Modularity Score

1
Approximating the Community Structure of the Long
Tail
Akshay Java, Anupam Joshi, Tim Finin
Problem Statement
Community Structure of the Long Tail
Approximate the membership of the blogs in the
long tail using only a small portion of the
entire graph
Motivation It is expensive to compute the
community structure for large networks. Blog
graphs are large, but extremely sparse and
exhibit the long tail/ core-periphery structure.
Intuition Communities emerge around the core (A).
The membership of the blogs in the long tail (B)
can be approximated by the structure of the core
and how the long tail links to the core.
CORE
PERIPHERY
Approximation Methods
Detecting Communities
Singular Value Decomposition (reduced
rank) Sampling-based Technique
A community is a set of nodes that has more
connections within the set than outside
it. Normalized Cut The graph can be
partitioned using the eigenspectrum of the
Laplacian. (Shi and Malik) The second smallest
eigenvector of the graph Laplacian is the Fiedler
vector.
By Nyström Approximation (Fowlkes et al.)
Thus eigenvectors of L can be easily approximated
by sampling.
Heuristic Method
Use the head of the distribution to find the
initial communities. Approximate membership of
the tail by using number of links to each
community in the head.
The graph can be recursively partitioned using
the sign of the values in its Fielder vector.
Conclusions and Ongoing Research
Evaluation
Conclusion Community structure of the entire
network can be well approximated by sampling and
heuristic methods. Advantage Achieve fast,
accurate approximation using much smaller sample
of the entire graph. Ongoing Research Applying
the approximation on temporal graphs Clustering
graph, tag information simultaneously
Modularity Score A measure of the quality of
community detection
Q (fraction of intra-community edges)-(expected
fraction, disregarding communities)