1. Large Graph Mining: Power Tools and a Practitioner’s guide
Task 4: Center-piece Subgraphs
Faloutsos, Miller and Tsourakakis
CMU
KDD'09
Faloutsos, Miller, Tsourakakis

2. Faloutsos, Miller, Tsourakakis
Outline
Introduction – Motivation
Task 1: Node importance
Task 2: Community detection
Task 3: Recommendations
Task 4: Connection sub-graphs
Task 5: Mining graphs over time …
Conclusions
KDD'09
Faloutsos, Miller, Tsourakakis

3. Faloutsos, Miller, Tsourakakis
Detailed outline
Problem definition
Solution
Results
H. Tong & C. Faloutsos Center-piece subgraphs: problem definition and fast solutions. In KDD, , 2006.
KDD'09
Faloutsos, Miller, Tsourakakis

4. Center-Piece Subgraph(Ceps)
Given Q query nodes
Find Center-piece ( )
Input of Ceps
Q Query nodes
Budget b
k softAnd number
App.
Social Network
Law Inforcement
Gene Network …
KDD'09
Faloutsos, Miller, Tsourakakis

5. Faloutsos, Miller, Tsourakakis
Challenges in Ceps
Q1: How to measure importance?
(Q2: How to extract connection subgraph?
Q3: How to do it efficiently?)
KDD'09
Faloutsos, Miller, Tsourakakis

6. Faloutsos, Miller, Tsourakakis
Challenges in Ceps
Q1: How to measure importance?
A: “proximity” – but how to combine scores?
(Q2: How to extract connection subgraph?
Q3: How to do it efficiently?)
KDD'09
Faloutsos, Miller, Tsourakakis

7. Faloutsos, Miller, Tsourakakis
AND: Combine Scores
Q: How to combine scores?
KDD'09
Faloutsos, Miller, Tsourakakis

8. Faloutsos, Miller, Tsourakakis
AND: Combine Scores
Q: How to combine scores?
A: Multiply
…= prob. 3 random particles coincide on node j
KDD'09
Faloutsos, Miller, Tsourakakis

9. K_SoftAnd: Relaxation of AND
Disconnected
Communities
Noise
What if AND query  No Answer?
KDD'09
Faloutsos, Miller, Tsourakakis

10. K_SoftAnd: Combine Scores
Generalization – SoftAND:
We want nodes close to k of Q (k<Q) query nodes.
Q: How to do that?
KDD'09
Faloutsos, Miller, Tsourakakis

11. K_SoftAnd: Combine Scores
Generalization – softAND:
We want nodes close to k of Q (k<Q) query nodes.
Q: How to do that?
A: Prob(at least k-out-of-Q will meet each other at j)
KDD'09
Faloutsos, Miller, Tsourakakis

12. AND query vs. K_SoftAnd query
x 1e-4
And Query
2_SoftAnd Query
KDD'09
Faloutsos, Miller, Tsourakakis

13. 1_SoftAnd query = OR query
KDD'09
Faloutsos, Miller, Tsourakakis

14. Faloutsos, Miller, Tsourakakis
Detailed outline
Problem definition
Solution
Results
KDD'09
Faloutsos, Miller, Tsourakakis

15. Faloutsos, Miller, Tsourakakis
Case Study: AND query
KDD'09
Faloutsos, Miller, Tsourakakis

16. Faloutsos, Miller, Tsourakakis
Case Study: AND query
KDD'09
Faloutsos, Miller, Tsourakakis

17. Faloutsos, Miller, Tsourakakis
database
Statistic
KDD'09
Faloutsos, Miller, Tsourakakis
2_SoftAnd query

18. Faloutsos, Miller, Tsourakakis
Conclusions
Proximity (e.g., w/ RWR) helps answer ‘AND’ and ‘k_softAnd’ queries
KDD'09
Faloutsos, Miller, Tsourakakis