Benchmark graphs for testing community detection algorithms

Lancichinetti, Andrea; Fortunato, Santo; Radicchi, Filippo

doi:10.1103/physreve.78.046110

Cited by 2,572 publications

(1,986 citation statements)

References 22 publications

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“…In the second approach, algorithms are tested against computer-generated networks that have some form of community structure artificially embedded within them. A number of standard benchmark networks have been proposed for this purpose, such as the 'four groups' networks 14 or so-called the LFR benchmark networks 32 . A number of studies have been published that compare the performance of proposed algorithms in these benchmark tests 33,34 .…”

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confidence: 99%

Communities, modules and large-scale structure in networks

2011

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Networks, also called graphs by mathematicians, provide a useful abstraction of the structure of many complex systems, ranging from social systems and computer networks to biological networks and the state spaces of physical systems. In the past decade there have been significant advances in experiments to determine the topological structure of networked systems, but there remain substantial challenges in extracting scientific understanding from the large quantities of data produced by the experiments. A variety of basic measures and metrics are available that can tell us about small-scale structure in networks, such as correlations, connections and recurrent patterns, but it is considerably more difficult to quantify structure on medium and large scales, to understand the 'big picture'. Important progress has been made, however, within the past few years, a selection of which is reviewed here.A network is, in its simplest form, a collection of dots joined together in pairs by lines (Fig. 1). In the jargon of the field, a dot is called a 'node' or 'vertex' (plural 'vertices') and a line is called an 'edge'. Networks are used in many branches of science as a way to represent the patterns of connections between the components of complex systems [1][2][3][4][5][6] . Examples include the Internet 7,8 , in which the nodes are computers and the edges are data connections such as optical-fibre cables, food webs in biology 9,10 , in which the nodes are species in an ecosystem and the edges represent predator-prey interactions, and social networks 11,12 , in which the nodes are people and the edges represent any of a variety of different types of social interaction including friendship, collaboration, business relationships or others.In the past decade there has been a surge of interest in both empirical studies of networks 13 and development of mathematical and computational tools for extracting insight from network data 1-6 . One common approach to the study of networks is to focus on the properties of individual nodes or small groups of nodes, asking questions such as, 'Which is the most important node in this network?' or 'Which are the strongest connections?' Such approaches, however, tell us little about large-scale network structure. It is this large-scale structure that is the topic of this paper.The best-studied form of large-scale structure in networks is modular or community structure 14,15 . A community, in this context, is a dense subnetwork within a larger network, such as a close-knit group of friends in a social network or a group of interlinked web pages on the World Wide Web (Fig. 1). Although communities are not the only interesting form of large-scale structure-there are others that we will come to-they serve as a good illustration of the nature and scope of present research in this area and will be our primary focus.Communities are of interest for a number of reasons. They have intrinsic interest because they may correspond to functional units within a networked system, an example of the kind of link...

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Communities, modules and large-scale structure in networks

2011

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“…In order to get a grasp on the magnitude of this challenge, we conduct a controlled analysis of topic-model algorithms for highly specified sets of synthetic data. This high degree of control allows us to tease apart the theoretical limitations of the algorithms from other sources of error that would remain uncontrolled with real-world data sets [26][27][28]. Our analyses reveal that standard techniques for likelihood optimization are significantly hindered by the roughness of the likelihood-function landscape, even for very simple cases.…”

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confidence: 92%

High-Reproducibility and High-Accuracy Method for Automated Topic Classification

et al. 2015

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Much of human knowledge sits in large databases of unstructured text. Leveraging this knowledge requires algorithms that extract and record metadata on unstructured text documents. Assigning topics to documents will enable intelligent searching, statistical characterization, and meaningful classification. Latent Dirichlet allocation (LDA) is the state of the art in topic modeling. Here, we perform a systematic theoretical and numerical analysis that demonstrates that current optimization techniques for LDA often yield results that are not accurate in inferring the most suitable model parameters. Adapting approaches from community detection in networks, we propose a new algorithm that displays high reproducibility and high accuracy and also has high computational efficiency. We apply it to a large set of documents in the English Wikipedia and reveal its hierarchical structure.

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“…Fortunately, recent work has shown that it is possible to derive this information from the spectra of the non-backtracking matrix [3] and the flow matrix [4], at least on the classic version of the planted partition model [5], where clusters have identical size and nodes the same degree (on average). We show that the prediction of the number of clusters remains accurate as well on the LFR benchmark graph [6], which extends the original planted partition model by introducing realistic features of community structure, i.e. heterogeneous distributions of degrees and cluster sizes.…”

Section: Introductionmentioning

confidence: 98%

Improving the performance of algorithms to find communities in networks

2014

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Most algorithms to detect communities in networks typically work without any information on the cluster structure to be found, as one has no a priori knowledge of it, in general. Not surprisingly, knowing some features of the unknown partition could help its identification, yielding an improvement of the performance of the method. Here we show that, if the number of clusters were known beforehand, standard methods, like modularity optimization, would considerably gain in accuracy, mitigating the severe resolution bias that undermines the reliability of the results of the original unconstrained version. The number of clusters can be inferred from the spectra of the recently introduced non-backtracking and flow matrices, even in benchmark graphs with realistic community structure. The limit of such two-step procedure is the overhead of the computation of the spectra.

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Benchmark graphs for testing community detection algorithms

Cited by 2,572 publications

References 22 publications

Communities, modules and large-scale structure in networks

Communities, modules and large-scale structure in networks

High-Reproducibility and High-Accuracy Method for Automated Topic Classification

Improving the performance of algorithms to find communities in networks

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