Identifying multi-scale communities in networks by asymptotic surprise

Abstract

Optimizing statistical measures for community structure is one of the most popular strategies for community detection, but many of them lack the flexibility of resolution and thus are incompatible with multi-scale communities of networks. Here, we further studied a statistical measure of interest for community detection, asymptotic surprise, an asymptotic approximation of surprise. We discussed the critical behaviors of asymptotic surprise in phase transition of community partition theoretically. Then, according to the theoretical analysis, a multi-resolution method based on asymptotic surprise was introduced, which provides an alternative approach to study multi-scale communities in networks, and an improved Louvain algorithm was proposed to optimize the asymptotic surprise more effectively. By a series of experimental tests in various networks, we validated the critical behaviors of the asymptotic surprise further and the effectiveness of the improved Louvain algorithm, displayed its ability to solve the first-type resolution limit and stronger tolerance against the second-type resolution limit, and confirmed its effectiveness of revealing multi-scale community structures in multi-scale networks.

Community Detection and Visualization in Complex Network by the Density-Canopy-Kmeans Algorithm and MDS Embedding

“…Therefore, in addition to the modularity, we also use several widely used measurement indicators [21] with F-measure, Rand index (RI), Adjusted Rand Index (ARI), Normalized Mutual Information (NMI) to evaluate networks of known structures. The algorithms that are used for comparison include MSCD-LFK [8], OSLOM [12], Lourvarinsprs [13], LouvainSgn [14], LPcopra [19], and Kmeans [30]. For the algorithm with randomness, we run 10 times and take the results corresponding to the optimal value of the module.…”

“…With the development of community detection algorithms, many evaluation parameters for community structure such as modularity and conductivity have been proposed [9]. As a result, there are many optimization-based algorithms proposed to optimize the objective functions based on these parameters, such as multiobjective genetic algorithm for community detection in networks (MOGA-NET) [10], heuristic artificial bee colony (HABC) [11], Order Statistics Local Optimization Method (OSLOM) [12], LouvainSprs [13], LouvainSgnf [14] and multi-objective discrete cuckoo search algorithm with local search (MDCL) [15]. Because of the intrinsic correlation between network structure and dynamical behaviors in the networks, many network dynamics-based algorithms utilize the dynamical characteristics of complex networks for community detection, e.g., random walks and diffusion on networks [16], maps of random walks on complex networks (Infomap) [17], the method using random walks (Walktrap) [18], the Label Propagation Algorithm (LPcopra) [19], and multiresolution community detection in large-scale networks (MSCD_HSLSW) [20].…”

Integrate multiscale module kernel for disease-gene discovery in biological networks

“…Given a module partition in a network, the mathematical form of general modularity Q can be expressed as, where e st denotes the fraction of links between modules s and t , While ( is the inner degree of module s ), m denotes the number of links in the network; A is the adjacent matrix of the network; c i denotes the module label of node i ; γ is the resolution parameter; the sum over all modules in the network. Modules at different scales can be detected by using effective algorithms to optimize the above modularity Q with different values of resolution parameter γ [65, 69, 70]. Small-size modules can be discovered if γ -value is large; large-size modules can be discovered if γ -value is small.…”

“…A group of single-node modules can be generated when 𝛾-value is large enough, e.g., 𝛾 > 2𝑚/𝑘 𝑚𝑖𝑛 2 , where 𝑘 𝑚𝑖𝑛 denotes minimum degree of nodes in the network [71]. Then, to cover all possible module scales, we define a semi-empirical interval of 𝛾 ∈ [𝛾 𝑚𝑖𝑛 , 𝛾 𝑚𝑎𝑥 ], and use exponential sampling (ES) to generate a set of 𝛾-values from continuous resolution space, since it can sample different meaningful scales in a network reasonably, according to previous work [67,69]. The exponential sampling will produce a set of 𝛾-values that are equally spaced on a logarithmic scale.…”

Identifying Communities in Dynamic Networks Using Information Dynamics

“…Systems in the real world can be abstracted into complex networks, and a large number of algorithms for complex network mining have been proposed [1][2][3][4][5], most of which focus on static networks. However, most networks in the real world are evolving over time.…”