MetaFac: Community Discovery via Relational Hypergraph Factorization

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MetaFac Community Discovery via Relational
Hypergraph Factorization
Tracking Multiple Relations in Social Media

• Yu-Ru Lin1, Jimeng Sun2, Paul Castro2,
• Ravi Konuru2, Hari Sundaram1 and Aisling
  Kelliher1
• 1Arts, Media and Engineering, Arizona State
  University
• 2IBM T.J. Watson Research Center

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The problem
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What does s/he like?
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Our approach
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Metagraph for modeling multi-relational social
data
node facet hyperedge relation
G
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community a cluster of people who interact
with resource and each other in a coherent manner
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pc
pic
j
xijk ? ?c pcpicpjcpkc
k
i
Clustering as factorization
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G
core tensor
facet factors
U(1)
U(2)
U(3)
U(4)
Factorization on metagraph
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Metagraph factorization (MetaFac) for community
extraction on metagraph
data tensor
facet factors
KL divergence
z, U can be solved with linear time complexity
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Metagraph factorization (MetaFac) for community
extraction on metagraph
O(n)
cost(G)? D(?(r)z ??m U(m))
MetaFac can be solved efficiently
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t-1
t-1
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Metagraph factorization for Time evolving data
(MFT)
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Results
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Dataset Digg
5 facets, 6 relations time span 3 weeks in
Aug 2008
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Community analysis
2-community results
4-community results
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Community analysis
C1 gamming industry news
C2 US election news
C4 general political news
C3 world news
Change in community size
Change in community keywords
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Prediction performance
Digg prediction
Comment prediction
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Prediction performance
Digg prediction
Comment prediction
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Prediction performance can be further improved
Effect of historic information
Effect of input relations
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Scalability evaluation
Our algorithm scales linearly with the data size
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Summary
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Problem How to track communities in dynamic
multi-relational data?
Approach MetaFac for community extraction on
metagraph
Results meaningful mining results and best
prediction quality
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Related work

• Evolutionary community characterization
• Measurement-driven Backstrom et al. 2006
  Leskovec et al. 2008
• Clustering methods Sun et al. 2007 Lin et al.
  2008 and latent space model Sarkar and Moore
  2005
• Multi-dimensional mining
• tensor based analysis Bader et al. 2006 Chi et
  al. 2008 Sun et al. 2007 or multi-graph mining
  Zhu et al. 2007
• Relational learning
• PRMs Friedman et al. 1999 and RMNs Taskar et
  al. 2002
• Pairwse relational learning Bekkerman et al.
  2005 Long et al. 2007 Tang et al. 2008 Wang et
  al. 2006
• Our work
• Flexible and scalable framework that exploits the
  relational context
• Unified approach for analyzing rich media social
  networks
• Multi-dimensional, sparse relational, evolving
  over time

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Thanks!
Code / data available online http//www.public.
asu.edu/ylin56/kdd09sup.html

• Questions? Suggestions?

• Yu-Ru.Lin_at_asu.edu