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DivRank: Interplay of Prestige and Diversity in Information Networks. Qiaozhu Mei 1,2 , Jian Guo 3 , Dragomir Radev 1,2 1. School of Information 2. Computer Science and Engineering 3. Department of Statistics University of Michigan. Diversity in Ranking. - PowerPoint PPT Presentation
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2010 © University of Michigan 1
DivRank: Interplay of Prestige and
Diversity in Information Networks
Qiaozhu Mei1,2, Jian Guo3, Dragomir Radev1,2
1.School of Information2.Computer Science and Engineering
3. Department of StatisticsUniversity of Michigan
2010 © University of Michigan
Diversity in Ranking
2
Ranking papers, people, web pages, movies, restaurants…
Web search; ads; recommender systems …
Network based ranking – centrality/prestige
2010 © University of Michigan
Ranking by Random Walks
3
ad
c
b
?Ranking using
stationary distribution
E.g., PageRank
Evu
TT upvupvp),(
1 )(),()(
2010 © University of Michigan
Reinforcements in Random Walks
• Random walks are not random - rich gets richer; – e.g., civilization/immigration – big cities attract larger population;– Tourism – busy restaurants attract more visitors;
4
Source - http://www.resettlementagency.co.uk/modern-world-migration/
Conformity!
2010 © University of Michigan
Vertex-Reinforced Random Walk (Pemantle 92)
5
Evu
TTT upvupvp),(
1 )(),()(
)(),( vNvup TT
a
d
c
b
Reinforced random walk: transition probability is reinforced by the weight (number of visits) of the target state
transition probabilities
change over time
2010 © University of Michigan
DivRank
• A smoothed version of Vertex-reinforced Random Walk
• Adding self-links;• Efficient approximations: use to approximate
6
)(
)(),()()1(),( 0*
uD
vNvupvpvup
T
TT
Random jump, could be personalized
“organic” transition probability
a
c
b
T
ttT vpvNE
0
)()]([ )()]([ vpvNE TT
)]([ vNE T )(vNT
Cumulative DivRank: Pointwise DivRank:
2010 © University of Michigan
Experiments
• Three applications– Ranking movie actors (in co-star network)
– Ranking authors/papers (in author/paper-citation network)
– Text summarization (ranking sentences)
• Evaluation metrics:– diversity: density of subgraph; country coverage (actors)
– quality: h-index (authors); # citation (papers);
– quality + diversity: movie coverage (actors); impact coverage (papers); ROUGE (text summarization)
7
2010 © University of Michigan
Results
• Divrank >> Grasshopper/MMR >> Pagerank
8
Divrank
GrasshopperPagerank
Density Impact coverage
Paper citation:
Text Summarization:
2010 © University of Michigan
Why Does it Work?
• Rich gets richer
– Related to Polya’s urn and preferential attachment
• Compete for resource in neighborhood
– Prestigious node absorbs weights of its neighbors
• An optimization explanation9
ab Stay here or go to
neighbors?
cb
2010 © University of Michigan
Summary
• DivRank – Prestige/Centrality + Diversity• Mathematical foundation: vertex-reinforced random walk• Connections:
– Polya’s Urn– Preferential Attachments– Word burstiness
• Why it works?– Rich-gets-richer– Local resource competition
• Future work: Query dependent DivRank;
10
2010 © University of Michigan
Thanks!
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