link prediction in online social networks using group...

IntroductionProposal

Experimental EvaluationConclusion

Link Prediction in Online Social NetworksUsing Group Information

Jorge Valverde-Rebazaand

Alneu de Andrade Lopes

Laboratory of Computational Intelligence (LABIC)University of São Paulo (USP)

Brazil

July 2014



Outline

1 Introduction

2 Proposal

3 Experimental Evaluation

4 Conclusion

Jorge Valverde-Rebaza and Alneu de Andrade Lopes Link Prediction in OSN using group information 2



Social NetworksGroups DetectionLink Prediction

Outline

1 Introduction

2 Proposal


4 Conclusion





Social Networks

Structure made up of a set of actors (individual ororganizations) and social relations between them

Social network analysis is an interesting research field ingraph and complex network theory, data mining, machinelearning and other areas

Rise of online social networks





Groups Detection

Real networks are characterized by high concentration oflinks within special groups of vertices and lowconcentrations of links between these groups

Online social networks offer a wide variety of possiblegroups: families, working and friendship circles, artistic oracademic preferences, towns, nations, etc.





Link Prediction Process





Link Prediction Measures

Based on global informationHigher accuracy

Very time-consuming computation

Usually infeasible for large-scalenetworks

E.g.: Katz index, Hitting time index,Simrank, etc. [Lü and Zhou, 2011]

Based on local information

Lower accuracy than measures based onglobal information

Faster computation

E.g.: Common neighbors (CN), Adamic Adar(AA), Jaccard (Jac), Resource Allocation(RA), Preferential Attachment (PA), etc.[Lü and Zhou, 2011]

Hybrid strategy based on communityinformation

As the community structure grows, the accuracy ofthese measures drastically improves

Perform better than most of measures based onlocal information

E.g.: PFF [Zheleva et al., 2010], CN1, RA1[Soundarajan and Hopcroft, 2012], WIC, W-measures[Valverde-Rebaza and Lopes, 2012], etc.

A node belongsto just one group




PreliminaryWOCGCNGTPOG

Outline

1 Introduction

2 Proposal


4 Conclusion





Preliminary

We consider that each node participates in multiple groups

In the network G(V ,E) exists M > 1 groups identified bydifferent group labels g1,g2, . . .gM

Each node x belongs to a set of node groupsG = {ga,gb, . . .gp} with size P > 0 and P ≤ M

The set of neighbors of a vertex x is Γ(x) = {y | (x , y) ∈ E}The set of all common neighbors (CN) of a vertex pair(x , y) is Λx ,y = Γ(x) ∩ Γ(y)





CN Within and Outside of Common Groups (WOCG)

Considering Gα,β = Gα ∩ Gβ

We redefine the set of CN as Λx ,y = ΛWCGx ,y ∪ ΛOCG

x ,y

ΛWCGx,y = {zGγ ∈ Λx,y | Gα,β ∩ Gγ 6= ∅} - the set of common

neighbors within common groups (WCG)

ΛOCGx,y = Λx,y − ΛWCG

x,y - the set of common neighbors outsideof the common groups (OCG)

Our final score, called as common neighbors within andoutside of common groups (WOCG) measure, is definedas:

sWOCGx ,y =

|ΛWCGx ,y ||ΛOCG

x ,y |(1)





Common Neighbors of Groups (CNG)

We define the set of common neighbors of groups asΛG

x ,y = {zGγ ∈ Λx ,y | Gα ∩ Gγ 6= ∅ ∨ Gβ ∩ Gγ 6= ∅}

Our final score, called as common neighbors of groups(CNG), is defined as:

sCNGx ,y = |ΛG

x ,y | (2)





CN with Total and Partial Overlapping of Groups(TPOG)

We redefine the set of CNG as ΛGx ,y = ΛTOG

x ,y ∪ ΛPOGx ,y

ΛTOGx,y = {zGγ ∈ ΛG

x,y | Gα ∩ Gγ 6= ∅ ∧ Gβ ∩ Gγ 6= ∅} - the setof CN with total overlapping of groups (TOG)

ΛPOGx,y = ΛG

x,y − ΛTOGx,y - the set of CN with partial overlapping

of groups (POG)

Our final score, called as the common neighbors withtotal and partial overlapping of groups (TPOG)measure, is defined as:

sTPOGx ,y =

|ΛTOGx ,y ||ΛPOG

x ,y |(3)




DatasetsExperimental setupResults

Outline

1 Introduction

2 Proposal


4 Conclusion





Datasets

Table : High-level topological features of our four social networks[Mislove et al., 2007]

Flickr LiveJournal Orkut YoutubeNumber of nodes 1,846,198 5,284,457 3,072,441 1,157,827Number of links 22,613,981 77,402,652 223,534,301 4,945,382Average degree per node 12.24 16.97 106.1 4.29Fraction of links symmetric 62.0% 73.5% 100.0% 79.1%

Average path length 5.67 5.88 4.25 5.10Diameter 27 20 9 21Average clustering coefficient 0.313 0.330 0.171 0.136Average assortativity coefficient 0.202 0.179 0.072 −0.033Number of node groups 103,648 7,489,073 8,730,859 30,087Average number of groups membership per node 4.62 21.25 106.44 0.25Average group size 82 15 37 10Average group clustering coefficient 0.47 0.81 0.52 0.34





Experimental setup

For a network G(V ,E), the set E is divided into the trainingset, ET , and the test set, EP

For EP are randomly selected 2/3 of links formed bynodes with average degree two times greater than theaverage. The remaining links constitute ET . This isperformed 10 times for each network

Evaluate traditional local measures: CN, AA, Jac, RA andPA, and our proposals: WOCG, CNG and TPOG





Experimental setup

For each network, create 5 types of characteristic vectorswere considered : VLocal (all the local measures),VGroup (all our proposals), VTop (three best localmeasures - CN, AA and RA - and two best of ourproposals - CNG and TPOG), VTop2 (the five best overallmeasures: TPOG, CNG, AA, WOCG and CN) and VTotal(all measures evaluated)

Table : Number of instances by class for all networks

Existent Non-existent TotalFlickr 500001 500001 1000002LiveJournal 300001 300001 600002Orkut 1500001 1500001 3000002Youtube 20001 20001 40002





Unsupervised results measured by AUC

Table : Prediction results measured by AUC

WOCG CNG TPOG CN AA Jac RA PAFlickr 0.637 (5.0) 0.728 (1.0) 0.728 (2.0) 0.674 (3.0) 0.656 (4.0) 0.431 (8.0) 0.616 (6.0) 0.566 (7.0)Livejournal 0.596 (4.0) 0.611 (3.0) 0.665 (1.0) 0.582 (5.0) 0.580 (6.0) 0.624 (2.0) 0.565 (7.0) 0.542 (8.0)Orkut 0.649 (2.0) 0.621 (3.0) 0.651 (1.0) 0.572 (7.0) 0.620 (4.0) 0.575 (6.0) 0.566 (8.0) 0.602 (5.0)Youtube 0.434 (7.0) 0.723 (5.0) 0.555 (6.0) 0.834 (4.0) 0.928 (1.0) 0.217 (8.0) 0.892 (3.0) 0.917 (2.0)Average rank 4.50 (4.0) 3.00 (2.0) 2.50 (1.0) 4.75 (5.0) 3.75 (3.0) 6.00 (7.5) 6.00 (7.5) 5.50 (6.0)

1 2 3 4 5 6 7 8

TPOGCNG

AAWOCG CN

PAJacRA

CD

Figure : Post-hoc test for results with CD = 5.25





Unsupervised results measured by precision

00 1,000 2,500 5,0000

0.20.40.60.8

1

L

Pre

cisi

on

(a) Flickr

00 1,000 2,500 5,0000

0.20.40.60.8

1

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Pre

cisi

on

(b) LiveJournal

00 1,000 2,500 5,0000

0.20.40.60.8

1

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Pre

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(c) Orkut

00 1,000 2,500 5,0000

0.20.40.60.8

1

LP

reci

sion

(d) Youtube

WOCG CNG TPOG CN AA Jac RA PA

Figure : Precision results on four social networks evaluated





Supervised results measured by f-measure

Table : Average of F-measure on four social networks

J48 NB MLP SMO J48 NB MLP SMOFlickr VLocal 0.777 0.507 0.713 0.651 Orkut VLocal 0.825 0.702 0.800 0.764Flickr VGroup 0.706 0.583 0.699 0.668 Orkut VGroup 0.781 0.676 0.773 0.737Flickr VTop 0.724 0.525 0.711 0.676 Orkut VTop 0.799 0.720 0.77 0.759Flickr VTop2 0.722 0.558 0.709 0.669 Orkut VTop2 0.793 0.722 0.773 0.758Flickr VTotal 0.777 0.548 0.712 0.680 Orkut VTotal 0.826 0.731 0.801 0.771LiveJournal VLocal 0.797 0.687 0.788 0.774 Youtube VLocal 0.823 0.531 0.73 0.565LiveJournal VGroup 0.768 0.698 0.768 0.750 Youtube VGroup 0.658 0.563 0.655 0.567LiveJournal VTop 0.791 0.700 0.787 0.772 Youtube VTop 0.789 0.543 0.724 0.617LiveJournal VTop2 0.79 0.691 0.781 0.772 Youtube VTop2 0.780 0.600 0.717 0.613LiveJournal VTotal 0.797 0.702 0.786 0.774 Youtube VTotal 0.826 0.577 0.723 0.623




Conclusion

Outline

1 Introduction

2 Proposal


4 Conclusion




Conclusion

Conclusion

Our proposals consider that a node can belong to morethan one group, as usually occurs in real networks

In an unsupervised strategy, our proposals outperform thelocal measures but there is no statistically significantwinner

In a supervised strategy, our proposals combined with localmeasures may improve the performance of classifiers

In general, our proposals improve the performance of linkprediction task by considering mainly the information ofcommon groups to which users belong to




Conclusion

References

Lü, L. and Zhou, T. (2011).Link prediction in complex networks: A survey.Physica A: Statistical Mechanics and itsApplications, 390(6):1150 – 1170.

Mislove, A., Marcon, M., Gummadi, K. P.,Druschel, P., and Bhattacharjee, B. (2007).Measurement and analysis of online socialnetworks.In ACM SIGCOMM IMC ’07, pages 29–42.

Soundarajan, S. and Hopcroft, J. (2012).Using community information to improve theprecision of link prediction methods.In Proceedings of the 21st InternationalConference Companion on World Wide Web,WWW ’12 Companion, pages 607–608.

Valverde-Rebaza, J. and Lopes, A. (2012).Link Prediction in Complex Networks Based onCluster Information.In Advances in Artificial Intelligence - SBIA2012, Lecture Notes in Computer Science,pages 92–101. Springer Berlin Heidelberg.

Zheleva, E., Getoor, L., Golbeck, J., and Kuter,U. (2010).Using friendship ties and family circles for linkprediction.In Proceedings of the Second InternationalConference on Advances in Social NetworkMining and Analysis, SNAKDD’08, pages97–113, Berlin, Heidelberg.




Conclusion

Thank you

Jorge Carlos Valverde-Rebaza

[email protected]

link prediction in online social networks using group...

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