29,780 research outputs found
Detecting Communities under Differential Privacy
Complex networks usually expose community structure with groups of nodes
sharing many links with the other nodes in the same group and relatively few
with the nodes of the rest. This feature captures valuable information about
the organization and even the evolution of the network. Over the last decade, a
great number of algorithms for community detection have been proposed to deal
with the increasingly complex networks. However, the problem of doing this in a
private manner is rarely considered. In this paper, we solve this problem under
differential privacy, a prominent privacy concept for releasing private data.
We analyze the major challenges behind the problem and propose several schemes
to tackle them from two perspectives: input perturbation and algorithm
perturbation. We choose Louvain method as the back-end community detection for
input perturbation schemes and propose the method LouvainDP which runs Louvain
algorithm on a noisy super-graph. For algorithm perturbation, we design
ModDivisive using exponential mechanism with the modularity as the score. We
have thoroughly evaluated our techniques on real graphs of different sizes and
verified their outperformance over the state-of-the-art
Overlapping Community Structure in Co-authorship Networks: a Case Study
Community structure is one of the key properties of real-world complex
networks. It plays a crucial role in their behaviors and topology. While an
important work has been done on the issue of community detection, very little
attention has been devoted to the analysis of the community structure. In this
paper, we present an extensive investigation of the overlapping community
network deduced from a large-scale co-authorship network. The nodes of the
overlapping community network represent the functional communities of the
co-authorship network, and the links account for the fact that communities
share some nodes in the co-authorship network. The comparative evaluation of
the topological properties of these two networks shows that they share similar
topological properties. These results are very interesting. Indeed, the network
of communities seems to be a good representative of the original co-authorship
network. With its smaller size, it may be more practical in order to realize
various analyses that cannot be performed easily in large-scale real-world
networks.Comment: 2014 7th International Conference on u- and e- Service, Science and
Technolog
Evidential Communities for Complex Networks
Community detection is of great importance for understand-ing graph structure
in social networks. The communities in real-world networks are often
overlapped, i.e. some nodes may be a member of multiple clusters. How to
uncover the overlapping communities/clusters in a complex network is a general
problem in data mining of network data sets. In this paper, a novel algorithm
to identify overlapping communi-ties in complex networks by a combination of an
evidential modularity function, a spectral mapping method and evidential
c-means clustering is devised. Experimental results indicate that this
detection approach can take advantage of the theory of belief functions, and
preforms good both at detecting community structure and determining the
appropri-ate number of clusters. Moreover, the credal partition obtained by the
proposed method could give us a deeper insight into the graph structure
On time-varying collaboration networks
The patterns of scientific collaboration have been frequently investigated in
terms of complex networks without reference to time evolution. In the present
work, we derive collaborative networks (from the arXiv repository)
parameterized along time. By defining the concept of affine group, we identify
several interesting trends in scientific collaboration, including the fact that
the average size of the affine groups grows exponentially, while the number of
authors increases as a power law. We were therefore able to identify, through
extrapolation, the possible date when a single affine group is expected to
emerge. Characteristic collaboration patterns were identified for each
researcher, and their analysis revealed that larger affine groups tend to be
less stable
Community core detection in transportation networks
This work analyses methods for the identification and the stability under
perturbation of a territorial community structure with specific reference to
transportation networks. We considered networks of commuters for a city and an
insular region. In both cases, we have studied the distribution of commuters'
trips (i.e., home-to-work trips and viceversa). The identification and
stability of the communities' cores are linked to the land-use distribution
within the zone system, and therefore their proper definition may be useful to
transport planners.Comment: 8 pages, 13 figure
Simplified Energy Landscape for Modularity Using Total Variation
Networks capture pairwise interactions between entities and are frequently
used in applications such as social networks, food networks, and protein
interaction networks, to name a few. Communities, cohesive groups of nodes,
often form in these applications, and identifying them gives insight into the
overall organization of the network. One common quality function used to
identify community structure is modularity. In Hu et al. [SIAM J. App. Math.,
73(6), 2013], it was shown that modularity optimization is equivalent to
minimizing a particular nonconvex total variation (TV) based functional over a
discrete domain. They solve this problem, assuming the number of communities is
known, using a Merriman, Bence, Osher (MBO) scheme.
We show that modularity optimization is equivalent to minimizing a convex
TV-based functional over a discrete domain, again, assuming the number of
communities is known. Furthermore, we show that modularity has no convex
relaxation satisfying certain natural conditions. We therefore, find a
manageable non-convex approximation using a Ginzburg Landau functional, which
provably converges to the correct energy in the limit of a certain parameter.
We then derive an MBO algorithm with fewer hand-tuned parameters than in Hu et
al. and which is 7 times faster at solving the associated diffusion equation
due to the fact that the underlying discretization is unconditionally stable.
Our numerical tests include a hyperspectral video whose associated graph has
2.9x10^7 edges, which is roughly 37 times larger than was handled in the paper
of Hu et al.Comment: 25 pages, 3 figures, 3 tables, submitted to SIAM J. App. Mat
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