Article

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.
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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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    • "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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