COMMUNITIES IN MULTI-MODE NETWORKS 1. Heterogeneous Network Heterogeneous kinds of objects in social media – YouTube Users, tags, videos, ads – Del.icio.us.

COMMUNITIES IN MULTI-MODE NETWORKS

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Heterogeneous Network• Heterogeneous kinds of objects in social media– YouTube

• Users, tags, videos, ads – Del.icio.us

• Users, tags, bookmarks• Heterogeneous types of interactions between actors– Facebook

• Send email, leave a message• write a comment, tag photos

– Same users interacting at different sites• Facebook, YouTube, Twitter

Reference: International Conference on Social Computing 2009 Tutorial on Community Detection and Behavior Prediction for Social Computing

Multi-Mode Network

Fig: Reference: L. Tang, H. Liu, J. Zhang, and Z. Nazeri. "Community Evolution in Dynamic Multi-Mode Networks", KDD'08: 677 - 685

YouTube

USER

VIDEO TAG

Figure-1: 3-mode Network in YouTube

NOTE: (1) Networks consists of multiple modes of nodes (2)presents correlations between different kinds of objects

Community Detection By Using: Co-clustering on 2-mode Networks

• A 2-mode network is a simple form of multi-mode network– E.g., user-tag network in social media

• The graph of a 2-mode network is a bipartite

Note: There is no relation between nodes of same type

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Reference: (1)Lei Tang and Huan Liu. Community Detection and Mining in Social Media, Morgan & Claypool Publishers, 2010, and(2) Huan Liu, Lei Tang and Nitin Agarwal. Tutorial on Community Detection and Behavior Study for Social Computing. Presented in The 1st IEEE International Conference on Social Computing (SocialCom'09), 2009.

Adjacency Matrix of 2-Mode Network

Note:Row of Matrix Represents User-Id’sColumn Represents, Tag-Id’s Why separate Row and Column for User and Tags ?

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Reference: (1)Lei Tang and Huan Liu. Community Detection and Mining in Social Media, Morgan & Claypool Publishers, 2010, and(2) Huan Liu, Lei Tang and Nitin Agarwal. Tutorial on Community Detection and Behavior Study for Social Computing. Presented in The 1st IEEE International Conference on Social Computing (SocialCom'09), 2009.

Co-Clustering

• Biclustering, co-clustering, or two-mode clustering is a data mining technique which allows simultaneous clustering of the rows and columns of a matrix [1].

• Given a set of m rows in n columns (i.e., an m X n matrix), the biclustering algorithm generates biclusters - a subset of rows which exhibit similar behavior across a subset of columns, or vice versa.

• Different biclustering algorithms have different definitions of bicluster.[2]– Bicluster with constant values,– Bicluster with constant values on rows or columns,– Bicluster with coherent values.

• The complexity of the biclustering problem depends on the exact problem formulation, and particularly on the merit function used to evaluate the quality of a given bicluster.

Reference:1. Van Mechelen I, Bock HH, De Boeck P (2004). "Two-mode clustering methods:a structured overview". Statistical Methods in Medical Research 13

(5): 363–94.2. Madeira SC, Oliveira AL (2004). "Biclustering Algorithms for Biological Data Analysis: A Survey". IEEE Transactions on Computational Biology and

Bioinformatics 1 (1): 24–45.

Co-Clustering for Community Detection

• Co-clustering: finding communities in two modes simultaneously– Output both communities of users and communities of tags for a user-tag

network

• A straightforward Approach: Minimize the cut in the graph

• The minimum cut is 1; a trivial solution is not desirable• Need to consider the size of communities

7Reference: (1)Lei Tang and Huan Liu. Community Detection and Mining in Social Media, Morgan & Claypool Publishers, 2010, and(2) Huan Liu, Lei Tang and Nitin Agarwal. Tutorial on Community Detection and Behavior Study for Social Computing. Presented in The 1st IEEE International Conference on Social Computing (SocialCom'09), 2009.

Spectral Co-Clustering• Minimize the normalized cut in a bipartite graph

– Similar as spectral clustering for undirected graph

• Compute normalized adjacency matrix

• Compute the top singular vectors of the normalized adjacency matrix

• Apply k-means to the joint community indicator Z to obtain communities in user mode and tag mode, respectively.

8Reference: (1)Lei Tang and Huan Liu. Community Detection and Mining in Social Media, Morgan & Claypool Publishers, 2010, and(2) Huan Liu, Lei Tang and Nitin Agarwal. Tutorial on Community Detection and Behavior Study for Social Computing. Presented in The 1st IEEE International Conference on Social Computing (SocialCom'09), 2009.

Spectral Co-Clustering Example

Two communities: { u1,u2, u3, u4, t1, t2, t3 }

{ u5, u6, u7, u8, u9, t4, t5, t6, t7}

Two communities: { u1,u2, u3, u4, t1, t2, t3 }

{ u5, u6, u7, u8, u9, t4, t5, t6, t7}

k-means

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Reference: (1)Lei Tang and Huan Liu. Community Detection and Mining in Social Media, Morgan & Claypool Publishers, 2010, and(2) Huan Liu, Lei Tang and Nitin Agarwal. Tutorial on Community Detection and Behavior Study for Social Computing. Presented in The 1st IEEE International Conference on Social Computing (SocialCom'09), 2009.

Generalization to A Star Structure• Spectral co-clustering can be interpreted as a block model approximation

to normalized adjacency matrix

generalize to a star structure

S(1) corresponds to the top left singular vectors of the following matrix

S(1) corresponds to the top left singular vectors of the following matrix

10Reference: (1)Lei Tang and Huan Liu. Community Detection and Mining in Social Media, Morgan & Claypool Publishers, 2010.

Generalization to Multi-Mode Networks

• For a multi-mode network, compute the soft community indicator of each mode one by one

• It becomes a star structure when looking at one mode vs. other modes

• Community Detection in Multi-Mode Networks– Normalize interaction matrix– Iteratively update community indicator as the top left singular vectors– Apply k-means to the community indicators to find partitions in each

mode

11Reference: (1)Lei Tang and Huan Liu. Community Detection and Mining in Social Media, Morgan & Claypool Publishers, 2010.

Reference

1. Lei Tang and Huan Liu. Community Detection and Mining in Social Media, Morgan & Claypool Publishers, 2010.

2. Huan Liu, Lei Tang and Nitin Agarwal. Tutorial on Community Detection and Behavior Study for Social Computing. Presented in The 1st IEEE International Conference on Social Computing (SocialCom'09), 2009.

3. Van Mechelen I, Bock HH, De Boeck P (2004). "Two-mode clustering methods:a structured overview". Statistical Methods in Medical Research 13 (5): 363–94.

4. Madeira SC, Oliveira AL (2004). "Biclustering Algorithms for Biological Data Analysis: A Survey". IEEE Transactions on Computational Biology and Bioinformatics 1 (1): 24–45.