Div Rank Interplay of Prestige and Diversity in

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Div. Rank: Interplay of Prestige and Diversity in Information Networks Qiaozhu Mei 1, 2,

Div. Rank: 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 2010 © University of Michigan 1

Diversity in Ranking papers, people, web pages, movies, restaurants… Web search; ads; recommender systems

Diversity in Ranking papers, people, web pages, movies, restaurants… Web search; ads; recommender systems … Network based ranking – centrality/prestige 2010 © University of Michigan 2

Ranking by Random Walks b d a c Ranking using stationary distribution E. g.

Ranking by Random Walks b d a c Ranking using stationary distribution E. g. , Page. Rank ? 2010 © University of Michigan 3

Reinforcements in Random Walks • Random walks are not random - rich gets richer;

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; Conformity! Source - http: //www. resettlementagency. co. uk/modern-world-migration/ 2010 © University of Michigan 4

Vertex-Reinforced Random Walk (Pemantle 92) b a d transition probabilities change over time c

Vertex-Reinforced Random Walk (Pemantle 92) b a d transition probabilities change over time c Reinforced random walk: transition probability is reinforced by the weight (number of visits) of the target state 2010 © University of Michigan 5

Div. Rank • A smoothed version of Vertex-reinforced Random Walk b a c Random

Div. Rank • A smoothed version of Vertex-reinforced Random Walk b a c Random jump, could be personalized • Adding self-links; • Efficient approximations: use Cumulative Div. Rank: “organic” transition probability to approximate Pointwise Div. Rank: 2010 © University of Michigan 6

Experiments • Three applications – Ranking movie actors (in co-star network) – Ranking authors/papers

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) 2010 © University of Michigan 7

Results • Divrank >> Grasshopper/MMR >> Pagerank Paper citation: Pagerank Grasshopper Density Impact coverage

Results • Divrank >> Grasshopper/MMR >> Pagerank Paper citation: Pagerank Grasshopper Density Impact coverage Divrank Text Summarization: 2010 © University of Michigan 8

Why Does it Work? • Rich gets richer c b – Related to Polya’s

Why Does it Work? • Rich gets richer c b – Related to Polya’s urn and preferential attachment • Compete for resource in neighborhood a b Stay here or go to neighbors? – Prestigious node absorbs weights of its neighbors • An optimization explanation 2010 © University of Michigan 9

Summary • Div. Rank – Prestige/Centrality + Diversity • Mathematical foundation: vertex-reinforced random walk

Summary • Div. Rank – 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 Div. Rank; 2010 © University of Michigan 10

Thanks! 2010 © University of Michigan 11

Thanks! 2010 © University of Michigan 11