1. 2010 © University of Michigan 1 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

2. 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

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

4. 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!

5. 2010 © University of Michigan Vertex-Reinforced Random Walk (Pemantle 92) 5 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

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

7. 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

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

9. 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 explanation 9 a b Stay here or go to neighbors? c b

10. 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

11. 2010 © University of Michigan Thanks! 11

12. 2010 © University of Michigan Optimization Interpretation Every time, the process distributes the weight towards the ratio of the reinforced degree 12