learning of first and second-order proximities
therehasbeenanincreasinginterestinbothacademiaandindustry andembedsproximitiesofallorderssimultaneously.
intheeffectivesearchandanalysisofinformationfromHINs.The GraRep[6]furtherextendsDeepWalktoutilizehigh-orderprox-
problemofclassifyingobjectsinaHINbyauthoritypropagationis imities.GraRepdoesnotscalewellinlargenetworksduetotheex-
studiedin[12]. Follow-upwork[13]investigatesacollectiveclas- pensivecomputationofthepowerofamatrixandtheinvolvement
sification problem in HINs using meta path based dependencies. ofSVDinthelearningprocess. SDNE[33]isasemi-supervised
PathSelClus[30]isalinkbasedclusteringalgorithmforHINs,in deepmodelthatcapturesthenon-linearstructuralinformationover
which a user can specify her clustering preference by providing thenetwork.ThesourcecodeofSDNEisnotavailable,sothisap-
Forexample,ametapathA −w−r−it→e P −w−r−it−e−−→1 Arepresentsthe
A A D coauthorrelationshipbetweentwoauthors.
AninstanceofthemetapathPisapathintheHIN,whichcon-
write
actIn direct
formstothepatternofP. Forexample, patha → p → a in
V publish P mention T P produce M compose C 1 3 2
cite Figure1isaninstanceofmetapathA−w−r−it→e P −w−r−it−e−−→1 A.
DEFINITION 3. (MetaPathbasedProximity)GivenaHING=
(a) DBLP (b) MOVIE
(V,E)andametapathP,theproximityoftwonodeso ,o ∈ V
s t
withrespecttoPisdefinedas:
Figure2:Schemasoftwoheterogeneousnetworks
(cid:88)
s(o ,o |P)= s(o ,o |p ) (1)
s t s t os→ot
pos→ot∈P
proachcannotbereproducedandcomparedtoours. Similarly,[5]
where p is a meta path instance of P linking from o to
embedsentitiesinknowledgebasesusinganinnovativeneuralnet- os→ot s
o ,ands(o ,o |p )isaproximityscorew.r.t. theinstance
workarchitectureandTriDNR[21]extendsthisembeddingmodel t s t os→ot
p .
toconsiderfeaturesfromthreeaspectsofthenetwork: 1)network os→ot
structure, 2) node content, and 3) label information. Our current
Therearedifferentwaystodefines(o ,o |p )intheliter-
workfocusesonmetapathbasedproximities, soitdoesnotcon- s t os→ot
ature.Here,weonlylisttwodefinitionsthatweuseastestcasesin
sideranyotherinformationintheHINbesidesthenetworkstruc-
ourexperiments.
tureandthetypesofnodesandedges.
• AccordingtothePathCount(PC)model,eachmetapathin-
3. PROBLEMDEFINITION stanceisequallyimportantandshouldbegivenequalweight.
Inthissection,weformulatetheproblemofheterogeneousinfor- Hence, s(os,ot | pos→ot) = 1 and the proximity between
mationnetwork(HIN)embeddingformetapathbasedproximities. two objects w.r.t. P equals the number of instances of P
WefirstdefineaHINasfollows: connectingthem,i.e.,s(os,ot|P)=|{pos→ot ∈P}|.1
DEFINITION 1. (HeterogeneousInformationNetwork)Ahet- • PathConstrainedRandomWalk(PCRW)[14]isamore
erogeneous information network (HIN) is a directed graph G = sophisticatedwaytodefinetheproximitys(os,ot|pos→ot)
(V,E) with an object type mapping function φ : V → L and a basedonaninstancepos→ot. Accordingtothisdefinition,
linktypemappingfunctionψ :E →R,whereeachobjectv ∈V s(os,ot |pos→ot)istheprobabilitythatarandomwalkre-
belongstoanobjecttypeφ(v) ∈ L,andeachlinke ∈ Ebelongs strictedonPwouldfollowtheinstancepos→ot.
toalinktypeψ(e)∈R.
Note that the embedding technique we introduce in this paper
Figure1illustratesasmallbibliographicHIN.Wecanseethat canalsobeeasilyadaptedtoothermetapathbasedproximitymea-
theHINcontainstwoauthors,threepapers,threevenues,twotop- sures,e.g.,PathSim[29],HeteSim[25]andBPCRW[17].
ics,andfourtypesoflinksconnectingthem.Fortheeaseofdiscus-
sion,weassumethateachobjectbelongstoasingletype;however, DEFINITION 4. (Proximity in HIN) For each pair of objects
o ,o ∈V,theproximitybetweeno ando inGisdefinedas:
ourtechniquecaneasilybeadaptedtothecasewhereobjectsbe- s t s t
longtomultipletypes. (cid:88)
s(o ,o )= s(o ,o |P) (2)
s t s t
DEFINITION 2. HINSchema. GivenaHING = (V,E)with P
mappingsφ : V → Landψ : E → R,theschemaTG ofGis wherePissomemetapath,ands(os,ot|P)istheproximityw.r.t.
adirectedgraphdefinedoverobjecttypesLandlinktypesR,i.e., themetapathPasdefinedinDefinition3.
T =(L,R).
G
AccordingtoDefinition4, theproximityoftwoobjectsequals
TheHINschemaexpressesallallowablelinktypesbetweenob- thesumoftheproximitiesw.r.t.allmetapaths.Intuitively,thiscan
jecttypes. Figure2(a)showstheschemaoftheHINinFigure1, captureallkindsofrelationshipsbetweenthetwoobjects.Wenow
where nodes A, P, T and V correspond to author, paper, topic provideadefinitionfortheproblemthatwestudyinthispaper.
and venue, respectively. There are also different edge types in
theschema, suchas‘publish’and‘write’. Figure2(b)showsthe DEFINITION 5. (HINEmbeddingforMetaPathbasedProx-
schemaofamovie-relatedHIN,withM,A,D,P,Crepresenting imity)GivenaHING=(V,E),developamappingf :V →Rd
movie,actor,director,producerandcomposer,respectively. that transforms each object o ∈ V to a vector in Rd, such that
InaHING,twoobjectso ,o maybeconnectedviamultiple the proximities between any two objects in the original HIN are
1 2
edgesorpaths. Conceptually,eachofthesepathsrepresentsaspe- preservedinRd.
cificdirectorcompositerelationshipbetweenthem. InFigure1,
authorsa anda areconnectedviamultiplepaths. Forexample, 4. HINE
1 2
a → p → a meansthata anda arecoauthorsofpaperp ,
1 3 2 1 2 3 In this section, we introduce our methodology for embedding
anda →p →p →a meansthata ’spaperp citesa ’spaper
1 1 2 2 2 2 1 HINs. We first discuss how to calculate the truncated estimation
p . Thesetwopathsrepresenttwodifferentrelationshipsbetween
1 ofmetapathbasedproximityinSection4.1. Then, weintroduce
authora anda .
1 2 ourmodelanddefinetheobjectivefunctionwewanttooptimizein
Eachdifferenttypeofarelationshipismodeledbyametapath
Section4.2. Finally,wepresentanegativesamplingapproachthat
[29]. Specifically, a meta path P is a sequence of object types
acceleratestheoptimizationoftheobjectivefunctioninSection4.3.
l ,...,l connectedbylinktypesr ,...,r asfollows:
1 n 1 n−1
1Fortheeaseofpresentation,weoverloadnotationPtoalsodenote
P =l −r→1 l ...l −r−n−−→1 l . thesetofinstancesofmetapathP.
1 2 n−1 n
Table1:Metapathsandinstancesconnectinga anda
1 2 Algorithm1:CalculateTruncatedProximity
Len2gth APPA a1→posp→3o→t a2 sP1C sP0C.2R5W IOnuptuptu:t:HTINruGnca=ted(VP,rEox)i,mleitnygMthatthrriexsShˆolldl
3 APPA a1→p1→p2→a2 1 0.5 1 Sˆ0←∅
4 APTPA aa11→→pp13→→tt12→→pp23→→aa22 11 00..2255 32 foroSˆs0∈[osV,odso]←1.0
APVPA a1→p3→v3→p3→a2 1 0.25 4 fork∈[1···l]do
··· ··· ··· ··· ··· 5 Sˆk←∅
6 foros∈V do
7 foro(cid:48)∈neighbor(os)do
4.1 TruncatedProximityCalculation 8 for(o(cid:48),ot)∈Sˆk−1do
AccordingtoDefinition4,inordertocomputetheproximityof 9 Sˆk[os,ot]←
twoobjectso ,o ∈ V,weneedtoaccumulatethecorresponding Sˆk[os,ot]+inc(os,o(cid:48),Sˆk−1[o(cid:48),ot])
metapathbasiedjproximityw.r.t. eachmetapathP. Forexample, 10 returnSˆl;
inTable1,welistsomemetapathsthathaveinstancesconnecting
a anda inFigure1. Wecanseethatthereisonelength-2meta
1 2
path,onelength-3metapathandtwolength-4metapathsthathave for PathCount, in which case we set inc(o ,o(cid:48),Sˆ [o(cid:48),o ]) =
s k−1 t
instancesconnectinga1anda2.Generallyspeaking,thenumberof Sˆk−1[o(cid:48),ot].
possiblemetapathsgrowsexponentiallywiththeirlengthandcan We now provide a time complexity analysis for computing the
beinfiniteforcertainHINschema(inthiscase,thecomputationof truncatedproximitiesonaHINusingAlgorithm1.Foreachobject
s(oi,oj)isinfeasible). os ∈ V,weneedtoenumerateallthemetapathinstanceswithin
As pointed out in [29], shorter meta paths are more informa- lengthl. SupposetheaveragedegreeintheHINisD;then,there
tivethanlongerones,becauselongermetapathslinkmoreremote areonaveragelDsuchinstances.Hence,thetotaltimecomplexity
objects (which are less related semantically). Therefore, we use forproximitycalculationisO(|V|·lD),whichislineartothesize
a truncated estimation of proximity, which only considers meta oftheHIN.
pathsuptoalengththresholdl. Thisisalsoconsistentwithpre-
viousworksonnetworkembedding, whichaimatreservinglow- 4.2 Model
order proximity (e.g., [22] reserves only second-order proximity,
We now introduce our HINE embedding method, which pre-
and[31]first-orderandsecond-orderproximities). Therefore,we
servesthemetapathbasedproximitiesbetweenobjectsasdescribed
define:
above.Foreachpairofobjectso ando ,weuseSigmoidfunction
i j
sˆ(o ,o )= (cid:88) s(o ,o |P) (3) todefinetheirjointprobability,i.e.,
l i j i j
len(P)≤l 1
p(o ,o )= (5)
asthetruncatedproximitybetweentwoobjectso ando . i j 1+e−vi·vj
i j
ForthecaseofPCRWbasedproximity, wehavethefollowing
where v (or v ) ∈ Rd is the low-dimensional representation of
property: i j
objecto (oro ). p : V2 → Risaprobabilitydistributionovera
i j
PROPERTY 1. pairofobjectsintheoriginalHIN.
IntheoriginalHING,theempiricaljointprobabilityofo and
sˆl(oi,oj)= (cid:88) pψoi(→oio,o(cid:48)(cid:48))×sˆl−1(o(cid:48),oj) oj canbedefinedas: i
(oi,o(cid:48))∈E s(o ,o )
wherepψoi(→oio,o(cid:48)(cid:48))isthetransitionprobabilityfromoitoo(cid:48)w.r.t.edge pˆ(oi,oj)= (cid:80)o(cid:48)∈Vis(oji,o(cid:48)) (6)
typeψ(o ,o(cid:48)).Iftherearenedgesfromo thatbelongtoedgetype
i i Topreservethemetapathbasedproximitys(·,·),anaturalob-
ψ(o ,o(cid:48)),thenψ(o ,o(cid:48))= 1.
i i n jectiveistominimizethedistanceofthesetwoprobabilitydistri-
PROOF. Assumethatp=oi →o(cid:48) →···→oj isametapath butions:
instanceoflengthl.AccordingtodefinitionofPCRW:
O=dist(pˆ,p) (7)
s(oi,oj |p[1:l])=pψoi(→oio,o(cid:48)(cid:48))×s(o(cid:48),oj |p[2:l]) (4) Inthispaper, wechooseKL-divergenceasthedistancemetric,
sowehave:
wherep[i:j]isthesubsequenceofpathinstancepfromthei-thto
(cid:88)
thej-thobjects,andp[2 :l]isalengthl−1pathinstance. Then, O=− s(oi,oj)logp(oi,oj) (8)
bysummingoverallthelength-lpathinstancesforEquation4,we oi,oj∈V
getProperty1.
4.3 NegativeSampling
Based on Property 1, we develop a dynamic programming ap- DirectlyoptimizingtheobjectivefunctioninEquation8isprob-
proach(Algorithm1)tocalculatethetruncatedproximities. Basi- lematic. Firstofall,thereisatrivialsolution: v = ∞foralli
cally, we compute the proximity matrix Sˆk for each k from 1 to andalld. Second,itiscomputationallyexpensivie,dtocalculatethe
l. We first initialize the proximity matrix Sˆ0 (lines 1-3). Then, gradient,asweneedtosumoverallthenon-zeroproximityscores
weusethetransitionfunctioninProperty1toupdatetheproxim- s(o ,o ) for a specific object o . To address these problems, we
i j i
ity matrix for each k (lines 4-9). If we use PCRW as the meta adoptnegativesamplingproposedin[19],whichbasicallysamples
path based proximity measure, inc(os,o(cid:48),Sˆk−1[o(cid:48),ot]) in line 9 asmallnumberofnegativeobjectstoenhancetheinfluenceofpos-
equals pψ(os,o(cid:48)) ×Sˆ [o(cid:48),o ]. The algorithm can also be used itiveobjects.
os→o(cid:48) k−1 t
Table2:StatisticsofDatasets
C D
|V| |E| Avg.degree |L| |R|
issue develop DBLP 15,649 51,377 6.57 4 4
R towards V mention K P publish G design S MOVIE 25,643 40,173 3.13 5 4
YELP 37,342 178,519 9.56 4 3
GAME 6,909 7,754 2.24 4 3
(a) YELP (b) GAME
Figure3:SchemasofTwoHINs • YELP.WeextractedaHINfromYELP,whichisaboutre-
views given to restaurants. It contains 33,360 reviews (V),
1,286customers(C),82food-relatedkeywords(K)and2,614
restaurants(R).Weonlyextractrestaurantsfromoneofthe
Formally,wedefineanobjectivefunctionforeachpairofobjects
followingtypes:fastfood,American,sushibar.Theschema
withnon-zerometapathbasedproximitys(o ,o ):
i j
oftheHINisshowninFigure3(a).
K • GAME. We extracted from Freebase [4] a HIN, which is
T(oi,oj)=−log(1+e−vivj)−(cid:88)Ev(cid:48)∈Pn(oi)[log(1+eviv(cid:48))] related to video games. The HIN consists of 4,095 games
1 (G),1,578publishers(P),2,043developers(D)and197de-
(9) signers(S).Allthegameobjectsextractedareofoneofthe
whereK isthetimesofsampling,andPn(v)issomenoisedistri- threegenres:action,adventure,andstrategy. Theschemais
bution. Assuggestedby[19],wesetPn(v) ∝ dout(v)3/4 where showninFigure3(b).
d (v)istheout-degreeofv.
out
Weadopttheasynchronousstochasticgradientdescent(ASGD) Competitors. Wecomparethefollowingnetworkembeddingap-
algorithm [23] to optimize the objective function in Equation 9. proaches:
Specifically, in each round of the optimization, we sample some
pairsofobjectso ando withnon-zeroproximitys(o ,o ).Then, • DeepWalk [22] is a recently proposed social network em-
i j i j
thegradientw.r.t.v canbecalculatedas: beddingmethod(seeSection2.3fordetails). Inourexperi-
i
mentsettings,weignoretheheterogeneityanddirectlyfeed
the HINs for embedding. We use default training settings,
∂O e−vivj
=−s(o ,o )· ·v (10) i.e.,windowsizew=5andlengthofrandomwalkt=40.
∂vi i j 1+e−vivj j
• LINE[31]isamethodthatpreservesfirst-orderandsecond-
5. EXPERIMENTS order proximities between vertices (see Section 2.3 for de-
tails). For each object, it computes two vectors; one for
In this section, we conduct extensive experiments in order to
thefirst-orderandoneforthesecond-orderproximitiessep-
test the effectiveness of our proposed HIN embedding approach.
aratelyandthenconcatenatesthem. Weuseequalrepresen-
Wefirstintroduceourdatasetsandthesetofmethodstobecom-
tation lengths for the first-order and second-order proxim-
pared in Section 5.1. Then, we evaluate the effectiveness of all
ities, and use the default training settings; i.e., number of
approachesonfiveimportantdataminingtasks: networkrecovery
negative samplings. K = 5, starting value of the learning
(Section5.2),classification(Section5.3),clustering(Section5.4),
rate ρ = 0.025, and total number of training samplings
k-NNsearch(Section5.5)andvisualization(Section5.6).Inaddi- 0
T =100M. SameasDeepWalk,wedirectlyfeedtheHINs
tion,weconductacasestudy(Section5.7)tocomparethequality
forembedding.
oftop-klists. WeevaluatetheinfluenceofparameterlinSection
5.8. Finally,weassesstheruntimecostofapplyingourproposed
• HINE_PCisourHINEmodelusingPathCountasthemeta
transformationinSection5.9.
pathbasedproximity. Weimplementedtheprocessofprox-
5.1 DatasetandConfigurations imitycomputinginC++ona16GBmemorymachinewith
Intel(R)Core(TM)[email protected],we
usel=2. InSection5.8,westudytheinfluenceofparame-
Datasets. We use four real datasets in our evaluation. Table 2
terl.
showssomestatisticsaboutthem.
• HINE_PCRWisourHINEmodelusingPCRWasthemeta
• DBLP. The schema of DBLP network is shown in Figure path based proximity. All the other configurations are the
2(a). We use a subset of DBLP, i.e., DBLP-4-Area taken sameasthoseofHINE_PC.
of[29],whichcontains5,237papers(P),5,915authors(A),
18venues(V),4,479topics(T).Theauthorsarefrom4ar- Unlessotherwisestated, thedimensionalitydoftheembedded
eas: database,datamining,machinelearningandinforma- vectorspaceequals10.
tionretrieval.
5.2 NetworkRecovery
• MOVIE.WeextractedasubsetfromYAGO[10],whichcon- Wefirstcomparetheeffectivenessofdifferentnetworkembed-
tainsknowledgeaboutmovies. TheschemaofMOVIEnet- ding methods at a task of link recovery. For each type of links
workisshowninFigure2(b). Itcontains7,332movies(M), (i.e.,edges)intheHINschema,weenumerateallpairsofobjects
10,789actors(A),1,741directors(D),3,392producers(P) (o ,o ) that can be connected by such a link and calculate their
s t
and1,483composers(C).Themoviesaredividedintofive proximityinthelow-dimensionalspaceafterembeddingo tov
s s
genres:action,horror,adventure,sci-fiandcrime. and o to v . Finally, we use the area under ROC-curve (AUC)
t t
toevaluatetheperformanceofeachembedding. Forexample,for
edge type write, we enumerate all pairs of authors a and papers
i
p inDBLPandcomputetheproximityforeachpair. Finally,us-
j
ingtherealDBLPnetworkasground-truth,wecomputetheAUC
valueforeachembeddingmethod.
The results for d = 10 are shown in Table 3. Observe that,
ingeneral, HINE_PCandHINE_PCRWhavebetterperformance
comparedtoLINEandDeepWalk. Inordertoanalyzethereasons
behindthebadperformanceofLINE,wealsoincludedtwospecial
versions of LINE: LINE_1st (LINE_2nd) is a simple optimiza- (a) LINE (b) DeepWalk
tionapproachthatjustusesstochasticgradientdescenttooptimize
just the first-order (second-order) proximity among the vertices.
LINE_1st has much better performance than LINE_2nd because
second-orderproximitypreservationdoesnotfacilitatelinkpredic-
tion. LINE,whichconcatenatesLINE_1standLINE_2ndvectors,
hasworseperformancethanLINE_1stbecauseitsLINE_2ndvec-
torcomponentharmslinkpredictionaccuracy. Thisisconsistent
with our expectation, that training proximities of multiple orders
simultaneouslyisbetterthantrainingthemseparately. Amongall
methods,HINE_PCRWhasthebestperformanceinpreservingthe (c) HINE_PC (d) HINE_PCRW
links of HINs; in the cases where HINE_PCRW loses by other
methods, its AUC is very close to them. HINE_PCRW outper-
Figure6:VisualizationResultsonDBLP
formsHINE_PC,whichisconsistentwithresultsinpreviouswork
that find PCRW superior to PC (e.g., [10]). The rationale is that
a random walk models proximity as probability, which naturally
Table 5 shows the results for d = 10. We can see that all
weighsnearbyobjectshighercomparedtoremoteones.
methodshavebetterresultsonDBLPandYELP,thanonMOVIE
5.3 Classification and GAME. This is because the average degree on MOVIE and
GAME is smaller, and the HINs are sparser (See Table 2). Ob-
servethatHINE_PCandHINE_PCRWoutperformDeepWalkand
Table5:ResultsofClassificationwithd=10
LINE in DBLP and MOVIE; HINE_PCRW performs the best in
LINE DeepWalk HINE_PC HINE_PCRW both datasets. On YELP, LINE has slightly better results than
HINE_PCRW (about 1%), while DeepWalk has a very poor per-
Macro-F1 0.816 0.839 0.844 0.868
DBLP Micro-F1 0.817 0.840 0.844 0.869 formance. OnGAME,DeepWalkisthewinner, whileLINEand
Macro-F1 0.324 0.280 0.346 0.365 HINE_PCRWperformsimilarly.Overall,wecanseethatHINE_PCRW
MOVIE
Micro-F1 0.369 0.328 0.387 0.406 hasthebest(orclosetothebest)performance,andLINEhasquite
Macro-F1 0.898 0.339 0.470 0.886 goodperformance.Ontheotherhand,DeepWalk’sperformanceis
YELP
Micro-F1 0.887 0.433 0.518 0.878 notstable.
Macro-F1 0.451 0.487 0.415 0.438 Wealsomeasuredtheperformanceofthemethodsfordifferent
GAME
Micro-F1 0.518 0.545 0.501 0.518 valuesofd. Figures5(a)and5(b)showtheresultsonDBLP.As
Macro-F1 0.622 0.486 0.519 0.639 d becomes larger, all approaches get better in the beginning, and
Overall
Micro-F1 0.648 0.537 0.563 0.668 thenconvergetoacertainperformancelevel.Observethatoverall,
HINE_PCRWhasthebestperformanceinclassificationtasks.
5.4 Clustering
Table6:ResultsofClusteringwithd=10
Wealsoconductedclusteringtaskstoassesstheperformanceof
NMI LINE DeepWalk HINE_PC HINE_PCRW themethods. InDBLPweclustertheauthors,inMOVIEweclus-
DBLP 0.3920 0.4896 0.4615 0.4870 terthemovies,inYELPweclustertherestaurants,andinGAME
MOVIE 0.0233 0.0012 0.0460 0.0460 we cluster the games. We use the same ground-truth as in Sec-
tion5.3.Weusenormalizedmutualinformation(NMI)toevaluate
YELP 0.0395 0.0004 0.0015 0.0121
performance.
GAME 0.0004 0.0002 0.0022 0.0004
Table 6 shows the results for d = 10. We can see that the
Overall 0.1138 0.1229 0.1278 0.1364
performance of all methods in clustering tasks is not as stable as
that in classification. All the embedding methods perform well
Weconductataskofmulti-labelclassification. ForDBLP,we onDBLP,buttheyhavearelativelybadperformanceontheother
usetheareasofauthorsaslabels. ForMOVIE,weusethegenres three datasets. On DBLP, DeepWalk and HINE have better per-
ofmoviesaslabels. ForYELP,weusetherestauranttypesasla- formance than LINE. On MOVIE, HINE_PC and HINE_PCRW
bels. ForGAME,weusethetypeofgamesaslabels. Wefirstuse outperformallotherapproaches. OnYELP,LINEhasbetterper-
differentmethodstoembedtheHINs.Then,werandomlypartition formancethanHINE_PCRW,andDeepWalkhasverypoorperfor-
thesamplesintoatrainingandatestingsetwithratio4 : 1. Fi- mance.OnGAME,DeepWalkoutperformstheothers.Overall,we
nally,weuseknearestneighbor(k−NN)classifierswithk=5to canseethatHINE_PCRWoutperformsalltheothermethodsinthe
predictthelabelsofthetestsamples. Werepeattheprocessfor10 taskofclustering.
timesandcomputetheaverageMacro-F1andMicro-F1scoresto Figure 5(c) shows performance of the approaches for different
evaluatetheperformance. dvaluesonDBLP.ObservethatHINE_PCRWingeneraloutper-
Table3:AccuracyofNetworkRecovery(d=10)
EdgeType LINE_1st LINE_2nd LINE DeepWalk HINE_PC HINE_PCRW
write 0.9885 0.7891 0.8907 0.9936 0.9886 0.9839
publish 0.9365 0.6572 0.8057 0.9022 0.9330 0.9862
DBLP
mention 0.9341 0.5455 0.7186 0.9202 0.8965 0.8879
cite 0.9860 0.9071 0.9373 0.9859 0.9598 0.9517
actIn 0.9648 0.5214 0.8425 0.7497 0.9403 0.9733
direct 0.9420 0.5353 0.8468 0.7879 0.9359 0.9671
MOVIE
produce 0.9685 0.5334 0.8599 0.7961 0.9430 0.9900
compose 0.9719 0.5254 0.8574 0.9475 0.9528 0.9864
issue 0.9249 0.4419 0.8744 1.0000 0.5083 0.9960
towards 0.9716 0.4283 0.9221 0.5372 0.5155 0.9981
YELP
mention 0.8720 0.4178 0.7738 0.5094 0.5951 0.8534
design 0.9599 0.4997 0.6781 0.9313 0.9219 0.9828
develop 0.9021 0.5043 0.7736 0.9328 0.8592 0.9843
GAME
publish 0.7800 0.4719 0.6786 0.9711 0.7617 0.9756
Overall Average 0.9359 0.5556 0.8185 0.8546 0.8365 0.9655
formsallothermethods. Onlyforanarrowrangeofd(d = 10)
1.00 1.00
DeepWalk slightly outperforms HINE_PCRW (as also shown in
0.90 0.90
Table 6). Generally speaking, HINE_PCRW best preserves the
proximitiesamongauthorsinthetaskofclustering. Macro-F1 00..7800 Micro-F1 00..7800
5.5 k-NNSearch 0.60 HINE_PC 0.60 HINE_PC
HINE_PCRW HINE_PCRW
Wecomparetheperformancesofthreemethods,i.e.,LINE,Deep- 0.50 0.50
1 2 3 4 5 1 2 3 4 5
Walk and HINE_PCRW, on k-NN search tasks. Specifically, we l l
conductacasestudyonDBLP,tocomparethequalityofknearest (a) Macro-F1w.r.t.l (b) Micro-F1w.r.t.l
authors for venue WWW in the embedded space. We first eval-
uate the quality of k-NN search by counting the average number
of papers that the authors in the k-NN result have published in 00..56 310 s) 67
WthaWttWhe,wnehaernesvtaaruytihnogrskfofruonmd1intothe10e0m(bFeidgduirneg4b(ay))H.IWNEe_cPaCnRsWee NMI 00..34 n Time ( 345
hinavWtheeemsthoperaencepusaspoeeftrLhseIpNtuoEbpla-isknhdeaDduteihneopWrWliWastlWkf.orcovmenpuaereWdWtoWtheinonthesefooruignid- 000...012 1 2 HINHE I_3NPEC_RPWC 4 5 Executio 012 2 4 6 8 10
nalDBLPnetworkasground-truth. Weusetwodifferentmetrics l l
to evaluate the quality of top-k lists in the embedded space, i.e., (c) NMIw.r.t.l (d) Executiontimew.r.t.l
Spearman’s footrule F and Kendall’s tau K [9]. The results are
showninFigures4(b)and4(c). Wecanseethatthetop-k listof Figure7:Performancesw.r.t.l
HINE_PCRWisclosertotheoneintheoriginalHIN.
5.6 Visualization
givenobjectinDBLP.Specifically, weshowinTable4thetop-5
Wecomparetheperformancesofallapproachesonthetaskofvi- closestvenues,authorsandtopicstoauthorJiaweiHaninDBLP.
sualization,whichaimstolayoutanHINona2-dimensionalspace. Bylookingattheresultsfortop-5venues,wecanseethatLINE
Specifically,wefirstuseanembeddingmethodtomapDBLPinto doesnotgiveagoodtop-5list, asitcannotrankKDDinthetop
avectorspace,then,wemapthevectorsofauthorstoa2-Dspace publishingvenuesoftheauthor. DeepWalkisslightlybetter,butit
usingthet-SNE[16]package. ranksICDMatthe5thposition, whileHINE_PCRWranksKDD
The results are shown in Figure 6. LINE can basically sepa- and ICDM as 1st and 2nd, respectively. Looking at the results
rate the authors from different groups (represented by the same forauthors,observethatHINE_PCRWgivesasimilartop-5listto
color),butsomebluepointsmixedwithothergroups.Theresultof DeepWalk,exceptthatHINE_PCRWpreferstopresearchers,e.g.,
DeepWalkisnotverygood,asmanyauthorsfromdifferentgroups ChristosFaloutsos. Lookingtheresultsfortopics, notethatonly
aremixedtogether. HINE_PCclearlyhasbetterperformancethan HINE_PCRWcanprovideageneraltopiclike“mining”.
DeepWalk. Compared with LINE, HINE_PC can better separate
differentgroups. Finally,HINE_PCRW’sresultisthebestamong 5.8 Effectofthel Threshold
thesemethods,becauseitclearlyseparatestheauthorsfromdiffer- Wenowstudytheeffectoflondifferentdataminingtasks,e.g.,
entgroups,leavingalotofemptyspacebetweentheclusters.This classificationandclustering. Figure7(a)and(b)showstheresults
is consistent with the fact that HINE_PCRW has the best perfor- of classification on DBLP. We can see that 1) HINE_PCRW has
manceinclassifyingtheauthorsofDBLP. quite stable performance w.r.t. l, and it achieves its best perfor-
mancewhenl=2.2)TheperformanceofHINE_PCisbestwhen
5.7 CaseStudy
l = 1. This is because PathCount views meta path instances of
We perform a case study, which shows the k-NN objects to a different length equally important, while PCRW assigns smaller
weightstothelongerinstanceswhenperformingtherandomwalk. [13] X.Kong,P.S.Yu,Y.Ding,andD.J.Wild.Metapath-based
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Table4:Top-5similarlistsforJiaweiHan
LINE DeepWalk HINE_PCRW
k conf author topic conf author topic conf author topic
1 PAKDD JiaweiHan clustermap KDD JiaweiHan itemsets KDD JiaweiHan closed
2 PKDD GaoCong orders PAKDD XifengYan farmer ICDM XifengYan mining
3 SDM LeiLiu summarizing PKDD KeWang closed SDM KeWang itemsets
4 KDD YilingYang ccmine SDM YaboXu tsp PAKDD ChristosFaloutsos sequential
5 ICDM DaesuLee concise ICDM JasonFlannick prefixspan PKDD XiaoxinYin massive
3.0 1.0 10
LINE LINE
2.5 DeepWalk 0.8 8 DeepWalk
HINE_PCRW HINE_PCRW
er 2.0
g. #pap 1.5 F 00..46 3K (10) 46
v 1.0
a LINE
0.5 0.2 DeepWalk 2
HINE_PCRW
0.0 0.0 0
20 40 60 80 100 20 40 60 80 100 20 40 60 80 100
k k k
(a) Avg.#paperw.r.t.k (b) F w.r.t.k (c) Kw.r.t.k
Figure4:ResultsofTop-klistsforvenueWWW
(a) Macro-F1 w.r.t. d (b) Micro-F1 w.r.t. d (c) NMI w.r.t. d
0.9 0.9 0.6
0.8 0.8 0.5
1 1 0.4
F 0.7 F 0.7
Macro- 0.6 Micro- 0.6 NMI 00..23
0.5 0.5 0.1
0.4 0.4 0.0
4 8 12 16 20 4 8 12 16 20 4 8 12 16 20
d d d
LINE DeepWalk HEMP_PC HEMP_PCRW
Figure5:PerformanceofClassificationandClusteringw.r.t.d