372 research outputs found
A Degenerate Agglomerative Hierarchical Clustering Algorithm for Community Detection
Community detection consists of grouping related vertices that usually show high intra-cluster connectivity and low inter-cluster connectivity. This is an important feature that many networks exhibit and detecting such communities can be challenging, especially when they are densely connected. The method we propose is a degenerate agglomerative hierarchical clustering algorithm (DAHCA) that aims at finding a community structure in networks. We tested this method using common classes of graph benchmarks and compared it to some state-of-the-art community detection algorithms
Statistical Mechanics of Community Detection
Starting from a general \textit{ansatz}, we show how community detection can
be interpreted as finding the ground state of an infinite range spin glass. Our
approach applies to weighted and directed networks alike. It contains the
\textit{at hoc} introduced quality function from \cite{ReichardtPRL} and the
modularity as defined by Newman and Girvan \cite{Girvan03} as special
cases. The community structure of the network is interpreted as the spin
configuration that minimizes the energy of the spin glass with the spin states
being the community indices. We elucidate the properties of the ground state
configuration to give a concise definition of communities as cohesive subgroups
in networks that is adaptive to the specific class of network under study.
Further we show, how hierarchies and overlap in the community structure can be
detected. Computationally effective local update rules for optimization
procedures to find the ground state are given. We show how the \textit{ansatz}
may be used to discover the community around a given node without detecting all
communities in the full network and we give benchmarks for the performance of
this extension. Finally, we give expectation values for the modularity of
random graphs, which can be used in the assessment of statistical significance
of community structure
Detecting hierarchical and overlapping network communities using locally optimal modularity changes
Agglomerative clustering is a well established strategy for identifying
communities in networks. Communities are successively merged into larger
communities, coarsening a network of actors into a more manageable network of
communities. The order in which merges should occur is not in general clear,
necessitating heuristics for selecting pairs of communities to merge. We
describe a hierarchical clustering algorithm based on a local optimality
property. For each edge in the network, we associate the modularity change for
merging the communities it links. For each community vertex, we call the
preferred edge that edge for which the modularity change is maximal. When an
edge is preferred by both vertices that it links, it appears to be the optimal
choice from the local viewpoint. We use the locally optimal edges to define the
algorithm: simultaneously merge all pairs of communities that are connected by
locally optimal edges that would increase the modularity, redetermining the
locally optimal edges after each step and continuing so long as the modularity
can be further increased. We apply the algorithm to model and empirical
networks, demonstrating that it can efficiently produce high-quality community
solutions. We relate the performance and implementation details to the
structure of the resulting community hierarchies. We additionally consider a
complementary local clustering algorithm, describing how to identify
overlapping communities based on the local optimality condition.Comment: 10 pages; 4 tables, 3 figure
Hierarchical structure-and-motion recovery from uncalibrated images
This paper addresses the structure-and-motion problem, that requires to find
camera motion and 3D struc- ture from point matches. A new pipeline, dubbed
Samantha, is presented, that departs from the prevailing sequential paradigm
and embraces instead a hierarchical approach. This method has several
advantages, like a provably lower computational complexity, which is necessary
to achieve true scalability, and better error containment, leading to more
stability and less drift. Moreover, a practical autocalibration procedure
allows to process images without ancillary information. Experiments with real
data assess the accuracy and the computational efficiency of the method.Comment: Accepted for publication in CVI
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