Limited Resolution and Multiresolution Methods in Complex Network Community Detection

Kumpula, Jussi M.; Saramäki, Jari; Kaski, Kimmo; Kertész, János

doi:10.1142/s0219477507003854

Cited by 39 publications

(42 citation statements)

References 21 publications

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“…Multiresolution methods [90,91,92,62,93] extend the ideas of community detection to identify the "best" division(s) over a range of network scales ("resolutions"). We test s independent realizations of the system ("replicas") over all relevant network scales by specifying different values of γ in Eq.…”

Section: Multiresolution Community Detectionmentioning

confidence: 99%

“…In the case of very stable system resolutions, local extrema can be replaced by plateaus in these information theory measures that indicate no change in the system solution over an extended range of resolution scales γ (as seen in the networks examined in [62] and, in the appendix of the current work, in some crisp lattice systems analyzed in Appendix O). We can further extract additional qualitative information about the "stability" of network partitions across a range of resolutions by examining the average number of clusters q [90,91,94], mutual information I [90], or the Shannon entropy H [62,94]. .…”

Section: Multiresolution Community Detectionmentioning

confidence: 99%

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Detecting hidden spatial and spatio-temporal structures in glasses and complex physical systems by multiresolution network clustering

Ronhovde

Chakrabarty

et al. 2011

Eur. Phys. J. E

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Abstract. We elaborate on a general method that we recently introduced for characterizing the "natural" structures in complex physical systems via a multi-scale network based approach for the data mining of such structures. The approach is based on "community detection" wherein interacting particles are partitioned into "an ideal gas" of optimally decoupled groups of particles. Specifically, we construct a set of network representations ("replicas") of the physical system based on interatomic potentials and apply a multiscale clustering ("multiresolution community detection") analysis using information-based correlations among the replicas. Replicas may be (i) different representations of an identical static system or (ii) embody dynamics by when considering replicas to be time separated snapshots of the system (with a tunable time separation) or (iii) encode general correlations when different replicas correspond to different representations of the entire history of the system as it evolves in space-time. Inputs for our method are the inter-particle potentials or experimentally measured two (or higher order) particle correlations. We apply our method to computer simulations of a binary Kob-Andersen Lennard-Jones system in a mixture ratio of A80B20, a ternary model system with components "A", "B", and "C" in ratios of A88B7C5 (as in Al88Y7Fe5), and to atomic coordinates in a Zr80Pt20 system as gleaned by reverse Monte Carlo analysis of experimentally determined structure factors. We identify the dominant structures (disjoint or overlapping) and general length scales by analyzing extrema of the information theory measures. We speculate on possible links between (i) physical transitions or crossovers and (ii) changes in structures found by this method as well as phase transitions associated with the computational complexity of the community detection problem. We briefly also consider continuum approaches and discuss the shear penetration depth in elastic media; this length scale increases as the system becomes increasingly rigid.

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Section: Multiresolution Community Detectionmentioning

confidence: 99%

Section: Multiresolution Community Detectionmentioning

confidence: 99%

Detecting hidden spatial and spatio-temporal structures in glasses and complex physical systems by multiresolution network clustering

Ronhovde

Chakrabarty

et al. 2011

Eur. Phys. J. E

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“…Arenas et al [36] defined a multiresolution method using modularity that makes novel use of the resolution limit [30]. Reichardt and Bornholdt [10], Arenas et al [36], Kumpula and coworkers [37], and Heimo et al [38] also study multiresolution applications of an RB Potts model.…”

Section: Introductionmentioning

confidence: 99%

Multiresolution community detection for megascale networks by information-based replica correlations

2009

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We use a Potts model community detection algorithm to accurately and quantitatively evaluate the hierarchical or multiresolution structure of a graph. Our multiresolution algorithm calculates correlations among multiple copies ("replicas") of the same graph over a range of resolutions. Significant multiresolution structures are identified by strongly correlated replicas. The average normalized mutual information, the variation of information, and other measures in principle give a quantitative estimate of the "best" resolutions and indicate the relative strength of the structures in the graph. Because the method is based on information comparisons, it can in principle be used with any community detection model that can examine multiple resolutions. Our approach may be extended to other optimization problems. As a local measure, our Potts model avoids the "resolution limit" that affects other popular models. With this model, our community detection algorithm has an accuracy that ranks among the best of currently available methods. Using it, we can examine graphs over 40 million nodes and more than one billion edges. We further report that the multiresolution variant of our algorithm can solve systems of at least 200 000 nodes and 10 million edges on a single processor with exceptionally high accuracy. For typical cases, we find a super-linear scaling, O(L 1.3 ) for community detection and O(L 1.3 log N ) for the multiresolution algorithm where L is the number of edges and N is the number of nodes in the system.

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“…A large number of heuristics were proposed to maximize modularity. They rely on simulated annealing [16], extremal optimization [17], mean field annealing [18], genetic search [19], dynamical clustering [20], multilevel partitioning [21], contraction-dilation [22], multistep greedy [23], quantum mechanics [24] and a variety of other approaches [25,26,27,28,29,30]. These heuristics provide, usually in moderate time, near optimal partitions for the modularity criterion or, possibly, optimal partitions but without the proof of their optimality.…”

mentioning

confidence: 99%

“…Two such examples will be discussed later. To paliate this problem several modifications to the modularity function were proposed [44,30] and heuristics generalized accordingly.…”

mentioning

confidence: 99%

Edge ratio and community structure in networks

2010

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Les textes publiés dans la série des rapports de recherche HEC n'engagent que la responsabilité de leurs auteurs. La publication de ces rapports de recherche bénéficie d'une subvention du Fonds québécois de la recherche sur la nature et les technologies. September 2009Les Cahiers du GERAD G-2009-55 Copyright c 2009 GERAD AbstractA new hierarchical divisive algorithm is proposed for identifying communities in complex networks. To that effect, the definition of community in the weak sense of Radicchi et al. is extended into a criterion for a bipartition to be optimal: one seeks to maximize the minimum for both classes of the bipartition of the ratio of inner edges to cut edges. A mathematical program is used within a dichotomous search to do this in an optimal way for each bipartition. This includes an exact solution of Wang et al.'s problem of detecting indivisible communities. The resulting hierarchical divisive algorithm is compared with exact modularity maximization on both artificial and real world datasets. For two problems of the former kind optimal solutions are found, for five problems of the latter kind the edge ratio algorithm always appears to be competitive. Moreover, it provides new information in several cases, notably through the use of the dendrogram summarizing the resolution. RésuméUn nouvel algorithme hiérarchique divisif est proposé pour l'identification des communautés dans les réseaux complexes. Pour ce faire, la définition de communauté au sens faible de Radicchi et al. est etendue en un critère pour qu'une bipartition soit optimale : on chercheà maximiser le minimum pour les deux classes de la bipartition du rapport du nombre d'arêtes internes au nombre d'arêtes coupées. Un programme mathématique est utiliséà l'intérieur d'une procédure de recherche dichotomique pour se faire de manière optimale pour chaque bipartition. On obtient ainsi une solution exacte au problème de Wang et al. de détecter des communautés indivisibles. L'algorithme hiérarchique divisif résultant est comparé avec la maximisation exacte de la modularité sur des ensembles de données artificielles et réelles. Pour deux problèmes de la première sorte, les solutions optimales sont obtenues et pour cinq problèmes de la seconde sorte l'algorithme proposé se montre toujours compétitif. De plus, il produit de l'information nouvelle dans plusieurs cas notamment par l'usage du dendrogramme résumant la résolution.

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Limited Resolution and Multiresolution Methods in Complex Network Community Detection

Cited by 39 publications

References 21 publications

Detecting hidden spatial and spatio-temporal structures in glasses and complex physical systems by multiresolution network clustering

Detecting hidden spatial and spatio-temporal structures in glasses and complex physical systems by multiresolution network clustering

Multiresolution community detection for megascale networks by information-based replica correlations

Edge ratio and community structure in networks

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