cs224w: analysis of networks jure leskovec,...

CS224W: Analysis of NetworksJure Leskovec, Stanford University

http://cs224w.stanford.edu

Korea Rep.

Uruguay

Switz.Liecht

Sri Lanka

GibraltarArmenia

Ireland

Portugal

Nicaragua

Ghana

Morocco

Brazil

Paraguay

El Salvador

Slovenia

Cuba

Bulgaria

Dominican Rp

Barbados

Bermuda

Belarus

Mauritania

Philippines

Korea D P Rp

Burkina Faso

Uzbekistan

Myanmar

Costa Rica

TFYR Macedna Sudan

Senegal

Mongolia

Angola

NigeriaMexico Iran

Iraq

Kuwait

Oman

Saudi Arabia

Untd Arab Em

TurkeyUK

Lithuania

Russian Fed

Libya

Venezuela

Algeria

South Africa

Cote Divoire

USAColombia

Ecuador

Bahamas

Panama

Syria

Denmark

Netherlands

Finland

Norway

Sweden

Egypt

Cameroon

Gabon

Dem.Rp.Congo

Canada

Argentina

Bolivia

Chile

Peru

Guatemala

Trinidad Tbg

Yemen

Afghanistan

Indonesia

Malaysia

Singapore

China

Viet Nam

Estonia

Australia

Papua N.Guin

Kazakhstan

Italy

Spain

Qatar

New Zealand

Pakistan

Tunisia

Georgia

Thailand

Guinea

Liberia

Niger

JapanIndia

Taiwan

Ukraine

Germany

Greece

France,Monac

Austria

IsraelHungary

Benin

Azerbaijan

Belgium-Lux

Malta

Latvia

Jamaica

Poland

Czech Rep

Yugoslavia

Cyprus

Romania

Slovakia

Croatia

Trade in crudepetroleum and petroleum products, 1998, source: NBER-United Nations Trade Data

10/9/17 JureLeskovec,StanfordCS224W:AnalysisofNetworks,http://cs224w.stanford.edu 2

Y

X

Y

X

Y X

Y

X

indegree

In each of the following networks, X has higher centrality than Y according to a particular measure

outdegree betweenness closeness


¡ Intuition: Howmanypairsofindividualswouldhavetogothroughyouinordertoreachoneanotherintheminimumnumberofhops?

Y X


Where 𝜎"#(𝑣) = the number of shortest paths 𝑠 − 𝑡 through node 𝑣

𝜎"# = the number of shortest paths from 𝑠 to 𝑡.

Where 𝜎"#(𝑣) is also called betweenness of a node 𝑣


¡ Non-normalized version of betweennesscentrality (numbers are centralities):


¡ Non-normalizedversion:

¡ Aliesbetweennotwoothervertices¡ BliesbetweenAand3othervertices:C,D,andE¡ Cliesbetween4pairsofvertices(A,D),(A,E),(B,D),(B,E)

¡ Notethattherearenoalternatepathsforthesepairstotake,soCgetsfullcredit

A B C ED


¡ ClosenessCentrality: Reciprocalofthemeanaverageshortestpathlengthfromnodex toallothernodesinthegraphy.

¡ Farnesscentrality: Avg.shortestpathlengthfromnodextoallothernodes


(we assume graph is connected)

¡ Betweenness (left),Closeness(right)


¡ Wewilltalkabouthumanbehavioronline

¡ Wewilltrytounderstandhowpeopleexpressopinionsabouteachotheronline§ Wewillusedataandnetworksciencetheorytomodelfactorsaroundhumanevaluations

§ ThiswillbeanexampleofComputationalSocialScienceresearch§ Wearemakingsocialscienceconstructsquantitativeandthenusecomputationtomeasurethem



Observations

Smalldiameter,Edgeclustering

Patternsofsignededgecreation

ViralMarketing,Blogosphere,Memetracking

Scale-Free

Densificationpowerlaw,Shrinkingdiameters

Strengthofweakties,Core-periphery

Models

Erdös-Renyi model,Small-worldmodel

Structuralbalance,Theoryofstatus

Independentcascademodel,Gametheoreticmodel

Preferentialattachment,Copyingmodel

Microscopicmodelofevolvingnetworks

Kronecker Graphs

Algorithms

Decentralizedsearch

Modelsforpredictingedgesigns

Influencemaximization,Outbreakdetection,LIM

PageRank,Hubsandauthorities

Linkprediction,Supervisedrandomwalks

Communitydetection:Girvan-Newman,Modularity

Inmanyonlineapplications usersexpresspositiveandnegativeattitudes/opinions:

¡ Throughactions:§ Ratingaproduct/person§ Pressinga“like”button

¡ Throughtext:§ Writingacomment,areview

¡ Successoftheseonlineapplicationsisbuiltonpeopleexpressingopinions§ Recommendersystems§ WisdomoftheCrowds§ Sharingeconomy


¡ Aboutitems:§ Movieandproductreviews

¡ Aboutotherusers:§ Onlinecommunities

¡ Aboutitemscreatedbyothers:§ Q&Awebsites


+

++

++

+

––

–

––

–

+

–

+–

+

–

+

–

+

¡ Manyonlinesettingswhereonepersonexpressesanopinionaboutanother(oraboutanother’scontent)§ Itrustyou[Kamvar-Schlosser-Garcia-Molina‘03]§ Iagreewithyou[Adamic-Glance’04]§ Ivoteinfavorofadmittingyouintothecommunity[Cosley etal.‘05,Burke-Kraut‘08]

§ Ifindyouranswer/opinionhelpful[Danescu-Niculescu-Mizil etal.‘09,Borgs-Chayes-Kalai-Malekian-Tennenholtz ‘10]


Someofthecentralissues:

¡ Factors:Whatfactorsdriveone’sevaluations?

¡ Synthesis:Howdowecreateacompositedescriptionthataccuratelyreflectsaggregateopinionofthecommunity?


§ Direct: Usertouser§ Indirect: Usertocontent(createdbyanothermemberofacommunity)

¡ Whereonlinedoesthisexplicitlyoccuronalargescale?


Direct Indirect

+

++

++

+

––

–

––

–+

–

+

¡ Wikipedia adminship elections§ Support/Oppose(120kvotesinEnglish)§ 4languages:EN,GER,FR,SP

¡ StackOverflow Q&Acommunity§ Upvote/Downvote (7.5Mvotes)

¡ Epinions productreviews§ Ratingsofothers’productreviews(13M)

§ 5=positive,1-4=negative

+

–

+


¡ Therearetwowaystolookatthis:Onepersonevaluatestheotherviaapositive/negativeevaluation


+

++

++

+

––

–

––

–

Then we will focus on evaluations in the

context of a network

BA

First we focus on a single evaluation

(without the context of a network)

¡ Whatdriveshumanevaluations?

¡ HowdopropertiesofevaluatorAandtargetB affectA’svote?§ Status andSimilarity aretwofundamentaldriversbehindhumanevaluations


BA

¡ Status:Levelofrecognition,merit,achievement,reputationinthecommunity

§ Wikipedia:#edits,#barnstars§ StackOverflow:#answers

¡ User-usersimilarity:§ OverlappingtopicalinterestsofA andB

§ Wikipedia: Similarityofthearticlesedited§ StackOverflow: Similarityofusersevaluated


[WSDM ‘12]

¡ HowdopropertiesofevaluatorAandtargetB affectA’svote?

¡ Twonatural(butcompeting)hypotheses:§ (1) Prob.thatBreceivesapositiveevaluationdependsprimarilyonthecharacteristicsofB§ ThereissomeobjectivecriteriaforuserBtoreceiveapositiveevaluation


BA

¡ HowdopropertiesofevaluatorAandtargetB affectA’svote?

¡ Twonatural(butcompeting)hypotheses:§ (2) Prob.thatBreceivesapositiveevaluationdependsonrelationshipbetweenthecharacteristicsofAandB§ UserAcomparesherselftouserBandthenmakestheevaluation


BA

¡ HowdoesstatusofBaffectA’sevaluation?§ Eachcurveisafixedstatusdifference:D =SA-SB

¡ Observations:§ Flatcurves: Prob.ofpositiveeval.P(+)doesn’tdependonB’sstatus

§ Differentlevels: DifferentvaluesofD resultindifferentbehavior


Target B status(# edits in Wikipedia)

BAWe keep increasing status of B, while keeping the status

difference (SA-SB) fixed

¡ Howdoespriorinteractionshapeevaluations?2hypotheses:§ (1)Evaluatorsaremoresupportiveoftargetsintheirarea§ “Themoresimilaryouare,themoreIlikeyou”

§ (2)Morefamiliarevaluatorsknowweaknessesandaremoreharsh§ “Themoresimilaryouare,thebetterIcanunderstandyourweaknesses”


2610/9/17 JureLeskovec,StanfordCS224W:AnalysisofNetworks,http://cs224w.stanford.edu

Prior interaction/ similarity boosts positive evaluations

Similarity: For each user create a set of words of all articles she edited. The similarity is then the Jaccard similarity between the two sets of words.Then sort the user pairs by similarity and bucket them into percentiles.


Status is a proxy for quality when evaluator does not know the target

¡ Whoshowsuptoevaluate?

¡ Selectioneffectinwhogivestheevaluation§ IfSA>SB thenAandBaremorelikelytobesimilar


Elite evaluators vote on targets in

their area of expertise

¡ WhatisP(+)asafunctionofΔ =SA-SB?§ Basedonfindingssofar:Monotonicallydecreasing


Δ, Status difference

P(+)

-10 (SA<SB)

0 (SA=SB)

10 (SA>SB)

¡ WhatisP(+)asafunctionofΔ =SA-SB?


Especially negativefor SA=SB

Reboundfor SA > SB

Status difference

[ICWSM ‘10]

Computed over 120k votes

¡ Whylowevals.ofusersofsamestatus?§ Notduetousersbeingtoughoneachother§ Butduetotheeffectsofsimilarity

§ Sowegetthe“mercy”bounceduetounevenmixingofvotes


Explanation: For negative status difference we have low similarity people which behave according to the red curve on the left plot. As status difference increases the similarity also increases (green curve). For positive status difference, similarity is high, and evaluations follow the blue curve (left). By having a particularly weighted combination of red, green, and blue curve we observe the “mercy bounce” from the previous slide.

¡ Sofar:Propertiesofindividualevaluations¡ But:Evaluationsneedtobe“summarized”§ Determiningrankingsofusersoritems§ Multipleevaluationsleadtoagroupdecision

¡ Howtoaggregateuserevaluationstoobtaintheopinionofthecommunity?§ Canweguesscommunity’sopinionfromasmallfractionofthemakeupofthecommunity?


¡ PredictWikipediaadminship electionresultswithoutseeingthevotes§ Observeidentitiesofthefirstk(=5)peoplevoting(butnothowtheyvoted)

§ Wanttopredicttheelectionoutcome§ Promotion vs.nopromotion

¡ Whyisithard?§ Don’tseethevotes(justvoters)§ Onlyseefirst5voters(outof~50)


[WSDM ‘12]

¡ Wanttomodelprob.userAvotes+inelectionofuserB

¡ Ourmodel:𝑃 𝐴 = + 𝐵 = 𝑃/ + 𝑑(𝑆/ − 𝑆2, 𝑠𝑖𝑚 𝐴, 𝐵 )§ PA …empiricalfractionof+votesofA§ d(status,similarity)…avg.deviationinfrac.of+votes

§ WhenA evaluatesB fromaparticular(status,similarity)quadrant,howdoesthischangetheirbehavioronaverage?§ Note: d(status,similarity) onlytakes4differentvalues(basedonthequadrantinthe(status,similarity)space).Valuecomputedempirically.

¡ Predict‘elected’if:10/9/17 JureLeskovec,StanfordCS224W:AnalysisofNetworks,http://cs224w.stanford.edu 34

B

Pki=1 P (Ai = +|B) > w

[WSDM ‘12]

¡ Basedononlywhoshowedtovotepredicttheoutcomeoftheelection

§ Othermethods:§ Guessinggives52%accuracy§ LogisticRegressiononstatusandsimilarityfeatures:67%§ Ifweseethefirstk=5 votes85%(goldstandard)


Number of voters seen Accuracy

Theme: Learning from implicit feedbackAudience composition tells us something about their reaction

¡ Socialmediasitesaregovernedby(oftenimplicit)userevaluations

¡ Wikipediavotingprocesshasanexplicit,publicandrecorded processofevaluation

¡ Maincharacteristics:§ Importanceofrelativeassessment:Status§ Importanceofpriorinteraction:Similarity§ Diversityofindividuals’responsefunctions

¡ Application: Ballot-blindprediction

3610/9/17 JureLeskovec,StanfordCS224W:AnalysisofNetworks,http://cs224w.stanford.edu

¡ Statusseemstobesalientfeature

¡ Similarity alsoplaysimportantrole

¡ Audiencecompositionhelpspredictaudience’sreaction


¡ Therearetwowaystolookatthis:Onepersonevaluatestheotherviaapositive/negativeevaluation


+

++

++

+

––

–

––

–

Now we will focus on evaluations in the

context of a network

BA

So far we focused on a single evaluation

(without the context of a network)

¡ Networkswithpositiveandnegativerelationships

¡ Ourbasicunitofinvestigationwill besignedtriangles

¡ Firstwetalkaboutundirectednetworksthendirected

¡ Plan:§ Model: Considertwosoc. theoriesofsignednets§ Data: Reasonabouttheminlargeonlinenetworks§ Application: PredictifAandBarelinkedwith+or-


--+

--+

¡ Networkswithpositive andnegativerelationships

¡ Consideranundirectedcompletegraph¡ Labeleachedgeaseither:§ Positive:friendship,trust,positivesentiment,…§ Negative:enemy,distrust,negativesentiment,…

¡ ExaminetriplesofconnectednodesA,B,C


¡ Startwiththeintuition[Heider ’46]:§ Friend ofmyfriend ismyfriend§ Enemy ofenemy ismyfriend§ Enemy offriendismyenemy

¡ Lookatconnectedtriplesofnodes:


+++

--+

++-

---

UnbalancedBalancedConsistent with “friend of a friend” or

“enemy of the enemy” intuitionInconsistent with the “friend of a friend”

or “enemy of the enemy” intuition


BalancedUnbalanced

¡ Graphisbalancedifeveryconnectedtripleofnodeshas:§ All3edgeslabeled+,or§ Exactly1edgelabeled+

¡ Balanceimpliesglobalcoalitions [Cartwright-Harary]

¡ Fact: Ifalltrianglesarebalanced,theneither:§ Thenetworkcontainsonlypositiveedges,or§ Nodescanbesplitinto2setswherenegativeedgesonlypointbetweenthesets


+ +L

+R

-


B+

C

D

E

+

–

–

L: Friends of A R: Enemies of A

Every node in L is enemy of R

+ +

–

AAny 2 nodesin L are friends

Any 2 nodesin R are friends

L

R

¡ Internationalrelations:§ Positive edge:alliance§ Negative edge:animosity

¡ SeparationofBangladeshfromPakistanin1971:USsupportsPakistan.Why?§ USSR wasenemyofChina§ ChinawasenemyofIndia§ IndiawasenemyofPakistan§ USwasfriendlywithChina§ ChinavetoedBangladeshfromU.N.


P

R

I

C

U

+

+ ––

–

+?

B–?–

¡ Sofarwetalkedaboutcompletegraphs


Balanced?

-+

Def 1: LocalviewFillinthemissingedgestoachievebalance

Def 2: GlobalviewDividethegraphintotwocoalitions

The2definitionsareequivalent!

--

-

¡ Graphisbalanced if andonlyifitcontainsnocyclewithanoddnumberofnegative edges

¡ Howtocomputethis?§ Findconnectedcomponentson+edges

§ Ifwefindacomponentofnodeson+edgesthatcontainsa–edgeÞ Unbalanced

§ Foreachcomponentcreateasuper-node§ ConnectcomponentsAandBifthereisanegativeedgebetweenthemembers

§ Assignsuper-nodestosidesusingBFS


Even length cycle

–

–––

–

–

––

–

Odd length cycle

¡ UsingBFSassigneachnodeaside¡ Graphisunbalanced ifanytwoconnectedsuper-nodesareassignedthesameside


L

R R

L LL

RUnbalanced!

û

¡ Projectisasubstantialpartoftheclass§ Studentsputsignificanteffortandgreatthingshavebeendone

¡ Typesofprojects:§ (1) Analysisofaninterestingdatasetwiththegoaltodevelopa(new)modeloranalgorithm

§ (2) Atestofamodeloralgorithm(thatyouhavereadaboutoryourown)onreal&simulateddata.§ Fastalgorithmsforbiggraphs.CanbeintegratedintoSNAP.

¡ Otherpoints:§ Theprojectshouldcontainsomemathematicalanalysis,andsomeexperimentationonrealorsyntheticdata

§ Theresultoftheprojectwilltypicallybean8pagepaper,describingtheapproach,theresults,andrelatedwork.

§ Cometousifyouneedhelpwithaprojectidea!10/9/17 JureLeskovec,StanfordCS224W:AnalysisofNetworks,http://cs224w.stanford.edu 54

Projectproposal: 3-5pages,teamsofupto3students¡ Projectproposalhas3parts:

§ (0)Quick200wordabstract§ (1)Relatedwork/Reactionpaper(2-3pages):

§ Read3papersrelatedtotheproject/class§ Doreadingbeyondwhatwascoveredinclass§ Thinkbeyondwhatyouread.Don’ttakeother’sworkforgranted!§ 2-3pages: Summary (~1page),Critique(~1page)

§ (2)Proposal(1-2pages):§ Clearlydefinetheproblemyouaresolving.§ HowdoesitrelatetowhatyoureadfortheReactionpaper?§ Whatdatawillyouuse?(makesureyoualreadyhaveit!)§ Whichalgorithm/modelwillyouuse/develop?Bespecific!§ Howwillyouevaluate/testyourmethod?

See http://cs224w.stanford.edu/info.html fordetailedinstructionsandexamplesofpreviousproposals


¡ Logistics:§ 1)RegisteryourgroupontheGoogleDochttp://bit.ly/1BNiHae

§ 2)SubmitPDF onGradeScope AND athttp://snap.stanford.edu/submit/

§ Duein9days:ThuOct19at23:59PST!§ Nolateperiods

¡ Ifyouneedhelp/ideas/advicecometoOfficehours/Emailus


¡ Foodwebs:¡ http://vlado.fmf.uni-lj.si/pub/networks/data/bio/foodweb/foodweb.htm

withmetadata:https://www.cbl.umces.edu/~atlss/

¡ Tradenetworksovertime:¡ http://faostat3.fao.org/download/F/FT/E

¡ StackExchange(replynetworks,Q/Anetworks):¡ https://archive.org/details/stackexchange

¡ Microfinancedata:¡ http://web.stanford.edu/~jacksonm/Data.html

¡ Reddit: Over1000subreddits foroneyear(2014).¡ Networkswhereuserswhocommentneareachother.Veryinterestingforcomparingdifferent

communitiesetc.Lotsofmetadata(e.g.,frompostsorcomments).Dataislarge(hundredsofGbs)

¡ Interpersonalexpertiseoverlapwithinacompany¡ Withinacompany,employeeswereaskedtorespondtothisquestion: Foreachpersoninthelistbelow,

pleaseshowhowstronglyyouagreeordisagreewiththefollowingstatement:“Ingeneral,thispersonhasexpertiseinareasthatareimportantinthekindofworkIdo.”

¡ Link: http://opsahl.co.uk/tnet/datasets/Cross_Parker-Consulting_info.txt¡ TypeofData:Originnode,destinationnode,weightofconnection(1-5)

¡ Moviegalaxies:¡ Socialnetworksof200moviesfrom www.moviegalaxies.com.Eachnetworkrepresentshowcharacters

interactinonemovie.


¡ TheNeuralNetworkofa Caenorhabditis elegans worm¡ Link: http://opsahl.co.uk/tnet/datasets/celegans_n306.txt¡ FormatofData:Originnode(Neuron),destinationnode(Neuron),weightoflink

¡ ThenetworkofairportsintheUnitedStates¡ Description:FlightsbetweenUSairportsin2002(undirected),weightedbyhowmanyavailableseats

whereonflightsbetweentwoairportsoverthecourseoftheyear.¡ Link: http://opsahl.co.uk/tnet/datasets/USairport500.txt¡ TypeofData:Airport1,Airport2,numberofseatsacrosstheentireyearthatwereavailable

¡ Citation/authorrelationships¡ Description:Asetofroughly630,000papers,andtheirrespectiveauthors¡ Link: https://aminer.org/citation¡ Link:https://www.microsoft.com/en-us/research/project/microsoft-academic-graph/¡ TypeofData:(wouldrequiresometextprocessingtoextract)Nameofpaper,indexofpaper,authors

¡ Pages/hostnetwork¡ Description:Asetofhostsfromthe.uk domainandthepagestheylinkto¡ Link: http://law.di.unimi.it/webdata/uk-2014/

¡ WolfePrimatesinteraction¡ Description:Thesedatarepresent3monthsofinteractionsamongatroopofmonkeys.Vertex

attributescontainadditionalinformation:(1)IDnumberoftheanimal;(2)ageinyears;(3)sex;(4)rankinthetroop.

¡ Link: http://nexus.igraph.org/api/dataset_info?id=45&format=html

¡ Pythondependencygraphforpypi¡ Description:Thelibrarieswhichdependonotherlibrariesinthepackagepypi¡ Link: https://ogirardot.wordpress.com/2013/01/05/state-of-the-pythonpypi-dependency-graph/¡ Format:nameofdependency,versionextracted,json stringofotherdependencies


cs224w: analysis of networks jure leskovec,...

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