Large graph mining power tools and a practitioner s guide
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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) query nodes.

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) query nodes.

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


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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