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

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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;

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Source - http://www.resettlementagency.co.uk/modern-world-migration/

Conformity!

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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

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DivRank

• A smoothed version of Vertex-reinforced Random Walk

• Adding self-links;• Efficient approximations: use to approximate

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)(

)(),()()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:

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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)

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Results

• Divrank >> Grasshopper/MMR >> Pagerank

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Divrank

GrasshopperPagerank

Density Impact coverage

Paper citation:

Text Summarization:

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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;

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2010 © University of Michigan

Thanks!

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