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Large Graph Mining: Power Tools and a Practitioner’s guide

Large Graph Mining: Power Tools and a Practitioner’s guide. Task 4: Center-piece Subgraphs Faloutsos, Miller and Tsourakakis CMU. Outline. Introduction – Motivation Task 1: Node importance Task 2: Community detection Task 3: Recommendations Task 4: Connection sub-graphs

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Large Graph Mining: Power Tools and a Practitioner’s guide

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

  2. 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 Faloutsos, Miller, Tsourakakis

  3. Detailed outline • Problem definition • Solution • Results H. Tong & C. Faloutsos Center-piece subgraphs: problem definition and fast solutions. In KDD, 404-413, 2006. 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 • … Faloutsos, Miller, Tsourakakis

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

  6. 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?) Faloutsos, Miller, Tsourakakis

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

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

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

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

  13. 1_SoftAnd query = OR query Faloutsos, Miller, Tsourakakis

  14. Detailed outline • Problem definition • Solution • Results Faloutsos, Miller, Tsourakakis

  15. Case Study: AND query Faloutsos, Miller, Tsourakakis

  16. Case Study: AND query Faloutsos, Miller, Tsourakakis

  17. database Statistic Faloutsos, Miller, Tsourakakis 2_SoftAnd query

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

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