1. RankClus: Integrating Clustering with Ranking for Heterogeneous Information Network Analysis
Yizhou Sun, Jiawei Han, Peixiang Zhao, Zhijun Yin, Hong Cheng, Tianyi Wu
Department of Computer Science
University of Illinois at Urbana-Champaign
EDBT’09, St.-Petersburg, Russia, March 2009
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2. The RankClus Algorithm Experiments Conclusion
Outline
Background
Motivation
The RankClus Algorithm
Experiments
Conclusion
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3. Information Networks Are Ubiquitos
Conference-Author Network
Co-author Network
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4. Two Kinds of Information Networks
Homogeneous Network
Objects belong to single type
E.g., co-author network, internet, friendship network, gene interaction network, and so on
Most current studies are on homogeneous networks
Heterogeneous Network
Objects belong to several types
E.g., conference-author network, paper-conference-author-topic network, movie-user network, webpage-tag-user network, and so on
Most real networks are heterogeneous networks, and many homogeneous networks are extracted from a more complex network
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5. How to Better Understand Information Networks?
Problem: Hard to understand large, raw networks
Huge number of objects
Links are “in a mess”
Solution: Extracting aggregate information from networks
Ranking
Clustering
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6. Ranking Goal Evaluate importance of objects in the network
A ranking function: map an object into a real non-negative score
Algorithms
PageRank (for homogeneous networks)
HITS (for homogeneous networks)
PopRank (for heterogeneous networks)
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7. Clustering
Goal
Group similar objects together and obtain the cluster label for each object
Algorithms
Spectral clustering: Min-Cut, N-Cut, and MinMax-Cut (for homogeneous networks)
Density-based clustering: SCAN (for homogeneous networks)
How to cluster heterogeneous networks?
Use SimRank to first extract pair-wise similarity for target objects (but time complexity is high)
Combined with spectral clustering
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8. The RankClus Algorithm Experiments Conclusion
Outline
Background
Motivation
The RankClus Algorithm
Experiments
Conclusion
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9. Why RankClus? More meaningful cluster
Within each cluster, ranking score for every object is available as well
More meaningful ranking
Ranking within a cluster is more meaningful than in the whole network
Address the problem of clustering in heterogeneous networks
No need to compute pair-wise similarity of objects
Mapping each object into a low measure space
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10. Global Ranking vs. Within-Cluster Ranking in a Toy Example
Two areas: 10 conferences and 100 authors in each area
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11. Difficulties in Clustering Heterogeneous Networks
What type of objects to be clustered?
Clustering on one specific type of objects (called target objects): specified by user
Clustering of target objects can induce a sub-network of the original network
Efficient algorithm of clustering
How to avoid calculating pair-wise similarities among target objects?
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12. The RankClus Algorithm Experiments Conclusion
Outline
Background
Motivation
The RankClus Algorithm
Experiments
Conclusion
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13. Algorithm Framework - Illustration
Sub-Network
Ranking
Clustering
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14. Algorithm Framework—Philosophy
Ranking and clustering can be mutually improved
Ranking: Once a cluster becomes more accurate, ranking will be more reasonable for such a cluster and will be the distinguished feature of the cluster
Clustering: Once ranking is more distinguished from each other, the clusters can be adjusted and get more accurate results
Objects preserve similarity under new measure space
E.g., consider VLDB and SIGMOD
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15. Algorithm Framework - Summary
Step 0. Initialization
Randomly partition target objects into K clusters
Step 1. Ranking
Ranking for each sub-network induced from each cluster, which serves as feature for each cluster
Step 2. Generating new measure space
Estimate mixture model coefficients for each target object
Step 3. Adjusting cluster
Step 4. Repeat Step 1-3 until stable
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16. Focus on A Bi-type Network Case
Conference-author network, links can exist between
Conference (X) and author (Y)
Author (Y) and author (Y)
Use W to denote the links and there weights
W =
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17. Step 1: Feature Extraction — Ranking
Simple Ranking
Proportional to degree counting for objects
E.g., number of publications of authors
Considers only immediate neighborhood in the network
Authority Ranking
Extension to HITS in weighted bi-type network
Rules:
Rule 1: Highly ranked authors publish many papers in highly ranked conferences
Rule 2: Highly ranked conferences attract many papers from many highly ranked authors
Rule 3: The rank of an author is enhanced if he or she co-authors with many authors or many highly ranked authors
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18. Rules in Authority Ranking
Rule 1: Highly ranked authors publish many papers in highly ranked conferences
Rule 2: Highly ranked conferences attract many papers from many highly ranked authors
Rule 3: The rank of an author is enhanced if he or she co-authors with many authors or many highly ranked authors
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19. Philosophy in Authority Ranking
Ranking score propagated by iterations using rules 2 and 1, or rules 2 and 3
The authority ranking of X and Y turned out to be primary eigenvectors of some symmetric matrix
Considers the impact from the overall network
Should be better than simple ranking
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20. Example: Authority Ranking in the 2-Area Conference-Author Network
Given the correct cluster, the ranking of authors are quite distinct from each other
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21. Step 2: Generate New Measure Space—A Naive Method
Mapping target object to a K-dimensional vector directly by considering a sub-network induced by it
r(Y|x) vs. r(Y|k)
Cosine similarity or KL-Divergence can be used
E.g., (cos(r(Y|x), r(Y|1)), …, cos(r(Y|x), r(Y|K)))
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22. Step 2: Generate New Measure Space—A Mixture Model Method
Consider each target object’s links are generated under a mixture distribution of ranking from each cluster
Consider ranking as a distribution: r(Y) → p(Y)
Each target object xi is mapped into a K-vector (πi,k)
Parameters are estimated using the EM algorithm
Maximize the log-likelihood given all the observations of links
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23. Example: 2-D Coefficients in the 2-Area Conference-Author Network
The conferences are well separated in the new measure space
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24. Step 3: Cluster Adjustment in New Measure Space
Cluster center in new measure space
Vector mean of objects in the cluster (K-dimensional)
Cluster adjustment
Distance measure: 1- Cosine similarity
Assign to the cluster with the nearest center
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25. A Running Case Illustration for 2-Area Conf-Author Network
Initially, ranking distributions are mixed together
Two clusters of objects mixed together, but preserve similarity somehow
Improved a little
Two clusters are almost well separated
Improved significantly
Well separated
Stable
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26. Ranking Function Analysis
Why “Authority Ranking” is better than “Simple Ranking”?
For authority ranking, each object’s score is determined by
The number of objects linking to it
The strength of these links (weight of link)
The quality of these objects (score)
For simple ranking, each object’s score is determined by
The quality of these objects are equal
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27. Re-examine the Rules
Rule 1: Highly ranked authors publish many papers in highly ranked conferences
An author publishing many papers in junk conferences will be ranked low
Rule 2: Highly ranked conferences attract many papers from many highly ranked authors
A conference accepting most papers from lowly ranked authors will be ranked low
Rule 3: The rank of an author is enhanced if he or she co-authors with many authors or many highly ranked authors
A highly ranked author in an area usually has many co-operations with others
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28. Why Better Ranking Function Derives Better Clustering?
Consider the measure space generation process
For naive method, highly ranked objects in a cluster play a more important role to decide a target object’s new measure
For mixture model, the same
Intuitively, if we can find the highly ranked objects in a cluster, equivalently, we get the right cluster
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29. Time Complexity Analysis
At each iteration, |E|: edges in network, m: number of target objects, K: number of clusters
Ranking for sparse network
~O(|E|)
Mixture model estimation
~O(K|E|+mK)
Cluster adjustment
~O(mK^2)
In all, linear to |E|
~O(K|E|)
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30. The RankClus Algorithm Experiments Conclusion
Outline
Background
Motivation
The RankClus Algorithm
Experiments
Conclusion
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31. Case Study: Dataset: DBLP
All the 2676 conferences and 20,000 authors with most publications, from the time period of year 1998 to year 2007.
Both conference-author relationships and co-author relationships are used.
K=15
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32. Accuracy Study Dataset: synthetic dataset
Simulate a bipartite network similar to conf-author network
P: control the node number of attribute objects
T: transition probability matrix, to control the overlap between clusters
K: fix to 3
Generating parameters for the five synthetic datasets
Data1: medium separated and medium density
P = [1000, 1500, 2000],
T = [0.8, 0.05, 0.15; 0.1, 0.8, 0.1; 0.1, 0.05, 0.85]
Data2: medium separated and low density
P = [800, 1300, 1200],
T = [0.8, 0.05, 0.15; 0.1, 0,8, 0.1; 0.1, 0.05, 0.85]
Data3: medium separated and high density
P = [2000, 3000, 4000],
Data4: highly separated and medium density
T = [0.9, 0.05, 0.05; 0.05, 0.9, 0.05; 0.1, 0.05, 0.85]
Data5: poorly separated and medium density
T = [0.7, 0.15, 0.15; 0.15, 0.7, 0.15; 0.15, 0.15, 0.7]
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33. Accuracy Study (Cont.) 5 (synthetic) dataset settings, 4 methods
For each setting, generate 10 datasets, run each method for each dataset 100 times
RankClus with authority ranking is the best overall
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34. Efficiency Study Varying size of attribute type of objects (×2)
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35. The RankClus Algorithm Experiments Conclusions
Outline
Background
Motivation
The RankClus Algorithm
Experiments
Conclusions
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36. Conclusions
A general framework is proposed in which ranking and clustering are successfully combined to analyze information networks
Formally study how ranking and clustering can mutually reinforce each other in information network analysis
A novel algorithm, RankClus, is proposed and its correctness and effectiveness are verified
A thorough experimental study on both synthetic and real datasets in comparison with the state-of-the-art algorithms, and the experimental results demonstrate the accuracy and efficiency of RankClus
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