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

This comprehensive guide explores center-piece subgraphs in graph mining, focusing on their importance in practical applications such as social networks, law enforcement, and gene networks. Covering various tasks including node importance measurement, community detection, and dynamic graph analysis, it presents efficient solutions to identify and extract center-piece subgraphs. Key challenges are addressed, emphasizing concepts like score combination and proximity metrics. This resource serves as a fundamental tool for practitioners interested in advanced graph mining techniques.

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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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