Discovering Overlapping Groups in Social Media

Xufei Wang, Lei Tang, Huiji Gao, and Huan Liuxufei.wang@asu.edu

Arizona State University

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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

Colleagues

Family

Neighbors

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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.

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u1

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u5

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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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u1

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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

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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 1

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Clustering Edges

• We can use any clustering algorithms (e.g., k-means) to group similar edges together

• Different similarity schemes

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Defining Edge Similarity

• Similarity between two edges e and e’ can be defined, but not limited, by

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),()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

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Independent Learning

• Assume users are independent, tags are independent

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Normalized Learning

• Differentiate nodes with varying degrees by normalizing each node with its nodal degree

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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

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• Compute user-user and tag-tag cosine similarity in the latent space

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Spectral Clustering Perspective• Graph partition can be solved by the Generalized

Eigenvalue problem

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Spectral Clustering Perspective• Plug in L,W,Z, we obtain

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01

• 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– xufei.wang@asu.edu– Arizona State University

• Lei Tang– ltang@yahoo-inc.com– Yahoo! Labs