On Modularity Clustering

Univ. of Konstanz, Konstanz
IEEE Transactions on Knowledge and Data Engineering (Impact Factor: 1.82). 03/2008; 20(2):172 - 188. DOI: 10.1109/TKDE.2007.190689
Source: IEEE Xplore

ABSTRACT Modularity is a recently introduced quality measure for graph clusterings. It has immediately received considerable attention in several disciplines, particularly in the complex systems literature, although its properties are not well understood. We study the problem of finding clusterings with maximum modularity, thus providing theoretical foundations for past and present work based on this measure. More precisely, we prove the conjectured hardness of maximizing modularity both in the general case and with the restriction to cuts and give an Integer Linear Programming formulation. This is complemented by first insights into the behavior and performance of the commonly applied greedy agglomerative approach.

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    • "However, it needs the absolute best and worst fitness values in the search space. We adopted modularity [15] as fitness value, and it has been proved that its value ranges between -0.5 and 1 [17]. Of course these limit values depend on the network structure. "
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    ABSTRACT: Community detection in complex networks that evolve over time is a challenging task, intensively studied in the last few years. An algorithm designed for this problem should be able to successfully do two things: discover if changes occurred in the network and quickly react by modifying the community structure for reflecting new connections and objects constituting the network. Evolutionary dynamic optimization revealed a powerful technique to solve time-dependent problems by applying evolutionary algorithms. In this paper we propose to exploit such a technique to obtain and trace community structure in time evolving environments. The approach uses a population-based model for change detection, and applies two different strategies to adapt to changes. Experimental results on synthetic networks show the very good performances of evolutionary dynamic optimization to deal with this kind of problem.
    6th International Conference on. Information, Intelligence, Systems and Applications ( IISA 2015 ), Corfu Greece; 07/2015
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    • "The modularity-maximization problem has been shown as being NP-complete [23], [24]. The existing algorithms for this problem can be broadly categorized into two types: (i) heuristic methods that solve this problem directly [25], and (ii) mathematical programming methods that relax it into an easier problem first [23], [26]. "
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    ABSTRACT: Signature-based botnet detection methods identify botnets by recognizing Command and Control (C\&C) traffic and can be ineffective for botnets that use new and sophisticate mechanisms for such communications. To address these limitations, we propose a novel botnet detection method that analyzes the social relationships among nodes. The method consists of two stages: (i) anomaly detection in an "interaction" graph among nodes using large deviations results on the degree distribution, and (ii) community detection in a social "correlation" graph whose edges connect nodes with highly correlated communications. The latter stage uses a refined modularity measure and formulates the problem as a non-convex optimization problem for which appropriate relaxation strategies are developed. We apply our method to real-world botnet traffic and compare its performance with other community detection methods. The results show that our approach works effectively and the refined modularity measure improves the detection accuracy.
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    • "A recent survey on overlapping community detection problem is provided in [6]. Both problems, disjoint and overlapping communities detection are NP-hard [7]. Existing algorithms apply different heuristics. "
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    ABSTRACT: Unfolding the community structure of complex networks is still to be one of the most important tasks in the field of complex network analysis. However, in many real settings, we seek to uncover the community of a given node rather than partitioning the whole graph into communities. A main trend in the area of ego-centred community identification consists in applying a greedy optimization approach of a local modularity measure. Different local modularity functions have been proposed in the scientific literature. In this work, we explore applying different ensemble approaches in order to combine different local modularity functions. Explored approaches include naive combine-and-rank approach, ensemble ranking approaches, and ensemble clustering. Experiments are conducted on different real and artificial benchmark networks for which ground truth community partitions are known. Results show that ensemble-ranking approaches provide better results than both state-of-the art approaches and other ensemble approaches.
    Neurocomputing 02/2015; 150. DOI:10.1016/j.neucom.2014.09.042 · 2.01 Impact Factor
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