258,532 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
Optimizing an Organized Modularity Measure for Topographic Graph Clustering: a Deterministic Annealing Approach
This paper proposes an organized generalization of Newman and Girvan's
modularity measure for graph clustering. Optimized via a deterministic
annealing scheme, this measure produces topologically ordered graph clusterings
that lead to faithful and readable graph representations based on clustering
induced graphs. Topographic graph clustering provides an alternative to more
classical solutions in which a standard graph clustering method is applied to
build a simpler graph that is then represented with a graph layout algorithm. A
comparative study on four real world graphs ranging from 34 to 1 133 vertices
shows the interest of the proposed approach with respect to classical solutions
and to self-organizing maps for graphs
A PAC-Bayesian Analysis of Graph Clustering and Pairwise Clustering
We formulate weighted graph clustering as a prediction problem: given a
subset of edge weights we analyze the ability of graph clustering to predict
the remaining edge weights. This formulation enables practical and theoretical
comparison of different approaches to graph clustering as well as comparison of
graph clustering with other possible ways to model the graph. We adapt the
PAC-Bayesian analysis of co-clustering (Seldin and Tishby, 2008; Seldin, 2009)
to derive a PAC-Bayesian generalization bound for graph clustering. The bound
shows that graph clustering should optimize a trade-off between empirical data
fit and the mutual information that clusters preserve on the graph nodes. A
similar trade-off derived from information-theoretic considerations was already
shown to produce state-of-the-art results in practice (Slonim et al., 2005;
Yom-Tov and Slonim, 2009). This paper supports the empirical evidence by
providing a better theoretical foundation, suggesting formal generalization
guarantees, and offering a more accurate way to deal with finite sample issues.
We derive a bound minimization algorithm and show that it provides good results
in real-life problems and that the derived PAC-Bayesian bound is reasonably
tight
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