3,386 research outputs found
Axioms for graph clustering quality functions
We investigate properties that intuitively ought to be satisfied by graph
clustering quality functions, that is, functions that assign a score to a
clustering of a graph. Graph clustering, also known as network community
detection, is often performed by optimizing such a function. Two axioms
tailored for graph clustering quality functions are introduced, and the four
axioms introduced in previous work on distance based clustering are
reformulated and generalized for the graph setting. We show that modularity, a
standard quality function for graph clustering, does not satisfy all of these
six properties. This motivates the derivation of a new family of quality
functions, adaptive scale modularity, which does satisfy the proposed axioms.
Adaptive scale modularity has two parameters, which give greater flexibility in
the kinds of clusterings that can be found. Standard graph clustering quality
functions, such as normalized cut and unnormalized cut, are obtained as special
cases of adaptive scale modularity.
In general, the results of our investigation indicate that the considered
axiomatic framework covers existing `good' quality functions for graph
clustering, and can be used to derive an interesting new family of quality
functions.Comment: 23 pages. Full text and sources available on:
http://www.cs.ru.nl/~T.vanLaarhoven/graph-clustering-axioms-2014
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Generative models for local network community detection
Local network community detection aims to find a single community in a large
network, while inspecting only a small part of that network around a given seed
node. This is much cheaper than finding all communities in a network. Most
methods for local community detection are formulated as ad-hoc optimization
problems. In this work, we instead start from a generative model for networks
with community structure. By assuming that the network is uniform, we can
approximate the structure of unobserved parts of the network to obtain a method
for local community detection. We apply this local approximation technique to
two variants of the stochastic block model. To our knowledge, this results in
the first local community detection methods based on probabilistic models.
Interestingly, in the limit, one of the proposed approximations corresponds to
conductance, a popular metric in this field. Experiments on real and synthetic
datasets show comparable or improved results compared to state-of-the-art local
community detection algorithms
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