1. A Generalized Co-HITS Algorithm and Its Application to Bipartite Graphs
Hongbo Deng, Michael R. Lyu and Irwin King
Department of Computer Science and Engineering
The Chinese University of Hong Kong
July 1st, 2009

2. Incorporate Content with Graph
Introduction
Many data can be modeled as bipartite graphs
IR Models
for
Link Analysis
for
Content
Graph
- VSM
- Language Model
- etc.
- HITS
- PageRank
- etc.
Relevance
Semantic relations
Incorporate Content with Graph
- Personalized PageRank (PPR)
- Linear Combination
- etc.

3. An Illustration HITS PPR More reasonable Noisy link data
Query suggestion
for query “map”:
Noisy link data
Lack of relevance constraints
HITS
PPR
More reasonable
mapquest
united states map
map of florida
us map
world map
google
mapquest
google.com
map quest
weather
mapquest
map quest
google
united states map
mapquest.com

4. Outline Introduction Generalized Co-HITS Experiments Conclusion
Preliminaries
Iterative Framework
Regularization Framework
Experiments
Conclusion

5. Preliminaries
Content
Graph X Y
Explicit links:
Hidden links:

6. Generalized Co-HITS Basic idea
Incorporate the bipartite graph with the content information from both sides
Initialize the vertices with the relevance scores x0, y0
Propagate the scores (mutual reinforcement)
Initial scores
Score propagation

7. Generalized Co-HITS
Iterative framework

8. Iterative  Regularization Framework
Consider the vertices on one side
Smoothness
Fit initial scores

9. Generalized Co-HITS Regularization Framework R1 R3 R2 Wuu Wvv
Intuition: the highly connected vertices are most likely to have similar relevance scores.

10. Generalized Co-HITS Regularization Framework The cost function:
Optimization problem:
Solution:

11. Application to Query-URL Bipartite Graphs
Bipartite graph construction
Edge weighted by the click frequency
Normalize to obtain the transition matrix
Overall Algorithm
In this paper, we apply the proposed method to the query-URL bipartite graph for query suggestion. Please refer to our paper for more details.

12. Outline Introduction Preliminaries Generalized Co-HITS Experiments
Iterative Framework
Regularization Framework
Experiments
Conclusion

13. Experimental Evaluation
Data collection
AOL query log data
Cleaning the data
Removing the queries that appear less than 2 times
Combining the near-duplicated queries
883,913 queries and 967,174 URLs
4,900,387 edges
250,127 unique terms

14. Evaluation: ODP Similarity
A simple measure of similarity among queries using ODP categories (query  category)
Definition:
Example:
Q1: “United States”  “Regional > North America > United States”
Q2: “National Parks”  “Regional > North America > United States > Travel and Tourism > National Parks and Monuments”
Precision at rank n
300 distinct queries
3/5

15. Experimental Results Comparison of Iterative Framework Result 1:
personalized PageRank one-step propagation general Co-HITS
Result 1:
The improvements of OSP and CoIter over the baseline (the dashed line) are promising when compared to the PPR. The initial relevance scores from both sides provide valuable information.

16. Experimental Results Comparison of Regularization Framework Result 2:
single-sided regularization double-sided regularization
Result 2:
SiRegu can improve the performance over the baseline. CoRegu performs better than SiRegu, which owes to the newly developed cost function R3. Moreover, CoRegu is relatively robust.

17. Experimental Results Detailed Results Result 3:
The CoRegu-0.5 achieves the best performance. It is very essential and promising to consider the double-sided regularization framework for the bipartite graph.

18. Conclusions
Propose the Co-HITS algorithm to incorporate the bipartite graph with the content information from both sides.
The Co-HITS algorithm is more general, which includes HITS and personalized PageRank as special cases.
The CoRegu is more robust with the newly developed cost function, which achieves the best performance with consistent and promising improvements.

19. Q&A
Thanks!