Multi-objective NSGA-II based community detection using dynamical evolution social network

Community detection is becoming a highly demanded topic in social networking-based applications. It involves finding the maximum intraconnected and minimum inter-connected sub-graphs in given social networks. Many approaches have been developed for community’s detection and less of them have focused on the dynamical aspect of the social network. The decision of the community has to consider the pattern of changes in the social network and to be smooth enough. This is to enable smooth operation for other community detection dependent application. Unlike dynamical community detection Algorithms, this article presents a non-dominated aware searching Algorithm designated as non-dominated sorting based community detection with dynamical awareness (NDS-CD-DA). The Algorithm uses a non-dominated sorting genetic algorithm NSGA-II with two objectives: modularity and normalized mutual information (NMI). Experimental results on synthetic networks and real-world social network datasets have been compared with classical genetic with a single objective and has been shown to provide superiority in terms of the domination as well as the convergence. NDS-CD-DA has accomplished a domination percentage of 100% over dynamic evolutionary community searching DECS for almost all iterations

Pearson coefficient matrix for studying the correlation of community detection scores in multi-objective evolutionary algorithm

Assessing a community detection algorithm is a difficult task due to the absence of finding a standard definition for objective functions to accurately identify the structure of communities in complex networks. Traditional methods generally consider the detecting of community structure as a single objective issue while its optimization generally leads to restrict the solution to a specific property in the community structure. In the last decade, new community detection models have been developed. These are based on multi-objective formulation for the problem, while ensuring that more than one objective (normally two) can be simultaneously optimized to generate a set of non-dominated solutions. However the issue of which objectives should be co-optimized to enhance the efficiency of the algorithm is still an open area of research. In this paper, first we generate a candidate set of partitions by saving the last population that has been generated using single objective evolutionary algorithm (SOEA) and random partitions based on the true partition for a given complex network. We investigate the features of the structure of communities which found by fifteen existing objectives that have been used in literature for discovering communities. Then, we found the correlation between any two objectives using the pearson coefficient matrix. Extensive experiments on four real networks show that some objective functions have a strong correlation and others either neutral or weak correlations

A novel clustering methodology based on modularity optimisation for detecting authorship affinities in Shakespearean era plays

© 2016 Naeni et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. In this study we propose a novel, unsupervised clustering methodology for analyzing large datasets. This new, efficient methodology converts the general clustering problem into the community detection problem in graph by using the Jensen-Shannon distance, a dissimilarity measure originating in Information Theory. Moreover, we use graph theoretic concepts for the generation and analysis of proximity graphs. Our methodology is based on a newly proposed memetic algorithm (iMA-Net) for discovering clusters of data elements by maximizing the modularity function in proximity graphs of literary works. To test the effectiveness of this general methodology, we apply it to a text corpus dataset, which contains frequencies of approximately 55,114 unique words across all 168 written in the Shakespearean era (16th and 17th centuries), to analyze and detect clusters of similar plays. Experimental results and comparison with state-of-the-art clustering methods demonstrate the remarkable performance of our new method for identifying high quality clusters which reflect the commonalities in the literary style of the plays

Community Detection in Complex Networks

Finding communities of connected individuals in social networks is essential for understanding our society and interactions within the network. Recently attention has turned to analyse these communities in complex network systems. In this thesis, we study three challenges. Firstly, analysing and evaluating the robustness of new and existing score functions as these functions are used to assess the community structure for a given network. Secondly, unfolding community structures in static social networks. Finally, detecting the dynamics of communities that change over time. The score functions are evaluated on different community structures. The behaviour of these functions is studied by migrating nodes randomly from their community to a random community in a given true partition until all nodes will be migrated far from their communities. Then Multi-Objective Evolutionary Algorithm Based Community Detection in Social Networks (MOEA-CD) is used to capture the intuition of community identi cation with dense connections within the community and sparse with others. This algorithm redirects the design of objective functions according to the nodes' relations within community and with other communities. This new model includes two new contradictory objectives, the rst is to maximise the internal neighbours for each node within a community and the second is to minimise the maximum external links for each node within a community with respect to its internal neighbours. Both of these objectives are optimised simultaneously to nd a set of estimated Pareto-optimal solutions where each solution corresponds to a network partition. Moreover, we propose a new local heuristic search, namely, the Neighbour Node Centrality (NNC) strategy which is combined with the proposed model to improve the performance of MOEA-CD to nd a local optimal solution. We also design an algorithm which produces community structures that evolve over time. Recognising that there may be many possible community structures that ex- plain the observed social network at each time step, in contrast to existing methods, which generally treat this as a coupled optimisation problem, we formulate the prob- lem in a Hidden Markov Model framework, which allows the most likely sequence of communities to be found using the Viterbi algorithm where there are many candi- date community structures which are generated using Multi-Objective Evolutionary Algorithm. To demonstrate that our study is effective, it is evaluated on synthetic and real-life dynamic networks and it is used to discover the changing Twitter communities of MPs preceding the Brexit referendum

Community Detection in Complex Networks

Finding communities of connected individuals in social networks is essential for understanding our society and interactions within the network. Recently attention has turned to analyse these communities in complex network systems. In this thesis, we study three challenges. Firstly, analysing and evaluating the robustness of new and existing score functions as these functions are used to assess the community structure for a given network. Secondly, unfolding community structures in static social networks. Finally, detecting the dynamics of communities that change over time. The score functions are evaluated on different community structures. The behaviour of these functions is studied by migrating nodes randomly from their community to a random community in a given true partition until all nodes will be migrated far from their communities. Then Multi-Objective Evolutionary Algorithm Based Community Detection in Social Networks (MOEA-CD) is used to capture the intuition of community identi cation with dense connections within the community and sparse with others. This algorithm redirects the design of objective functions according to the nodes' relations within community and with other communities. This new model includes two new contradictory objectives, the rst is to maximise the internal neighbours for each node within a community and the second is to minimise the maximum external links for each node within a community with respect to its internal neighbours. Both of these objectives are optimised simultaneously to nd a set of estimated Pareto-optimal solutions where each solution corresponds to a network partition. Moreover, we propose a new local heuristic search, namely, the Neighbour Node Centrality (NNC) strategy which is combined with the proposed model to improve the performance of MOEA-CD to nd a local optimal solution. We also design an algorithm which produces community structures that evolve over time. Recognising that there may be many possible community structures that ex- plain the observed social network at each time step, in contrast to existing methods, which generally treat this as a coupled optimisation problem, we formulate the prob- lem in a Hidden Markov Model framework, which allows the most likely sequence of communities to be found using the Viterbi algorithm where there are many candi- date community structures which are generated using Multi-Objective Evolutionary Algorithm. To demonstrate that our study is effective, it is evaluated on synthetic and real-life dynamic networks and it is used to discover the changing Twitter communities of MPs preceding the Brexit referendum

Multi-Objective Evolutionary Algorithms to Find Community Structures in Large Networks

Real-world complex systems are often modeled by networks such that the elements are represented by vertices and their interactions are represented by edges. An important characteristic of these networks is that they contain clusters of vertices densely linked amongst themselves and more sparsely connected to nodes outside the cluster. Community detection in networks has become an emerging area of investigation in recent years, but most papers aim to solve single-objective formulations, often focused on optimizing structural metrics, including the modularity measure. However, several studies have highlighted that considering modularityas a unique objective often involves resolution limit and imbalance inconveniences. This paper opens a new avenue of research in the study of multi-objective variants of the classical community detection problem by applying multi-objective evolutionary algorithms that simultaneously optimize different objectives. In particular, they analyzed two multi-objective variants involving not only modularity but also the conductance metric and the imbalance in the number of nodes of the communities. With this aim, a new Pareto-based multi-objective evolutionary algorithm is presented that includes advanced initialization strategies and search operators. The results obtained when solving large-scale networks representing real-life power systems show the good performance of these methods and demonstrate that it is possible to obtain a balanced number of nodes in the clusters formed while also having high modularity and conductance values

An efficient multi-objective community detection algorithm in complex networks

Detekcija zajednice u složenim mrežama često se smatra problemom jednokriterijske optimizacije, a teško je jednokriterijskom optimizacijom identificirati moguću strukturu zajednice punu značenja. Stoga je algoritam višekriterijske optimizacije primijenjen na područje detekcije zajednice. Međutim, algoritam višekriterijske detekcije zajednice sklon je lokalnoj optimizaciji i slaboj raznovrsnosti niza Pareto-optimalnih rješenja. Imajući to u vidu, u ovom se radu predlaže višekriterijski algoritam za detekciju zajednice, nazvan I-NSGAII, zasnovan na sustavu NSGAII. Taj algoritam može simultano optimizirati dvije suprotstavljene kriterijske funkcije procjenjujući gustoću veza unutar zajednice i nedostatak veza između zajednica te dobiti niz Pareto optimalnih rješenja koja imaju strukturu zajednice različitih hijerarhija; on također predlaže razvojnu strategiju raznolikosti (diverziteta), omogućujući algoritmu proširenje područja pretraživanja te tako izbjegava lokalnu optimizaciju niza Pareto-optimalnih rješenja. Uz to, kako bi se poboljšala mogućnost pretraživanja algoritma, I-NSGAII algoritam usvaja strategije predstavljanja susjedstva prema mjestu (locus-based adjacency representation), jedinstvenog naziva, crossovera u jednom smjeru i lokalne mutacije. Ispitivanja na sintetičkim i mrežama stvarnog svijeta te usporedbe s mnogim state-of-the-art algoritmima potvrđuju validnost i izvedivost I-NSGAII-a.Community detection in complex networks is often regarded as the problem of single-objective optimization and it is hard for single-objective optimization to identify potential community structure of meaningfulness. Thus, algorithm of multi-objective optimization is applied to the field of community detection. However, multi-objective community detection algorithm is prone to local optimization and weak diversity of the set of Paretooptimal solutions. In view of this, based on the framework of NSGAII, a multi-objective community detection algorithm, named I-NSGAII, is proposed in this paper. This algorithm is able to optimize simultaneously the two conflicting objective functions evaluating the density of intra-community connections and the sparsity of inter-community connections, and obtain the set of Pareto optimal solutions having diverse hierarchal community structures; it also proposes diversity evolutionary strategy enabling the algorithm to expand searching space and thus avoids local optimization of the set of Pareto-optimal solutions. In addition, to improve algorithm’s searching ability, I-NSGAII algorithm adopts the strategies of locus-based adjacency representation, unified label, one-way crossover and local mutation. Tests on synthetic and real-world networks and comparisons with many state-of-theart algorithms verify the validity and feasibility of I-NSGAII

Detecting Communities with Different Sizes for Social Network Analysis

National Natural Science Foundation of China; Yunnan Educational Department Foundation; Program for Young and Middle-aged Skeleton Teachers, Yunnan Universit