A fuzzy adaptive resonance theory inspired overlapping community detection method for online social networks
Introduction
Networks are used to represent many complex systems in sociology, biology and computer science. When the number of entities that are part of a network is very large and the associations between them are also large, then such a network can be called as complex network. World Wide Web, information systems, social networks and collaboration networks are some of the real world systems which are represented using complex networks [1]. Any system possessing a large number of interacting elements can be represented using complex network. The study of complex network has grown rapidly in recent years especially due to the advancement in computing and communication technology [2]. Most of the complex networks will not have a centralized authority and are self-organized. Complex network analysis is defined as the mathematical analysis of the relation between entities in the network to obtain useful inferences about the network. Complex network analysis is also used to identify and predict the growth of the network [3].
In this paper, we consider online social networks, which have become one of the most popular complex networks. The popularity of Online Social networks (OSNs) has gained much importance with the proliferation of mobile computing devices. Online social network analysis (OSNA) has become one of the hot topics with the increased amount of information spread across the nodes in the social networks. OSN is a complex network in which the nodes represent actors/nodes in the network and the edges between them illustrate the friendship between them. The complex network can be a directed graph (as in case of Twitter) or can be undirected (as in case of Facebook, LinkedIn). The networks considered for OSNA in this paper are undirected graphs. Adjacency matrices and adjacency lists are the common mathematical representation of undirected as well as directed graphs.
The selection of friends in online social network depends on numerous factors such as offline relationship, personality traits and is not limited to the number of common friends. These factors are not concisely bounded with any values and are vague in nature. The factors such as personality traits vary with perception and cannot be defined precisely. Crisp set (sharp) approach cannot be used to define the criteria for community detection as the boundary will be vague in nature. Fuzzy logic can be made use in these situations where the values cannot be distinctly defined and processed. Social network analysis deals with different issues such as centrality, community detection, sentimental analysis, collaborative filtering and recommender systems where fuzzy logic can be implemented to get realistic results [4]. The major point that has to be considered in community detection is that humans are capable of filling many roles in diverse contexts and a strict partitioning may not be realistic [5]. Each vertex in the network may belong to each community to a different extent. Illustrations of both crisp and fuzzy overlapping can be found in real networks. For instance, in a social network website such as Facebook, a person regularly has a place with numerous groups of diverse sorts: such as partners, previous associates and relatives, to mention a few [2]. This is an illustration of crisp overlapping. Alternately, collaboration network of researchers, the overlapping might be fuzzy in light of the fact that a specialist who has a place with a few groups can't be completely included with every one of them because of constrained time and assets. Fuzzy and crisp overlapping can likewise be found in biological networks and other types of networks. This paper focus on the crisp overlapping community detection in social networks and fuzzy overlapping community detection is not within the scope of this paper.
This paper is divided into six sections. Section 2 discusses the various community detection techniques and the related work in overlapping community detection. Section 3 proposes a Possibilistic mathematical model for community detection in online social networks. Community detection based on Fuzzy adaptive resonance theory is proposed and discussed in Section 4. The algorithm is implemented and the results are described in Section 5. The future possibilities of the algorithm are discussed in Section 6.
Section snippets
Community detection in online social networks
In the study of complex network systems, a network is said to have a community structure if the network's nodes can be effectively gathered into (possibly covering) sets of nodes such that every arrangement of nodes is thickly joined inside. In the specific instance of non-covering community discovering, this infers that the network separates actually into cluster of nodes with thick associations inside and sparser associations between clusters. Communities can effectively help in understanding
A possibilistic mathematical model for overlapping community detection in online social networks
We propose and validate a probabilistic mathematical model for online social networks and overlapping community detection in online social networks. Some of the notations used in this mathematical model are described below.
xj- Number of nodes connected with node j
rj- Average number of interaction of node j
σij – Covariance of number of interaction between node j and node i
kj- Increase in modularity by adding a node j to a community.
m- The maximum number of nodes in a community 1 ≤ m ≤ n
∈ j −
Overlapping community detection using fuzzy adaptive resonance theory
Adaptive resonance theory (ART) is a hypothesis created by Stephen Grossberg and Gail Carpenter after thoroughly researching on information processing by the human brain [27]. The human brain has the unique ability as a primitive function to group objects and concepts and to think abstractly to perform clustering. ART is widely used for pattern recognition, clustering and prediction. The plasticity stability problem has been solved using Adaptive resonance theory. The Adaptive resonance theory1
Results and discussion
The initial task involved in the experiment was to obtain the value for vigilance threshold. In order to achieve this, the fuzzy ART inspired overlapping community detection algorithm was initially tested with Amazon dataset to fix the vigilance threshold value. A higher vigilance threshold will result in the detection of smaller fragmented communities while a smaller vigilance threshold will lead to a larger imprecise community.
Conclusion and further study
This paper, as demonstrated in the previous sections, proposes and implements a novel fuzzy ART inspired algorithm for overlapping community detection in social networks. It also draws attention to various limitations of existing community detection algorithms and points out that the previous information of the nodes is not taken into account in these analyses. This, the paper argues, leads to plasticity stability problem. The Fuzzy ART inspired community detection algorithm solves the
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