Community Detection Based on Differential Evolution Using Social Spider Optimization

You-Hong Li, Jian-Qiang Wang, Xue-Jun Wang, Yue-Long Zhao, Xing-Hua Lu, Da-Long Liu
2017 Symmetry  
Community detection (CD) has become an important research direction for data mining in complex networks. Evolutionary algorithm-based (EA-based) approaches, among many other existing community detection methods, are widely used. However, EA-based approaches are prone to population degradation and local convergence. Developing more efficient evolutionary algorithms thus becomes necessary. In 2013, Cuevas et al. proposed a new differential evolution (DE) hybrid meta-heuristic algorithm based on
more » ... e simulated cooperative behavior of spiders, known as social spider optimization (SSO). On the basis of improving the SSO algorithm, this paper proposes a community detection algorithm based on differential evolution using social spider optimization (DESSO/CD). In this algorithm, the CD detection process is done by simulating the spider cooperative operators, marriage, and operator selection. The similarity of nodes is defined as local fitness function; the community quality increment is used as a screening criterion for evolutionary operators. Populations are sorted according to their contribution and diversity, making evolution even more different. In the entire process, a random cloud crossover model strategy is used to maintain population diversity. Each generation of the mating radius of the SSO algorithm will be adjusted appropriately according to the iterative times and fitness values. This strategy not only ensures the search space of operators, but also reduces the blindness of exploration. On the other hand, the multi-level, multi-granularity strategy of DESSO/CD can be used to further compensate for resolution limitations and extreme degradation defects based on modular optimization methods. The experimental results demonstrate that the DESSO/CD method could detect the community structure with higher partition accuracy and lower computational cost when compared with existing methods. Since the application of the SSO algorithm in CD research is just beginning, the study is competitive and promising. Symmetry 2017, 9, 183 2 of 20 community in complex networks is helpful for understanding complex systems [6] [7] [8] , where objects are represented as nodes and the relationships among the objects are represented as edges [1] . Complex networks have characteristics of discrete distribution and dynamic evolution [9] unlike simple networks such as lattices or random graphs. Thus, simple modeling and analysis based on network topology gradually fails to meet the needs of community detection. Recent studies have paid much attention to community detection and have developed various algorithms from different perspectives. According to the principle of division, community structures now can be detected through many different methods, such as division-based [1,10,11], cohesion-based [12, 13] , spectral-based [14, 15] , statistical-inference-based [16, 17] , and optimization-based [18] [19] [20] [21] [22] [23] [24] [25] [26] methods. Recently, the optimization-based methods have drawn steady attention to community detection [4, 20, 27, 28] . The community detection problem can be translated into an optimization problem [29] , where modularity function Q [10] is a widely adopted in optimization objective, even if maximizing Q is usually non-deterministic polynomial hard (NP-hard) [21] . In community structure detection, optimization is based on the monotonic increase and the approximate maximum two characteristics of the Q function [30] . Although Q functions are limited in resolution [28] and extreme degradation [31], they are widely used by researchers. Blondel [32] and Khadivi et al. [33] found that the design of multi-level, multi-granularity, and weighted methods can ease resolution limits and extreme degradation. Evolutionary algorithm (EA)-based strategies are effective in optimization approaches [33] . Compared to other strategies, there are three main advantages. Firstly, EAs are similar to the simulation network evolution process [34] . Secondly, the multi-level, multi-granularity strategy of EAs can be used to further compensate for resolution limitations and extreme degradation defects based on modular optimization methods [35] . Thirdly, they are more suitable for solving complex and discrete problems (EAs change their current state to the next state with the strategy adopted, while maintaining some degrees of randomness to ensure the exploration of solution space). However, in the EA-based for CD algorithm, too much fitness calculation and premature convergence of the population are still the main obstacles in the community testing process. In addition, maintaining the diversity of the population and balancing the algorithm convergence is the key issue to improving the performance of EAs [36] . Thus, researchers have designed a number of algorithms to overcome obstacles [36] . Recently, the differential evolution (DE) hybrid meta-heuristic-based optimization algorithms of CD research have made great progress [20] [21] [22] [23] [24] 27, 37, 38] . Typically, the parent's mutation operator of the DE algorithm is chosen randomly from the population. This is different from other EAs, in which the probability of all individuals being treated as parents is equal. Such a strategy could damage the population diversity [2, [39] [40] [41] . Therefore, Wang [40] presented a new differential strategy, whereby individuals in the current population are first sorted according to their fitness and diversity contribution by non-dominant sorting, thus, the promising individuals with better fitness and diversity have a greater opportunity to be selected as parents in order to achieve a good balance between exploration and exploitation. However, the above strategy does not evaluate fitness and diversity information in real time in each generation. If it is used to model the discovery of the community, it may lead to loss of diversity information and be difficult to converge. Based on the above analysis and inspiration, this paper proposes a community detection algorithm based on differential evolution using social spider optimization (DESSO/CD). In this algorithm, a new community detection algorithm framework based on social spider optimization (SSO) is presented. In initializing the population process, nodes in the network are initialized as populations in the SSO algorithm. In the cooperative operators' process, the fitness function of the SSO algorithm is defined according to the local similarity strategy of nodes. The populations are divided into two categories: elite and non-elite based on the fitness value, which further improves the differential evolution strategy of the SSO algorithm (the effect of the strategy corresponds to the hybrid differential evolution scheme proposed in [40] ). At the same time, a random cloud crossover model is adopted to keep the diversity of population. In the mating operator process of DESSO/CD, the mating radius will automatically be Symmetry 2017, 9, 183 3 of 20
doi:10.3390/sym9090183 fatcat:tbd5oe4j4nenzl47r7g274c6ya