Post on 19-Dec-2015
Discovering Overlapping Groups in Social Media
Xufei Wang, Lei Tang, Huiji Gao, and Huan Liuxufei.wang@asu.edu
Arizona State University
3
Social Media• Facebook
– 500 million active users– 50% of users log on to Facebook everyday
• Twitter– 100 million users– 300, 000 new users everyday– 55 million tweets everyday
• Flickr– 12 million members– 5 billion photos
5
Activities in Social Media
• Connect with others to form “Friends”
• Interact with others (comment, discussion, messaging)
• Bookmark websites/URLs (StumbleUpon, Delicious)
• Join groups if explicitly exist (Flickr, YouTube)
• Write blogs (Wordpress,Myspace)
• Update status (Twitter, Facebook)
• Share content (Flickr, YouTube, Delicious)
6
Community Structure
• Behavior Studying– Individual ? Too many users– Site level ? Lose too much details– Community level. Yes, provide information with
vary granularity
9
Related Work
• Disjoint Community Detection– Modularity Maximization– Based on Link Structure, (how to understand ?)
• Overlapping Community Detection– Soft Clustering (Clustering is dense)– CFinder (Efficiency and Scalability)
• Co-clustering– Disjoint– Understanding groups by words (tags)
10
Problem Statement
• Given a User-Tag subscription matrix M, and the number of clusters k, find k overlapping communities which consist of both users and tags.
u3
t2
u1
u2
t1
t4u4
u5
t3
11
Our Contributions
• Extracting overlapping communities that better reflect reality
• Clustering on a user-tag graph. Tags are informative in identifying user interests
• Understanding groups by looking at tags within each group
12
u3t2
u1
u2t1
t4u4
u5
t3
Edge-centric View
• Cluster edges instead of nodes into disjoint groups– One node can belong to multiple groups – One edge belongs to one group
u3
t2
u1
u2
t1
t4
u4
u5
t3
13
Edge-centric View
• In an Edge-centric viewedge u1 u2 u3 u4 u5 t1 t2 t3 t4
e1 1 0 0 0 0 1 0 0 0
e2 1 0 0 0 0 0 1 0 0
e3 0 1 0 0 0 1 0 0 0
e4 0 1 0 0 0 0 1 0 0
e5 0 0 1 0 0 0 1 0 0
e6 0 0 1 0 0 0 0 1 0
e7 0 0 0 1 0 0 0 1 0
e8 0 0 0 1 0 0 0 0 1e9 0 0 0 0 1 0 0 1 0
e10 0 0 0 0 1 0 0 0 1
14
Clustering Edges
• We can use any clustering algorithms (e.g., k-means) to group similar edges together
• Different similarity schemes
k
i Cxijc
Cij
cxSk 1
),(1
maxarg
15
Defining Edge Similarity
• Similarity between two edges e and e’ can be defined, but not limited, by
ui
ujtp
tq
),()1(),()',( qptjiue ttSuuSeeS
• α is set to 0.5, which suggests the equal importance of user and tag
• Define user-user and tag-tag similarity
16
Independent Learning
• Assume users are independent, tags are independent
nm
nmnm
ttuueeS qpjie
,0
,1),(
)),(),((2
1)',(
17
Normalized Learning
• Differentiate nodes with varying degrees by normalizing each node with its nodal degree
)0,...,0,1
,0,...,0,1,0,...0(),(
pi tupi ddtue
2222
),(),()',(
qpji
jiqp
ttuu
qpuujitt
edddd
ttdduuddeeS
18
Correlational Learning• Tags are semantically close– Tags cars, automobile, autos, car reviews are used to
describe a blog written by sid0722 on BlogCatalog
u Х t u Х k
• Compute user-user and tag-tag cosine similarity in the latent space
)~~
~~
~~
~~(2
1)',(
qp
qp
ji
jie
tt
tt
uu
uueeS
19
Spectral Clustering Perspective• Graph partition can be solved by the Generalized
Eigenvalue problem
V
UZ
M
MW
DM
MDL
WzLz
T
T
z
0
0
min
2
1
20
Spectral Clustering Perspective• Plug in L,W,Z, we obtain
VDUM
UDVM
V
U
D
D
V
U
DM
MD
TT
T
T
2
1
2
1
)1(
)1(
20
01
• U and V are the right and left singular vectors corresponding to the top k largest singular values of user-tag matrix M
21
Synthetic Data Sets
• Synthetic data sets– Number of clusters, users, and tags – Inner-cluster density and Inter-cluster density (1%
of total user-tag links)– Normalized mutual Information• Between 0 and 1• The higher, the better
22
Synthetic Performance• We fix the number of users, tags, and density,
but vary the number of clusters
23
Synthetic Performance• We fixed the number of users, tags, and
clusters, but vary the inner-cluster density
24
Social Media Data Sets
• BlogCatalog– Tags describing each blog– Category predefined by BlogCatalog for each blog
• Delicious– Tags describing each bookmark– Select the top 10 most frequently used tags for
each person
25
Inferring Personal Interests
• Category information reveals personal interests, view group affiliation as features to infer personal interests via cross-validation
26
Connectivity Study• The correlation between the number of co-occurrence
of two users in different affiliations and their connectivity in real networks.
• The larger the co-occurrence of two users, the more likely they are connected
30
Conclusions and Future Work• Overlapping communities on a User-Tag graph• Propose an edge-centric view and define edge
similarity– Independent Learning– Normalized Learning– Correlational Learning
• Evaluate results in synthetic and real data sets• Many applications: link prediction, Scalability
31
References• I. S. Dhillon, “Co-clustering documents and words using bipartite spectral graph partitioning,”
in KDD ’01, NY, USA• L. Tang and H. Liu, “Scalable learning of collective behavior based on sparse social
dimensions,” in CIKM’09, NY, USA.• L. Tang and H. Liu, “Community Detection and Mining in Social Media,” Morgan & Claypool
Publishers, Synthesis Lectures on Data Mining and Knowledge Discovery, 2010.• G. Palla, I. Dernyi, I. Farkas, and T. Vicsek, “Uncovering the overlapping community structure
of complex networks in nature and society,” Nature’05, vol.435, no.7043, p.814• K. Yu, S. Yu, and V. Tresp, “Soft clustering on graphs,” in NIPS, p. 05, 2005.• U. Luxburg, “A tutorial on spectral clustering,” Statistics and Computing, vol. 17, no. 4, pp.
395–416, 2007.• M. E. J. Newman and M. Girvan, “Finding and evaluating community structure in networks,”
Phys. Rev. E, vol. 69, no. 2, p. 026113, Feb 2004.• S. Fortunato, “Community detection in graphs,” Physics Reports, vol. 486, no. 3-5, pp. 75 –
174, 2010.
32
Contact the Authors
• Xufei Wang– xufei.wang@asu.edu– Arizona State University
• Lei Tang– ltang@yahoo-inc.com– Yahoo! Labs