Fast Random Walk with Restart and Its Applications - PowerPoint PPT Presentation

About This Presentation
Title:

Fast Random Walk with Restart and Its Applications

Description:

Fast Random Walk with Restart and Its Applications Hanghang Tong, Christos Faloutsos and Jia-Yu (Tim) Pan ICDM 2006 ... – PowerPoint PPT presentation

Number of Views:229
Avg rating:3.0/5.0
Slides: 47
Provided by: csCmuEdu70
Learn more at: http://www.cs.cmu.edu
Category:

less

Transcript and Presenter's Notes

Title: Fast Random Walk with Restart and Its Applications


1
Fast Random Walk with Restart and Its Applications
  • Hanghang Tong, Christos Faloutsos and Jia-Yu
    (Tim) Pan

ICDM 2006
Dec.
18-22, HongKong
2
Motivating Questions
  • Q How to measure the relevance?
  • A Random walk with restart
  • Q How to do it efficiently?
  • A This talk tries to answer!

3
Random walk with restart
4
Random walk with restart
Node 4
Node 1 Node 2 Node 3 Node 4 Node 5 Node 6 Node 7 Node 8 Node 9 Node 10 Node 11 Node 12 0.13 0.10 0.13 0.22 0.13 0.05 0.05 0.08 0.04 0.03 0.04 0.02
Nearby nodes, higher scores
Ranking vector
More red, more relevant
5
Automatic Image Caption
  • Q




Sea
Sun
Sky
Wave
?
A RWR! Pan KDD2004
6
Region
Image
Test Image
Keyword
7
Region
Image
Test Image
Grass, Forest, Cat, Tiger
Sea
Sun
Sky
Wave
Cat
Forest
Tiger
Grass
Keyword
8
Neighborhood Formulation


Q what is most related conference to ICDM
A RWR! Sun ICDM2005


Conference
Author
9
NF example
10
Center-Piece Subgraph(CePS)
Q
?
Original Graph Black query nodes
CePS
A RWR! Tong KDD 2006
11
CePS Example
12
Other Applications
  • Content-based Image Retrieval He
  • Personalized PageRank Jeh, Widom,
    Haveliwala
  • Anomaly Detection (for node link) Sun
  • Link Prediction Getoor, Jensen
  • Semi-supervised Learning Zhu, Zhou

13
Roadmap
  • Background
  • RWR Definitions
  • RWR Algorithms
  • Basic Idea
  • FastRWR
  • Pre-Compute Stage
  • On-Line Stage
  • Experimental Results
  • Conclusion

14
Computing RWR
Starting vector
Restart p
Adjacent matrix
Ranking vector
1
n x n
n x 1
n x 1
15
Beyond RWR
Maxwell Equation for Web!
Chakrabarti
P-PageRank Haveliwala
SM Learning Zhou, Zhu
RL in CBIR He
PageRank Haveliwala
RWR Pan, Sun
Fast RWR Finds the Root Solution !
16
  • Q Given query i, how to solve it?

?
?
17
OntheFly
No pre-computation/ light storage
Slow on-line response
O(mE)
18
PreCompute
10
9
12
2
8
1
11
R
3
4
6
5
7
Haveliwala
19
PreCompute
Fast on-line response
Heavy pre-computation/storage cost
O(n )
3
O(n )
2
20
Q How to Balance?
On-line
Off-line
21
Roadmap
  • Background
  • RWR Definitions
  • RWR Algorithms
  • Basic Idea
  • FastRWR
  • Pre-Compute Stage
  • On-Line Stage
  • Experimental Results
  • Conclusion

22
Basic Idea
Find Community
Combine
Fix the remaining
23
Pre-computational stage
-1
  • Q
  • A A few small, instead of ONE BIG, matrices
    inversions

Efficiently compute and store Q
24
On-Line Query Stage
-1
  • Q Efficiently recover one column of Q
  • A A few, instead of MANY, matrix-vector
    multiplication


25
Roadmap
  • Background
  • RWR Definitions
  • RWR Algorithms
  • Basic Idea
  • FastRWR
  • Pre-Compute Stage
  • On-Line Stage
  • Experimental Results
  • Conclusion

26
Pre-compute Stage
  • p1 B_Lin Decomposition
  • P1.1 partition
  • P1.2 low-rank approximation
  • p2 Q matrices
  • P2.1 computing (for each partition)
  • P2.2 computing (for concept space)

27
P1.1 partition
10
9
12
2
8
1
11
3
4
6
5
7
Within-partition links
cross-partition links
28
P1.1 block-diagonal
10
9
12
2
8
1
11
3
4
6
5
7
29
P1.2 LRA for
10
9
12
2
8
1
11
3
4
6
5
7

S ltlt W2
30


31
p2.1 Computing
32
Comparing and
  • Computing Time
  • 100,000 nodes 100 partitions
  • Computing 100,00x is Faster!
  • Storage Cost
  • 100x saving!


33
  • Q How to fix the green portions?




?

34
p2.2 Computing
-1
_
U
V

35
We have
Communities
Bridges
SM Lemma says
36
Roadmap
  • Background
  • RWR Definitions
  • RWR Algorithms
  • Basic Idea
  • FastRWR
  • Pre-Compute Stage
  • On-Line Stage
  • Experimental Results
  • Conclusion

37
On-Line Stage
  • Q

?

Query
Result
Pre-Computation
  • A (SM lemma)

38
On-Line Query Stage
39
(No Transcript)
40
Roadmap
  • Background
  • RWR Definitions
  • RWR Algorithms
  • Basic Idea
  • FastRWR
  • Pre-Compute Stage
  • On-Line Stage
  • Experimental Results
  • Conclusion

41
Experimental Setup
  • Dataset
  • DBLP/authorship
  • Author-Paper
  • 315k nodes
  • 1,800k edges
  • Approx. Quality Relative Accuracy
  • Application Center-Piece Subgraph

42
Query Time vs. Pre-Compute Time
Log Query Time
  • Quality 90
  • On-line
  • Up to 150x speedup
  • Pre-computation
  • Two orders saving

Log Pre-compute Time
43
Query Time vs. Pre-Storage
Log Query Time
  • Quality 90
  • On-line
  • Up to 150x speedup
  • Pre-storage
  • Three orders saving

Log Storage
44
Roadmap
  • Background
  • RWR Definitions
  • RWR Algorithms
  • Basic Idea
  • FastRWR
  • Pre-Compute Stage
  • On-Line Stage
  • Experimental Results
  • Conclusion

45
Conclusion
  • FastRWR
  • Reasonable quality preservation (90)
  • 150x speed-up query time
  • Orders of magnitude saving pre-compute storage
  • More in the paper
  • The variant of FastRWR and theoretic
    justification
  • Implementation details
  • normalization, low-rank approximation, sparse
  • More experiments
  • Other datasets, other applications

46
QA
  • Thank you!
  • htong_at_cs.cmu.edu
  • www.cs.cmu.edu/htong
Write a Comment
User Comments (0)
About PowerShow.com