Meta Fac Community Discovery via Relational Hypergraph Factorization

Meta. Fac: Community Discovery via Relational Hypergraph Factorization Tracking Multiple Relations in Social Media Yu-Ru Lin 1, Jimeng Sun 2, Paul Castro 2, Ravi Konuru 2, Hari Sundaram 1 and Aisling Kelliher 1 1 Arts, Media and Engineering, Arizona State University 2 IBM T. J. Watson Research Center

The problem

raustin What does s/he like?

(Q 1) History How to model multirelational social data? Dugg Comments Favorites tweets Friends raustin Favorites following

(Q 1) How to model multirelational social data? (Q 2) How to reveal communities consistent across multi-relations? History Dugg Comments Favorites tweets Friends raustin (Q 3) Favorites following How to track these communities over time?

Our approach

(Q 1) How to model multi-relational social data?

Metagraph for modeling multi-relational social data G node: facet hyperedge: relation

(Q 2) How to reveal communities consistent across multirelations? community : = a cluster of people who interact with resource and each other in a coherent manner

pc pi|c i j xijk c pc∙pi|c∙pj|c∙pk|c k Clustering as factorization core tensor facet factors

G core tensor facet factors U(1) Factorization on metagraph U(2) U(3) U(4)

Metagraph factorization (Meta. Fac) for community extraction on metagraph data tensor core tensor facet factors objective function cost(G)= D( (r)||[z] m U(m)) r E m: v(m)~e(r) KL divergence z, {U} can be solved with linear time complexity

How to track these communities over time? (Q 3) t-1 t-1 t t

Metagraph factorization for Time evolving data (MFT) t-1 t t t objective function cost(G) = (1 - = D( (r)||[z] m U(m)) ) + {D(zt-1||z)+ D(Ut-1(q)||U(q))} temporal cost

Results

Dataset: Digg 5 facets, 6 relations time span: 3 weeks in Aug 2008

Community analysis C 1: gamming industry news C 2: US election news C 4: general political news Change in community size C 3: world news Change in community

Prediction performance Digg prediction Comment prediction

Summary

Problem: How to track communities in dynamic multi-relational data? Approach: Meta. Fac for community extraction on metagraph Results: meaningful mining results and best prediction quality

Code / data – available online: http: //www. public. asu. edu/~ylin 56/kdd 09 sup. html Questions? Suggestions? Yu-Ru. Lin@asu. edu Thanks! 27