SCAN: A Structural Clustering Algorithm for Networks

1
SCAN A Structural Clustering Algorithm for
Networks

• Xiaowei Xu (???)

Joint Work with Nurcan Yuruk (UALR) and Thomas A.
J. Schweiger (Acxiom)
2
Network Clustering Problem

• Networks made up of the mutual relationships of
  data elements usually have an underlying
  structure. Because relationships are complex, it
  is difficult to discover these structures. How
  can the structure be made clear?
• Stated another way, given simply information of
  who associates with whom, could one identify
  clusters of individuals with common interests or
  special relationships (families, cliques,
  terrorist cells).

3
An Example of Networks

• How many clusters?
• What size should they be?
• What is the best partitioning?
• Should some points be segregated?

4
A Social Network Model

• Individuals in a tight social group, or clique,
  know many of the same people, regardless of the
  size of the group.
• Individuals who are hubs know many people in
  different groups but belong to no single group.
  Politicians, for example bridge multiple groups.
• Individuals who are outliers reside at the
  margins of society. Hermits, for example, know
  few people and belong to no group.

5
The Neighborhood of a Vertex
Define ?(?) as the immediate neighborhood of a
vertex (i.e. the set of people that an individual
knows ).
6
Structure Similarity

• The desired features tend to be captured by a
  measure we call Structural Similarity
• Structural similarity is large for members of a
  clique and small for hubs and outliers.

7
Structural Connectivity 1

• ?-Neighborhood
• Core
• Direct structure reachable
• Structure reachable transitive closure of direct
  structure reachability
• Structure connected

1 M. Ester, H. P. Kriegel, J. Sander, X. Xu
(KDD'97)
8
Structure-Connected Clusters

• Structure-connected cluster C
• Connectivity
• Maximality
• Hubs
• Not belong to any cluster
• Bridge to many clusters
• Outliers
• Not belong to any cluster
• Connect to less clusters

hub
outlier
9
Algorithm
? 2 ? 0.7
10
Algorithm
2
3
? 2 ? 0.7
5
1
4
7
6
0
11
8
12
10
9
0.63
13
11
Algorithm
2
3
? 2 ? 0.7
5
1
4
7
6
0
0.67
11
8
0.82
12
10
0.75
9
13
12
Algorithm
? 2 ? 0.7
13
Algorithm
2
3
? 2 ? 0.7
5
1
4
7
6
0
11
8
12
10
9
0.67
13
14
Algorithm
2
3
? 2 ? 0.7
5
1
4
7
6
0
11
0.73
8
0.73
12
0.73
10
9
13
15
Algorithm
2
3
? 2 ? 0.7
5
1
4
7
6
0
11
8
12
10
9
13
16
Algorithm
2
3
? 2 ? 0.7
5
1
4
7
0.51
6
0
11
8
12
10
9
13
17
Algorithm
2
3
? 2 ? 0.7
5
1
4
7
6
0
0.68
11
8
12
10
9
13
18
Algorithm
2
3
? 2 ? 0.7
5
1
4
7
6
0
11
8
12
0.51
10
9
13
19
Algorithm
2
3
? 2 ? 0.7
5
1
4
7
6
0
11
8
12
10
9
13
20
Algorithm
2
3
? 2 ? 0.7
5
1
0.51
4
7
0.68
6
0
0.51
11
8
12
10
9
13
21
Algorithm
2
3
? 2 ? 0.7
5
1
4
7
6
0
11
8
12
10
9
13
22
Running Time

• Running time O(E)
• For sparse networks O(V)

2 A. Clauset, M. E. J. Newman, C. Moore,
Phys. Rev. E 70, 066111 (2004).
23
Are you ready for some football?

• Given only the 2006 schedule of what schools each
  NCAA Division 1A team met on a football field,
  what underlying structures could one discover?

24
789 Contests

• 119 Division 1A school who play
• schools in their conference
• schools in other 1A conferences
• independent 1A schools (e.g. Army)
• schools in sub-1A conferences (e.g. Maine)

25
Consider Arkansas Schedule

• USC Pacific 10
• Utah State Western Athletic
• Vanderbilt SEC
• Alabama SEC
• Auburn SEC
• Southeast Missouri State Non 1A
• Mississippi SEC
• Louisiana Monroe Sun Belt
• SouthCarolina SEC
• Tennessee SEC
• Mississippi State SEC
• LSU SEC
• Florida SEC
• Wisconsin Big 10

26
The Network
27
The 1A Conference
28
Result of Our Algorithm
29
Result of FastModularity Alg. 2
2 A. Clauset, M. E. J. Newman, C. Moore,
Phys. Rev. E 70, 066111 (2004).
30
Conclusion

• We propose a novel network clustering algorithm
• It is fast O(E), for scale free networks
  O(V)
• It can find clusters, as well as hubs and
  outliers
• For more information
• See you in poster session this evening at poster
  board 4
• Email xwxu_at_ualr.edu
• URL http//ifsc.ualr.edu/xwxu
• Thank you!