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Discovering Overlapping Groups in Social Media. Xufei Wang , Lei Tang, Huiji Gao, and Huan Liu [email protected] Arizona State University. Social Media. Facebook 500 million active users 50% of users log on to Facebook everyday Twitter 100 million users 300, 000 new users everyday - PowerPoint PPT Presentation
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Discovering Overlapping Groups in Social Media
Xufei Wang, Lei Tang, Huiji Gao, and Huan Liu
[email protected] State University
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
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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)
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Community Structure
• Behavior Studying– Individual ? Too many users– Site level ? Lose too much details– Community level. Yes, provide information
with vary granularity
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Overlapping Communities
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Colleagues
Family
Neighbors
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)
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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
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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
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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
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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 0 113
Clustering Edges• We can use any clustering algorithms
(e.g., k-means) to group similar edges together
• Different similarity schemes
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k
i Cxijc
Cij
cxSk 1
),(1maxarg
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 15
Independent Learning
• Assume users are independent, tags are independent
nmnm
nm
ttuueeS qpjie
,0,1
),(
)),(),((21)',(
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Normalized Learning
• Differentiate nodes with varying degrees by normalizing each node with its nodal degree
)0,...,0,1,0,...,0,1,0,...0(),(pi tu
pi ddtue
2222
),(),()',(
qpji
jiqp
ttuu
qpuujitte
dddd
ttdduuddeeS
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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
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)~~~~
~~~~
(21)',(
qp
qp
ji
jie tt
ttuuuu
eeS
Spectral Clustering Perspective• Graph partition can be solved by the Generalized
Eigenvalue problem
VU
Z
MM
W
DMMD
L
WzLz
T
T
z
00
min
2
1
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Spectral Clustering Perspective• Plug in L,W,Z, we obtain
VDUM
UDVM
VU
DD
VU
DMMD
TT
T
T
2
1
2
1
)1(
)1(
2001
• U and V are the right and left singular vectors corresponding to the top k largest singular values of user-tag matrix M
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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
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Synthetic Performance• We fix the number of users, tags, and
density, but vary the number of clusters
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Synthetic Performance• We fixed the number of users, tags, and
clusters, but vary the inner-cluster density
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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
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Inferring Personal Interests
• Category information reveals personal interests, view group affiliation as features to infer personal interests via cross-validation
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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
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Understanding Groups via Tag Cloud
• Tag cloud for Category Health
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Understanding Groups via Tag Cloud
• Tag cloud for Cluster Health
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Understanding Groups via Tag Cloud
• Tag cloud for Cluster Nutrition
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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
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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.
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Contact the Authors
• Xufei Wang– [email protected]– Arizona State University
• Lei Tang– [email protected]– Yahoo! Labs
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