<b>Enhanced Multi-Objective Evolutionary Algorithm for Community Detection Using a Community Strength-Based Mutation Strategy</b>

Cultures of the Central Highlands, New Guinea

Recently, multi-objective evolutionary algorithms (MOEAs) have been shown promising performance for detecting overlapping community structure in complex networks. However, it is still challenging to design MOEAs for overlapping community detection on large-scale complex networks due to the curse of dimensionality. Along this avenue, this paper proposes a local-to-global scheme-based MOEA named LG-MOEA for overlapping community detection on large-scale complex networks, which mainly consists of two stages: a local community structure detection stage and a global community structure determination stage. To be specific, in the local community structure detection stage, the key nodes that are central to community and essential to the connectedness of community are firstly identified. Then for each key node, an MOEA with the proposed community boundary control strategy is suggested to detect a set of local overlapping communities through local expansion around the key node. In the global community structure determination stage, a single objective evolutionary algorithm is adopted to search for a suitable local overlapping community for each key node and combine them as one global community partition of the whole network. The proposed LG-MOEA is compared with several competitive overlapping community detection algorithms on both real-world small-scale and large-scale networks, and the experimental results show its superiority for overlapping community detection in terms of the generalized normalized mutual information gNMI and the extended modularity $$Q_{ov}$$ , especially has competitive superiority for large-scale complex networks.

A parallel multi-objective evolutionary algorithm for community detection in large-scale complex networks

Community detection in social networks has become a dominating topic of the current data research as it has a direct implication in many different areas of importance, whether social network, citation network, traffic network, metabolic network, protein-protein network or web graph etc. Mining meaningful communities in a real-world network is a hard problem owing to the dynamic nature of these networks. The existing algorithms for community detection depend chiefly on the network topologies and are not effective for such sparse graphs. Thus, there is a great need to optimize those algorithms. Evolutionary algorithms have emerged as a promising solution for optimized approximation of hard problems. We propose to optimize the community detection method based on modularity and normalized mutual information (NMI) using the latest grey wolf optimization algorithm. The results demonstrate the effectiveness of the algorithms, when compared with other contemporary evolutionary algorithms.

Community detection is useful for better understanding the structure of complex networks. It aids in the extraction of the required information from such networks and has a vital role in different fields that range from healthcare to regional geography, economics, human interactions, and mobility. The method for detecting the structure of communities involves the partitioning of complex networks into groups of nodes, with extensive connections within community and sparse connections with other communities. In the literature, two main measures, namely the Modularity (Q) and Normalized Mutual Information (NMI) have been used for evaluating the validation and quality of the detected community structures. Although many optimization algorithms have been implemented to unfold the structures of communities, the influence of NMI on the Q, and vice versa, between a detected partition and the correct partition in signed and unsigned networks is unclear. For this reason, in this paper, we investigate the correlation between Q and NMI in signed and unsigned networks. The results show that there is no direct relationship between Q and NMI in both types of networks.

Community structure is an important topological property of complex networks, which has great significance for understanding the function and organization of networks. Generally, community detection can be formulated as a single-objective or multi-objective optimization problem. Most existing optimization-based community detection algorithms are only applicable to disjoint community structure. However, it has been shown that in most real-world networks, a node may belong to multiple communities implying overlapping community structure. In this paper, we propose a multi-objective evolutionary algorithm for identifying overlapping community structure in complex networks based on the framework of non-dominated sorting genetic algorithm. Two negatively correlated evaluation metrics of community structure, termed as negative fitness sum and unfitness sum, are adopted as the optimization objectives. In our algorithm, link-based adjacency representation of overlapping community structure and a population initialization method based on local expansion are proposed. Extensive experimental results on both synthetic and real-world networks demonstrate that the proposed algorithm is effective and promising in detecting overlapping community structure in complex networks.

Chapter 7 - MOEA-based community detection

Community detection has arisen as an important topic of many different research areas such as sociology, biology and computer science. However, with the appearance of big data and the rapid increasing size of real-world networks, a traditional evolutionary algorithm is unable or inefficient to solve the community detection problem in large-scale networks. In this paper, a distributed multi-objective evolutionary algorithm (DMOCD) for community detection is proposed. DMOCD is implemented based on Apache Spark and Resilient Distributed Datasets. The proposed distributed framework maintains a set of evolving populations (sub-populations) which evolve separately with different crossover and mutation parameters and an external repository as an elite archive to store the non-dominated individuals. A label propagation-based initialization method, a segmented crossover and mutation tactic for large-scale network are introduced. Experiments on both artificial and real-world networks prove that the proposed method is effective for community detection problems in small-scale networks and is able to process the large-scale networks which the stand-alone multi-objective evolutionary algorithms cannot deal with.

Community detection is useful for better understanding of the structure of complex networks, and aids in the extraction of required information from such networks. Community detection problem can be modelled as an NP-hard combinatorial optimization problem. Many optimization algorithms (both single -objective and multi-objectives) have been implemented to address community detection problem, where the first objective is usually representing the maximization of the internal connections, while the second objective represents the minimization of the external connections between the communities or clusters. In this research, an enhanced mutation operator is proposed for improving the search performance of multi-objective evolutionary algorithm with decomposition (MOEA/D), based on the types of the connections between the nodes. The proposed algorithm was evaluated based on a set of five benchmark datasets, in terms of Normalized Mutual Information (NMI), Weighted NMI (WNMI), Signed Modularity (Qs), and Error rate (Error). The results showed that our proposed enhanced algorithm has attained the best position as compared to the standard version of MOEA/D, and other state of art research papers.

A multi-objective adaptive evolutionary algorithm to extract communities in networks

Community detection is crucial in the analysis of social networks. Its main goal is to find groups of users densely connected among them, and sparsely connected between themselves. There are so many algorithms which makes it difficult for researchers to choose the best one for a specific dataset. In this paper, we provide a thorough comparison between five Community Detection (CD) algorithms- Girman-Newman (GN), Clauset-Newman-Moore (CNM), Label Propagation Algorithm (LPA), Louvain and Leiden. To evaluate in real social network datasets like Zachary's Karate Club, Dolphin networks and bigger ones such as Facebook, Twitter, LinkedIn along with citation networks we used different metrics modularity and NMI. We employed Normalized Mutual Information (NMI) to quantify the agreement of detected communities with their true ground-truth score and modularity for evaluating the overall quality of partitions given by diverse methods. Our experiments show that greedy and modularity-optimization algorithms are particularly well-suited. Notably, the Leiden algorithm had a better modularity value than Louvain (Q = 0.9141 and Q = 0.9051 of LinkedIn Network respectively) in most of the dataset. The NMI plot provided more explanation about Clauset-Newman-Moore (CNM), Louvain and Label Propagation Algorithm (LPA)which are in good agreement on community detection and their NMI score. These results would allow us to choose more rationally among the different community detection algorithms for social network analysis, by providing accurate quantitative benchmarks.

Community Detection is used to discover a non-trivial organization of the network and to extract the special relations among the nodes which can help in understanding the structure and the function of the networks. However, community detection in social networks is a vast and challenging task, in terms of detected communities accuracy and computational overheads. In this paper, we propose a new algorithm Enhanced Algorithm for Community Detection in Social Networks – CGraM, for community detection using the graph measures eccentricity, harmonic centrality and modularity. First, the centre nodes are identified by using the eccentricity and harmonic centrality, next a preliminary community structure is formed by finding the similar nodes using the jaccard coefficient. Later communities are selected from the preliminary community structure based on the number of inter-community and intra-community edges between them. Then the selected communities are merged till the modularity improves to form the better resultant community structure. This method is tested on the real networks and the results are evaluated using the evaluation metrics modularity and Normalized Mutual Information (NMI). The results are visualized and also compared with the state-of-the-art algorithms that covers louvian, walktrap, infomap, label propagation, fast greedy and eigen vector for more accurate analysis. CGraM achieved the better modularity and improved NMI values comparatively with other algorithms and gives improved results collaboratively when compared to previous methods.

Notice of Violation of IEEE Publication Principles<br><br>"Non-uniform circular-shaped antenna array design and synthesis — A Multi-Objective Evolutionary approach"<br><br>by Jubin Hazra<br>in the International Conference on Computer Communication and Informatics (ICCCI), 2012, pp. 1 – 4<br><br>After careful and considered review of the content and authorship of this paper by a duly constituted expert committee, this paper has been found to be in violation of IEEE's Publication Principles.<br><br>This paper contains significant portions of original text from the paper cited below. The original text was copied with insufficient attribution (including appropriate references to the original author(s) and/or paper title) and without permission.<br><br>Due to the nature of this violation, reasonable effort should be made to remove all past references to this paper, and future references should be made to the following article:<br><br>"Non-uniform Circular-Shaped Antenna Array Design and Synthesis - A Multi-Objective Approach"<br>by Saurav Ghosh, Subhrajit Roy, Sk. Minhazul Islam , Shizheng Zhao, Ponnuthurai Nagaratnam Suganthan, and Swagatam Das<br>in the Lecture Notes in Computer Science, Volume 7077, Swarm, Evolutionary, and Memetic Computing, 2011, pp. 223 – 230<br><br> <br/> Design of non-uniform circular antenna arrays is one of the important optimization problems in electromagnetic domain. While designing a non-uniform circular array the goal of the designer is to achieve minimum side lobe levels with maximum directivity. In contrast to the single-objective methods that attempt to minimize a weighted sum of the four objectives considered here, in this article we consider these as four distinct objectives that are to be optimized simultaneously in a multi-objective (MO) framework using one of the best known Multi-Objective Evolutionary Algorithms (MOEAs) called NSGA-II. This MO approach provides greater flexibility in design by producing a set of final solutions with different trade-offs among the four objective from which the designer can choose one as per requirements. To the best of our knowledge, other than the single objective approaches, no MOEA has been applied to design a non-uniform circular array before. Simulations have been conducted to show that the best compromise solution obtained by NSGA-II is far better than the best results achieved by the single objective approaches by using the differential evolution (DE) algorithm and the Particle Swarm Optimization (PSO) algorithm.

Community detection in social networks plays a vital role. The understanding and detection of communities in social networks is a challenging research problem. There exist many methods for detecting communities in large scale networks. Most of these methods presume the predefined number of communities and apply detection methods to exactly find out the predefined number of communities. However, there may not be the predefined number of communities naturally occurring in the social networks. Application of brute force inorder to predefine the number of communities goes against the natural occurrence of communities in the networks. In this paper, we propose a method for community detection which explores Self Organizing Maps for natural cluster selection and modularity measure for community strength identification. Experimental results on the real world network datasets show the effectiveness of the proposed approach.

The authors use four criteria to examine a novel community detection algorithm: (a) effectiveness in terms of producing high values of normalized mutual information (NMI) and modularity, using well-known social networks for testing; (b) examination, meaning the ability to examine mitigating resolution limit problems using NMI values and synthetic networks; (c) correctness, meaning the ability to identify useful community structure results in terms of NMI values and Lancichinetti-Fortunato-Radicchi (LFR) benchmark networks; and (d) scalability, or the ability to produce comparable modularity values with fast execution times when working with large-scale real-world networks. In addition to describing a simple hierarchical arc-merging (HAM) algorithm that uses network topology information, we introduce rule-based arc-merging strategies for identifying community structures. Five well-studied social network datasets and eight sets of LFR benchmark networks were employed to validate the correctness of a ground-truth community, eight large-scale real-world complex networks were used to measure its efficiency, and two synthetic networks were used to determine its susceptibility to two resolution limit problems. Our experimental results indicate that the proposed HAM algorithm exhibited satisfactory performance efficiency, and that HAM-identified and ground-truth communities were comparable in terms of social and LFR benchmark networks, while mitigating resolution limit problems.