47,592 research outputs found
A General Optimization Technique for High Quality Community Detection in Complex Networks
Recent years have witnessed the development of a large body of algorithms for
community detection in complex networks. Most of them are based upon the
optimization of objective functions, among which modularity is the most common,
though a number of alternatives have been suggested in the scientific
literature. We present here an effective general search strategy for the
optimization of various objective functions for community detection purposes.
When applied to modularity, on both real-world and synthetic networks, our
search strategy substantially outperforms the best existing algorithms in terms
of final scores of the objective function; for description length, its
performance is on par with the original Infomap algorithm. The execution time
of our algorithm is on par with non-greedy alternatives present in literature,
and networks of up to 10,000 nodes can be analyzed in time spans ranging from
minutes to a few hours on average workstations, making our approach readily
applicable to tasks which require the quality of partitioning to be as high as
possible, and are not limited by strict time constraints. Finally, based on the
most effective of the available optimization techniques, we compare the
performance of modularity and code length as objective functions, in terms of
the quality of the partitions one can achieve by optimizing them. To this end,
we evaluated the ability of each objective function to reconstruct the
underlying structure of a large set of synthetic and real-world networks.Comment: MAIN text: 14 pages, 4 figures, 1 table Supplementary information: 19
pages, 8 figures, 5 table
Quality functions in community detection
Community structure represents the local organization of complex networks and
the single most important feature to extract functional relationships between
nodes. In the last years, the problem of community detection has been
reformulated in terms of the optimization of a function, the Newman-Girvan
modularity, that is supposed to express the quality of the partitions of a
network into communities. Starting from a recent critical survey on modularity
optimization, pointing out the existence of a resolution limit that poses
severe limits to its applicability, we discuss the general issue of the use of
quality functions in community detection. Our main conclusion is that quality
functions are useful to compare partitions with the same number of modules,
whereas the comparison of partitions with different numbers of modules is not
straightforward and may lead to ambiguities.Comment: 10 pages, 4 figures, invited paper to appear in the Proceedings of
SPIE International Conference "Fluctuations and Noise 2007", Florence, Italy,
20-24 May, 200
Modularity functions maximization with nonnegative relaxation facilitates community detection in networks
We show here that the problem of maximizing a family of quantitative
functions, encompassing both the modularity (Q-measure) and modularity density
(D-measure), for community detection can be uniformly understood as a
combinatoric optimization involving the trace of a matrix called modularity
Laplacian. Instead of using traditional spectral relaxation, we apply
additional nonnegative constraint into this graph clustering problem and design
efficient algorithms to optimize the new objective. With the explicit
nonnegative constraint, our solutions are very close to the ideal community
indicator matrix and can directly assign nodes into communities. The
near-orthogonal columns of the solution can be reformulated as the posterior
probability of corresponding node belonging to each community. Therefore, the
proposed method can be exploited to identify the fuzzy or overlapping
communities and thus facilitates the understanding of the intrinsic structure
of networks. Experimental results show that our new algorithm consistently,
sometimes significantly, outperforms the traditional spectral relaxation
approaches
Multistart Methods for Quantum Approximate Optimization
Hybrid quantum-classical algorithms such as the quantum approximate
optimization algorithm (QAOA) are considered one of the most promising
approaches for leveraging near-term quantum computers for practical
applications. Such algorithms are often implemented in a variational form,
combining classical optimization methods with a quantum machine to find
parameters to maximize performance. The quality of the QAOA solution depends
heavily on quality of the parameters produced by the classical optimizer.
Moreover, the presence of multiple local optima in the space of parameters
makes it harder for the classical optimizer. In this paper we study the use of
a multistart optimization approach within a QAOA framework to improve the
performance of quantum machines on important graph clustering problems. We also
demonstrate that reusing the optimal parameters from similar problems can
improve the performance of classical optimization methods, expanding on similar
results for MAXCUT
Detection of Communities within the Multibody System Dynamics Network and Analysis of Their Relations
Multibody system dynamics is already a well developed branch of theoretical, computational and applied mechanics. Thousands of documents can be found in any of the well-known scientific databases. In this work it is demonstrated that multibody system dynamics is built of many thematic communities. Using the Elsevier’s abstract and citation database SCOPUS, a massive amount of data is collected and analyzed with the use of the open source visualization tool Gephi. The information is represented as a large set of nodes with connections to study their graphical distribution and explore geometry and symmetries. A randomized radial symmetry is found in the graphical representation of the collected information. Furthermore, the concept of modularity is used to demonstrate that community structures are present in the field of multibody system dynamics. In particular, twenty-four different thematic communities have been identified. The scientific production of each community is analyzed, which allows to predict its growing rate in the next years. The journals and conference proceedings mainly used by the authors belonging to the community as well as the cooperation between them by country are also analyzed
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