1,812 research outputs found
Partitioning networks into cliques: a randomized heuristic approach
In the context of community detection in social networks, the term community can be grounded in the strict way that simply everybody should know each other within the community. We consider the corresponding community detection problem. We search for a partitioning of a network into the minimum number of non-overlapping cliques, such that the cliques cover all vertices. This problem is called the clique covering problem (CCP) and is one of the classical NP-hard problems. For CCP, we propose a randomized heuristic approach. To construct a high quality solution to CCP, we present an iterated greedy (IG) algorithm. IG can also be combined with a heuristic used to determine how far the algorithm is from the optimum in the worst case. Randomized local search (RLS) for maximum independent set was proposed to find such a bound. The experimental results of IG and the bounds obtained by RLS indicate that IG is a very suitable technique for solving CCP in real-world graphs. In addition, we summarize our basic rigorous results, which were developed for analysis of IG and understanding of its behavior on several relevant graph classes
RASCAL: calculation of graph similarity using maximum common edge subgraphs
A new graph similarity calculation procedure is introduced for comparing labeled graphs. Given a minimum similarity threshold, the procedure consists of an initial screening process to determine whether it is possible for the measure of similarity between the two graphs to exceed the minimum threshold, followed by a rigorous maximum common edge subgraph (MCES) detection algorithm to compute the exact degree and composition of similarity. The proposed MCES algorithm is based on a maximum clique formulation of the problem and is a significant improvement over other published algorithms. It presents new approaches to both lower and upper bounding as well as vertex selection
Community Detection via Maximization of Modularity and Its Variants
In this paper, we first discuss the definition of modularity (Q) used as a
metric for community quality and then we review the modularity maximization
approaches which were used for community detection in the last decade. Then, we
discuss two opposite yet coexisting problems of modularity optimization: in
some cases, it tends to favor small communities over large ones while in
others, large communities over small ones (so called the resolution limit
problem). Next, we overview several community quality metrics proposed to solve
the resolution limit problem and discuss Modularity Density (Qds) which
simultaneously avoids the two problems of modularity. Finally, we introduce two
novel fine-tuned community detection algorithms that iteratively attempt to
improve the community quality measurements by splitting and merging the given
network community structure. The first of them, referred to as Fine-tuned Q, is
based on modularity (Q) while the second one is based on Modularity Density
(Qds) and denoted as Fine-tuned Qds. Then, we compare the greedy algorithm of
modularity maximization (denoted as Greedy Q), Fine-tuned Q, and Fine-tuned Qds
on four real networks, and also on the classical clique network and the LFR
benchmark networks, each of which is instantiated by a wide range of
parameters. The results indicate that Fine-tuned Qds is the most effective
among the three algorithms discussed. Moreover, we show that Fine-tuned Qds can
be applied to the communities detected by other algorithms to significantly
improve their results
Finding Non-overlapping Clusters for Generalized Inference Over Graphical Models
Graphical models use graphs to compactly capture stochastic dependencies
amongst a collection of random variables. Inference over graphical models
corresponds to finding marginal probability distributions given joint
probability distributions. In general, this is computationally intractable,
which has led to a quest for finding efficient approximate inference
algorithms. We propose a framework for generalized inference over graphical
models that can be used as a wrapper for improving the estimates of approximate
inference algorithms. Instead of applying an inference algorithm to the
original graph, we apply the inference algorithm to a block-graph, defined as a
graph in which the nodes are non-overlapping clusters of nodes from the
original graph. This results in marginal estimates of a cluster of nodes, which
we further marginalize to get the marginal estimates of each node. Our proposed
block-graph construction algorithm is simple, efficient, and motivated by the
observation that approximate inference is more accurate on graphs with longer
cycles. We present extensive numerical simulations that illustrate our
block-graph framework with a variety of inference algorithms (e.g., those in
the libDAI software package). These simulations show the improvements provided
by our framework.Comment: Extended the previous version to include extensive numerical
simulations. See http://www.ima.umn.edu/~dvats/GeneralizedInference.html for
code and dat
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