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Fuzzy C-means (FCM) is a clustering method used for collecting similar data elements within the group according to specific measurements. Tabu is a heuristic algorithm. In this paper, Probabilistic Tabu Search for FCM implemented to find a global clustering based on the minimum value of the Fuzzy objective function. The experiments designed for different networks, and cluster’s number the results show the best performance based on the comparison that is done between the values of the objective function in the case of using standard FCM and Tabu-FCM, for the average of ten runs.

This paper presents a problem of community detection in sparse network. Graph represents the network with {0, 1} symmetric matrix, this matrix is defined to be sparse when most of its entries are zeros. The problem of community detection of this type of networks is non-deterministic polynomial-time hardness (NP-hard) problem. Here, we give a simple idea to regularize the sparse matrix by adding a heuristic parameter to the entries of the matrix. This work performs integrating Tabu Search via Fuzzy C-mean to compute variants of the modularity maximization. The results show the ability of the proposed method to define structure of the network by optimizing different types of the quality functions; the results show the global function gives the high value in must runs when apply it on a large sparse real networks.

Structure of network, which is known as community detection in networks, has received a great attention in diverse topics, including social sciences, biological studies, politics, etc. There are a large number of studies and practical approaches that were designed to solve the problem of finding the structure of the network. The definition of complex network model based on clustering is a non-deterministic polynomial-time hardness (NP-hard) problem. There are no ideal techniques to define the clustering. Here, we present a statistical approach based on using the likelihood function of a Stochastic Block Model (SBM). The objective is to define the general model and select the best model with high quality. Therefore, integrating the Tabu Search method with Fuzzy c-Mean (FCM) is implemented in different settings. The experiments are designed to find the best structure for different types of networks by maximizing the objective functions. SBM selections are computed by applying two types of criteria, namely Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC). The results show the ability of the proposed method to find the best community of the given networks.

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