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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

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

Task 4: Center-piece Subgraphs

Faloutsos, Miller and Tsourakakis

CMU

Faloutsos, Miller, Tsourakakis

outline
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

detailed outline
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

ce nter p iece s ubgraph ceps
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

challenges in ceps
Challenges in Ceps
  • Q1: How to measure importance?
  • (Q2: How to extract connection subgraph?
  • Q3: How to do it efficiently?)

Faloutsos, Miller, Tsourakakis

challenges in ceps1
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

and combine scores
AND: Combine Scores
  • Q: How to combine scores?

Faloutsos, Miller, Tsourakakis

and combine scores1
AND: Combine Scores
  • Q: How to combine scores?
  • A: Multiply
  • …= prob. 3 random particles coincide on node j

Faloutsos, Miller, Tsourakakis

k softand relaxation of and
K_SoftAnd: Relaxation of AND

What if AND query No Answer?

Disconnected

Communities

Noise

Faloutsos, Miller, Tsourakakis

k softand combine scores
K_SoftAnd: Combine Scores

Generalization – SoftAND:

We want nodes close to k of Q (k

Q: How to do that?

Faloutsos, Miller, Tsourakakis

k softand combine scores1
K_SoftAnd: Combine Scores

Generalization – softAND:

We want nodes close to k of Q (k

Q: How to do that?

A: Prob(at least k-out-of-Q will meet each other at j)

Faloutsos, Miller, Tsourakakis

and query vs k softand query
AND query vs. K_SoftAnd query

And Query

x 1e-4

2_SoftAnd Query

Faloutsos, Miller, Tsourakakis

1 softand query or query
1_SoftAnd query = OR query

Faloutsos, Miller, Tsourakakis

detailed outline1
Detailed outline
  • Problem definition
  • Solution
  • Results

Faloutsos, Miller, Tsourakakis

case study and query
Case Study: AND query

Faloutsos, Miller, Tsourakakis

case study and query1
Case Study: AND query

Faloutsos, Miller, Tsourakakis

slide17
database

Statistic

Faloutsos, Miller, Tsourakakis

2_SoftAnd query

conclusions
Conclusions

Proximity (e.g., w/ RWR) helps answer ‘AND’ and ‘k_softAnd’ queries

Faloutsos, Miller, Tsourakakis

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