linkscan*: overlapping community detection using the link-space transformation sungsu lim †,...
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LinkSCAN*: Overlapping Community Detection Using the Link-Space Trans-formation
Sungsu Lim †, Seungwoo Ryu ‡, Sejeong Kwon§,Kyomin Jung ¶, and Jae-Gil Lee †
† Dept. of Knowledge Service Engineering, KAIST ‡ Samsung Advanced Institute of Technology§ Graduate School of Cultural Technology, KAIST¶ Dept. of Electrical and Computer Engineering, SNU
ICDE 2014
April 1,2014 2
Contents
Motivation
Link-Space Transformation
Proposed Algorithm: LinkSCAN*
Experiment Evaluation
Conclusions
April 1,2014 3
Community Detection
Network communitiesSets of nodes where the nodes in the same set
are similar (more internal links) and the nodes in different sets are dissimilar (less external links)
Communities, clusters, modules, groups, etc.
Non-overlapping community detectionFinding a good partition of nodes
Clusters are NOT over-
lapped
April 1,2014 4
OverlappingCommunity Detection
A person (node) can belong to multiple communities, e.g., family, friends, col-leagues, etc.
Overlapping community detection allows that a node can be included in different groups
fam-ily,
friends,
col-leagues,
April 1,2014 5
Existing Methods
Node-based: A node overlaps if more than one be-longing coefficient values are larger than some threshold Label Propagation (COPRA) [Gregory 2010, Subelj and Ba-
jec 2011] Structure-based: A node overlaps if it partici-
pates in multiple base structures with different memberships Clique Percolation (CPM) [Palla et al. 2005, Derenyi et al.
2005] Link Partition [Evans and Lambiotte 2009 , Ahn et al.
2010]
f(i,c1)=0.35, f(i,c2)=0.05, f(i,c3)=0.4, …
f(i,c)=mean(f(j,c))j nbr(i)
ii i
Base struc-ture:
cliques of size
Base struc-ture: links
=4=0.3
April 1,2014 6
Limitations of Existing Methods
The existing methods do not perform well for1. networks with many highly overlapping
nodes,2. networks with various base structures, and3. networks with many weak-ties
ii
f(i,c1)=0.2, f(i,c2)=0.15, f(i,c3)=0.25, f(i,c4)=0.2, …
c1
c4
c2
c3
=0.3 𝑘≥3i
Weak-tie
i: overlappingCOPRA fails
i: non-overlappingCPM fails
i: non-overlap-pingLink partition fails
April 1,2014 7
Contents
Motivation
Link-Space Transformation
Proposed Algorithm: LinkSCAN*
Experiment Evaluation
Conclusions
April 1,2014 8
Our Solution
We propose a new framework called the link-space transformation that transforms a given graph into the link-space graph
We develop an algorithm that performs a non-overlapping clustering on the link-space graph, which enables us to discover overlapping clustering
OriginalGraph
Overlap-ping
Communi-ties
LinkCommuni-
ties
Link-SpaceGraph
Link-Space Transformation
Non-overlap-ping Clustering
Membership Translation
April 1,2014 9
Overall Procedure
We propose an overlapping clustering al-gorithm using the link-space transforma-tion
OriginalGraph
Overlap-ping
Communi-ties
LinkCommuni-
ties
Link-SpaceGraph
Link-Space Transformation
Non-overlap-ping Clustering
Membership Translation
April 1,2014 10
Link-Space Transformation
Topological structure Each link of an original graph maps to a node of the link-
space graph Two nodes of the links-space graph are adjacent if the cor-
responding two links of the original graph are incident Weights
Weights of links of the link-space graph are calculated from the similarity of corresponding links of the original graph
65 7
k
8
4
i
1 2 3
j
0i1 j1
i0 i2
ik
j2 j3
j4jk
k5 k8
k6 k7𝑤 (𝑣𝑖𝑘 ,𝑣 𝑗𝑘 )=𝜎 (𝑒𝑖𝑘 ,𝑒 𝑗𝑘 )
April 1,2014 11
Overall Procedure
Overlapping clustering algorithm using the link-space transformation
OriginalGraph
Overlap-ping
Communi-ties
LinkCommuni-
ties
Link-SpaceGraph
Link-Space Transformation
Membership Translation
Non-overlap-ping Clustering
April 1,2014 12
Clustering on Link-Space Graph
Applying a non-overlapping clustering al-gorithm to the link-space graph
We use structural clustering that can as-sign a node into hubs or outliers (neutral membership)
Original graph Non-overlapping clustering on the link-space graph
1
2
3
4
5
1/2
12
3413
23 35 45
003
1/2 1/2
1/211
Another weights are less than 1/3
April 1,2014 13
Overall Procedure
Overlapping clustering algorithm using the link-space transformation
OriginalGraph
Overlap-ping
Communi-ties
LinkCommuni-
ties
Link-SpaceGraph
Link-Space Transformation
Membership Translation
Non-overlap-ping Clustering
April 1,2014 14
Membership Translation
Memberships of nodes of the link-space graph map to the memberships of links of the original graph
Memberships of a node of the original graph are from the memberships of inci-dent links of the node
Membership translationNon-overlapping clustering on the link-space graph
1/2
12
3413
23 35 45
03
1/2 1/2
1/211
1
2
3
4
5
0
April 1,2014 15
Advantages of Link-Space Graph
Inheriting the advantages of the link-space graph, finding disjoint communities enables us to find overlapping communities where its original struc-ture is preserved since similarity properly reflect the structure of the original graph.
Easier to find overlapping communities
Preserving the orig-inal structure
Easier to find overlapping com-munities while preserving the original structure
Link-space graph
+¿
April 1,2014 16
Contents
Motivation
Link-Space Transformation
Proposed Algorithm: LinkSCAN*
Experiment Evaluation
Conclusions
April 1,2014 17
LinkSCAN*
We propose an efficient overlapping clus-tering algorithm using the link-space transformation
OriginalGraph
Overlap-ping
Communi-ties
LinkCommuni-
ties
Link-SpaceGraph
Link-Space Transformation
Structural Clus-tering
Membership Translation
For a massive graph, it may be
dense
April 1,2014 18
LinkSCAN*
We propose an efficient overlapping clus-tering algorithm using the link-space transformation
OriginalGraph
LinkCommuni-
ties
Link-SpaceGraph
Link-Space Transformation
Structural Clus-tering
Overlap-ping
Communi-ties
Membership Translation
Sam-pling
process
April 1,2014 19
LinkSCAN*
We propose an efficient overlapping clus-tering algorithm using the link-space transformation
OriginalGraph
LinkCommuni-
ties
Link-SpaceGraph
Link-Space Transformation
Structural Clus-tering
Overlap-ping
Communi-ties
Membership Translation
Sampled Graph
LinkSampling
April 1,2014 20
Link Sampling
Sampling Strategy: For each node , we sample incident links of , where and is the degree of
Thm 1 guarantees that sampling errors are not significant even when is small
For real nets, a sampled graph and the link-space graph are close (NMI>0.9) , while sam-pling rate is small (~0.1)
Thm 1 (Error bound)Applying Chernoff bound, the estimation error of se-
lecting core nodes decreases exponentially as the ’s increase.
April 1,2014 21
Contents
Motivation
Link-Space Transformation
Proposed Algorithm: LinkSCAN*
Experiment Evaluation
Conclusions
April 1,2014 22
Network Datasets
Synthetic network: LFR benchmark net-works[Lancichinetti and Fortunato 2009]
Real network: Social and information net-works [snap.stanford.edu/data/ and www.nd.edu/~net-works/resources.htm]# nodes # links Aver. de-
greeClust. Co-
eff.
DBLP 1,068,037 3,800,963 7.50 0.19
Amazon 334,863 925,872 5.53 0.21
Enron-email
36,692 183,831 10.02 0.08
Brightkite 58,228 214,078 7.35 0.11
Facebook 63,392 816,886 25.77 0.15
WWW 325,729 1,090,108 6.69 0.09
April 1,2014 23
Performance Evalua-tion
When ground-truth is known NMI for overlapping clustering [ancichietti et al. 2009] F-score (performance of identifying overlapping nodes)
When ground-truth is unknown Quality (Mov): Modularity for overlapping clustering [Lazar
et al. 2010] Coverage (CC): Clustering coverage [Ahn et al. 2010]
April 1,2014 24
Problem 1
For networks with many highly overlapping nodes, LinkSCAN* outperforms the existing methods.
April 1,2014 25
Problem 2
For networks with various base-structures, our method performs well compared to the existing methods
April 1,2014 26
Problem 3
For networks with many weak ties, the ex-isting methods fail for the following toy networks. But, LinkSCAN* detects all the clusters well
April 1,2014 27
Real Networks
For real network datasets, the normalized measure of (Quality + Coverage) indicates that LinkSCAN* is better than the existing methods.
April 1,2014 28
Link Sampling
The comparisons between the use of the link-space graph (LinkSCAN) and the use of sampled graphs (LinkSCAN*) show that LinkSCAN* improves efficiency with small errors
Enron-email network# nodes = 37K# links = 184K
April 1,2014 29
Scalability
The running time of LinkSCAN∗ for a set of LFR benchmark networks shows that LinkSCAN∗ has near-linear scalability
LFR benchmark networks# nodes = 1K to 1M# links = 10K to 10M
April 1,2014 30
Contents
Motivation
Link-Space Transformation
Proposed Algorithm: LinkSCAN*
Experiment Evaluation
Conclusions
April 1,2014 31
Conclusions
We propose a notion of the link-space transformation and develop a new over-lapping clustering algorithms LinkSCAN* that satisfy membership neutrality
LinkSCAN* outperforms existing algo-rithms for the networks with many highly overlapping nodes and those with various base-structures
April 1,2014 32
Acknowledgement
Coauthors
Funding AgenciesThis research was supported by National Re-
search Foundation of Korea
April 1,2014 33
Thank You!