Supervised Rank Aggregation Approach for Link Prediction ... · PDF fileSupervised Rank Aggregation Approach for Link Prediction in Complex Networks Manisha Pujari & Rushed Kanawati

Supervised Rank Aggregation Approach for LinkPrediction in Complex Networks

Manisha Pujari & Rushed Kanawati

[email protected]

17/10/2012

Outline Link Prediction Supervised Rank Aggregation Experiment Conclusion

1 Link Prediction

2 New Approach: Supervised Rank Aggregation

3 Experiment

4 Conclusion

M. Pujari & R. Kanawati Link Prediction by Supervised Rank Aggregation 2/28


Link Prediction Problem

Link Prediction

Predicting missing/hidden/new links between nodes of a graph.

Applications

Recommender systems

Academic/Professionalcollaborations

Identification of structures ofcriminal networks

Biological networks



Link Prediction Approaches

Dyadic: Computation of link score for unlinked vertices

Structural: Mining rules for evolution of sub-graphs

Topology based: Attributes computed for graph

Node-feature based: Attributes computed for nodes

Hybrid: Combination of the two

Temporal: Consider dynamics of the networks

Static: Do not consider the dynamics of a network



Link Prediction Approaches

Dyadic: Computation of link score for unlinked vertices

Structural: Mining rules for evolution of sub-graphs

Topology based: Attributes computed for graph

Node-feature based: Attributes computed for nodes

Hybrid: Combination of the two

Temporal: Consider dynamics of the networks

Static: Do not consider the dynamics of a network



Dyadic Topological Approaches

Work of [Liben-Nowell & al.,2007]



Dyadic Topological Approaches

Work of [Liben-Nowell & al.,2007]



Combining the effect of different topological measures:Application of supervised machine learning algorithms

Work of [Hasan & al., 2006]

Examples:(Nodex ,Nodey ) −→[a0, a1, ...., an]

[3, 1,Positive][1, 0.33,Negative]

...




Work of [Benchettara & al.,2010]





Can we apply rank aggregation methods ?





Can we apply rank aggregation methods ?M. Pujari & R. Kanawati Link Prediction by Supervised Rank Aggregation 9/28


Rank Aggregation (Social choice theory)

Combining various lists of ranked candidates to find a single listwith minimum possible disagreement

Expert1 =⇒ L1 = [A,B,C ,D]Expert2 =⇒ L2 = [B,D,A,C ]Expert3 =⇒ L3 = [C ,D,A,B]

...

...

...Expertn =⇒ Ln = [D,C ,A,B]

———————————————Laggregate = [?, ?, ?, ?]



Supervised Rank Aggregation

Combining different rankings to get an aggregation giving differentweights to the experts

w1 ← Expert1 =⇒ L1 → [k elements]w2 ← Expert2 =⇒ L2 → [k elements]w3 ← Expert3 =⇒ L3 → [k elements]

...

...

...wn ← Expertn =⇒ Ln → [k elements]

We propose

Link prediction based on

1 Supervised Borda

2 Supervised Kemeny



Supervised Borda Aggregation

Borda score:

B(x) =n∑

i=1

BLi (x) ;where BLi (x) = {count(y)|Li (y) > Li (x)&y ∈ Li} (1)

Supervised Borda score:

B(x) =n∑

i=1

wi ∗ BLi (x) (2)

NOTE: Li (x) represent the

rank (or index) of element x

in input list Li . The lower the

value of rank, the higher is

the preference. U is the set

of all elements in the lists.



Kemeny Optimal Aggregation [Dwork & al.,2001]

Based on relative ranking of elements

NP-hard

Approximate Kemeny



Supervised Kemeny Aggregation

Inputs: Ranked lists [L1, L2, . . . , Ln], Weights [w1,w2, . . . ,wn] , each listwith m elements (U)Steps:

1 Initial aggregation R

2 ∀(x , y) ∈ R, Compute

score(x , y) =∑n

i=1(wi ∗ Prefi (x , y)) where

Prefi (x , y) =

{0 if y � x i .e. Li (x) > Li (y)

1 if x � y i .e. Li (x) < Li (y)

3 If score(x , y) >wT

2where wT =

∑ni=1 wi , then x �w y

4 Apply a sorting algorithm on R: Swap(x , y) only if y �w x

5 R is the final aggregation.



Supervised Kemeny Aggregation



Link Prediction based on Supervised Rank Aggregation

Examples: (Nodex ,Nodey ) −→ [a0, a1, a2, ...., an]

Steps:

Learning

1 Rank learning examples by attribute values

2 Consider only top t examples and compute attribute weight wai

Validation

1 Rank test examples by attribute to get n ranked lists

2 Apply supervised rank aggregation

3 Consider only top k examples of the aggregate list and computeperformance.



Link Prediction Based on Supervised Rank Aggregation

Computation of attribute weights:

Maximization of identification positive examples:

Wai = n ∗ Precisionai (3)

where n is the total number of attributes and Precisionai is the precisionof attribute ai .

precision = fraction of retrieved examples that are really positive

Minimization of identification of negative examples:

Wai = n ∗ (1− FPRai ) (4)

where n is the total number of attributes FPRai is the false positive rateof attribute ai .

false positive rate = fraction of negative examples retrieved as positive



DBLP data

Author-Document bipartite graphs

Datasets Training TimeGraph

Authors Publications EdgesDataset1 [1970,1973] 2661 1487 6634Dataset2 [1972,1975] 4536 2542 10855

Projected graphs

DatasetsAuthor Graph Publication Graph

Nodes Edges Nodes EdgesDataset1 2661 2575 1487 1520Dataset2 4536 4510 2542 2813

Examples

DatasetsTraining Labeling Testing Training examples Test examples

Time Time Time Pos Neg Pos NegDataset1 [1970,1973] [1974,1975] [1971,1974] 30 1663 41 3430Dataset2 [1972,1975] [1976,1977] [1973,1976] 87 19245 82 18675



Topological Attributes

Neighborhood-based attributes:

Common neighbors : VC(x , y))=‖ Γ(x) ∩ Γ(y) ‖Jaccard’s coefficient : JC(x , y))= ‖Γ(x)∩Γ(y)‖

‖Γ(x)∪Γ(y)‖Adamic Adar: AD(x , y)=

∑z∈Γ(x)∩Γ(y)

1log‖Γ(z)‖ [Adamic & al.2003]

Preferential attachment: AP(x , y)=‖ Γ(x)× Γ(y) ‖[Huang & al., 2005]

Distance-based attributes:

Shortest path distance(Dis)

Katz: Katz(x , y) = Σ∞l=1β

`× ‖ path(`)x,y ‖, where path

(`)x,y is the

number of paths between x and y of length ` and β is a positiveparameter which favours shortest paths [Katz,1953]Maximum forest algorithm (MFA) [Fouss & al., 2007]

Centrality-based attributes:

Product of PageRank (PPR)[Brin & al., 1998]Product of degree centrality (PCD)Product of clustering coefficient (PCF)



Results

Results(average precision) obtained by ranking the test examples byattribute values

Attributes Dataset1 Dataset2Katz 0 0MFA 0.0244 0.0732PPR 0.0244 0.0244PCF 0.0732 0.0244PCD 0 0VC 0.5122 0.4268JC 0.2195 0.1707AD 0.1463 0.1463AP 0.0488 0Dis 0 0.0122

Attributes Dataset1 Dataset2Indirect Katz 0.1220 0.1098Indirect MFA 0.0488 0.0732Indirect PPR 0.0488 0Indirect PCF 0.4878 0.4756Indirect PCD 0.0244 0.0122Indirect VC 0.0488 0.0488Indirect JC 0.0488 0.1098Indirect AD 0.0976 0.0488Indirect AP 0.0244 0Indirect Dis 0.6098 0.5366



Experiment-1

Performance measure:

Precision =|Positive links ∩ Predicted links|

|Predicted links|

Figure: Precision for complete test set by learning on complete training set



Experiment-2(a): Performance of supervised Kemeny byvarying K for validation

Dataset-1

Figure: Precision Figure: Recall



Experiment-2(b): Performance of supervised Borda byvarying K for validation

Dataset-1

Figure: Precision Figure: Recall



Conclusion

X Link prediction and temporal dyadic approaches

X A new definition for supervised Kemeny aggregation

X Application of supervised rank aggregation to link prediction

Perspectives

⇒ Application of top − k aggregation[Kumar & al., 2009]: Reducecomplexity caused due to rank aggregation

⇒ Use of communities and community based information (work withZied Yakoubi)

⇒ Application on heterogeneous scientific collaboration network

⇒ Application for tag recommendation in folksonomy



MERCI

et

QUESTION ?



References I

[Benchettara & al.,2010] N. Benchettara, R. Kanawati, C. Rouveirol. Supervised machine learning applied to link prediction in

bipartite social networks . In International Conference on Advances in Social Network Analysis and Mining, ASONAM 2010, 2010.

[Brin & al., 1998] Sergey Brin, Lawerence Page. The anatomy of a large scale hypertextual web search. Proceedings of seventh

International conference on the world wide web, 1998.

[Dwork & al.,2001] C. Dwork, R. Kumar, M. Naor, D.Sivakumar. Rank Aggregation method for Web. WWW 01: Proceedings of

10th international conference on World Wide Web, pages 613-622 (2001).

[Kumar & al., 2001] C. Dwork, R. Kumar, M. Naor, D.Sivakumar. Rank aggregation revisited . Manuscript, 1953.

[Katz,1953] L.Katz. A new status index derived from socimetric analysis. (article) . Vol. 18, pages 39-43, 2001.

[Borda, 1781] J.C.Borda FAG03 Memoire sur les elections au Scrutin . Histoire de l’Academie Royale des Sciences,1781 .

[Fagin & al., 2003] R.Fagin, R.Kumar,D. Sivakumar. Efficient similarity search and classification via rank aggregation.

Proceedings of the 2003 ACM SIGMOD international conference on Management of data, pages 301-312, 2003, New York.

[Sculley,2007] D.Sculley. Rank Aggregation for Similar Items. Proceedings of the Seventh SIAM International Conference on Data

Mining, April 26-28, 2007, Minneapolis, Minnesota, USA (2007)).

[Adamic & al.2003] L. A. Adamic, O. Buyukkokten, and E. Adar. A social network caught in the web. First Monday, Vol. 8, No.

6. (June 2003).

[Bisson & al., 2008] G. Bisson and F. Hussain. χ-Sim: A new similarity measure for the co- clustering task. In Seventh

International Conference on Machine Learning and Application(ICMLA), IEEE Computer Society (2008) , pages 211-217.



References II

[Mrosek & al.,2009] J. Mrosek, S. Bussmann, H. Albers, K. Posdziech, B. Hengefeld, N. Opperman, S. Robert and G. Spirar.

Content- and graph-based tag recommendation: Two variatons. ECML PKDD Discovery Challenge 2009 DC09, 497, pages189-199. Bled, Slovenia, CEUR Workshop Proceedings, September 2009.

[Lipczak, 2008] M.Lipczak. Tag recommendation for folksonomies oriented towards individual users . In Proceedings of ECML

PKDD Discovery Challenge (RSDC08) (2008), pages. 84-95.

[Liben-Nowell & al.,2007] David Liben-Nowell, and Jon Kleinberg The link prediction problem for social networks. In Proceedings

of the 16th international conference on World Wide Web, pages. 481-490,New York, USA,2007.

[Hasan & al., 2006] Mohammad Al Hasan, Vineet Chaoji, Saeed Salem, and Mohammed Zaki. Link prediction using supervised

learning. SIAM Workshop on Link Analysis, Counterterrorism and Security with SIAM Data Mining Conference, 2006.

[Huang & al., 2005] Zan Huang, Xin Li and Hsinchun Chen. Link prediction approach to collaborative filtering. Proceedings of the

5th ACM/IEEE-CS Joint Conference on Digital Libraries,pages. 141-142,New York, USA , 2005.

[Fouss & al., 2007] Francois Fouss, Alain Pirotte, Jean-Michel Renders and Marco Sarens. Random-Walk Computation of

Similarities between Nodes of a Graph with Application to Collaborative Recommandation IEEE Transactions on knowledge anddata engineering, pages. 355-369, 2007.

[Acar & al.,2009] Evrim Acar, Daniel M. Dunlavy and Tamara G Kolda. Link Prediction on Evolving Data Using Matrix and

Tensor Factorizations.. ICDM Workshops, pages.262-269, 2009.

[Lahiri & al., 2007] Mayank Lahiri and Tanya Y. Berger-Wolf Structure Prediction in Temporal Networks using Frequent

Subgraphs. CIDM, pages 35-42,2007.

[Kumar & al., 2009] Ravi Kumar, Kunal Punera, Torsten Suel and Sergei Vassilvitskii. Top-k aggregation using intersections of

ranked inputs. Proceedings of the Second ACM International Conference on Web Search and Data Mining, pages. 222-231,WSDM, 2009,Barcelona, Spain.



References III

[Pujari & al., 2011] Manisha Pujari and Rushed Kanawati. Supervised machine learning link prediction approach for tag

recommandation. 4th International Conference on Online Communities and Social Computing @ HCI International,Orlando,Florida9-14 July 2011.

[Pujari & al., 2012] Manisha Pujari and Rushed Kanawati. Tag recommendation by link prediction based on supervised machine

learning. Sixth International AAAI Conference on Weblogs and Social Media (ICWSM 2012). 5-8 June 2012, Dublin.

[Subbian & al., 2011] K. Subbian and P. Melville. Supervised rank aggregation for predicting influence in networks. In the

proceedings of the IEEE Conference on Social Computing (SocialCom-2011)., Boston, October 2011.

[Liu & al., 2007] Yu-Ting Liu, Tie-Yan Liu, Tao Qin, Zhi-Ming Ma, and Hang Li. Supervised rank aggregation. In Proceedings of

the16th international conference on World Wide Web,WWW ’07, pages 481-490, New York, NY, USA, 2007. ACM.


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Supervised Rank Aggregation Approach for Link Prediction ... · PDF fileSupervised Rank Aggregation Approach for Link Prediction in Complex Networks Manisha Pujari & Rushed Kanawati