The information available in multi-attributed road-social networks includes network structure, location information, and numerical attributes. Most studies mainly focus on mining communities by combining structure with attributes or structure with location, which do not consider structure, attributes, and location simultaneously. Therefore, we propose a parameter-free algorithm, called LCDMRS, to mine local communities in multi-attributed road-social networks. LCDMRS extracts a sub-network surrounding the given node and embeds it to generate the vector representations of nodes, which incorporates both structural and attributed information. Based on the vector representations of nodes, the average cosine similarity between nodes is designed to ensure both the structural and attributed cohesiveness of the community, while the community node density is designed to ensure the spatial cohesiveness of the community. Targeting the community node density and cosine similarity of nodes, LCDMRS takes the given node as the starting node and employs the community dominance relation to expand the community outward. Experimental results on multiple real-world datasets demonstrate LCDMRS outperforms comparison algorithms.

Local spatial-aware community detection refers to detecting a spatial-aware community for a given node using local information. A spatial-aware community means that nodes in the community are tightly connected in structure, and their locations are close to each other. Existing studies focus on detecting the local non-overlapping spatial-aware community, i.e., detecting a spatial-aware community containing the given node. However, many geosocial networks often contain overlapping spatial-aware communities. Therefore, we propose a local overlapping spatial-aware community detection (LOSCD) problem, which aims to detect all spatial-aware communities that contain a given node with local information. To address LOSCD problem, we design an algorithm based on Spatial Modularity and Edge Similarity, called SMES. SMES contains two processes: spatial expansion and structure detection. The spatial expansion process involves using spatial modularity to identify nodes that are spatially close, while the structural detection process employs edge similarity to identify nodes that are structurally close. Experimental results demonstrate that SMES outperforms comparison algorithms in terms of both structural and spatial cohesiveness.

Individuals are often involved in multiple online social networks. Considering that owners of these networks are unwilling to share their networks, some global algorithms combine information from multiple networks to detect all communities in multiple networks without sharing their edges. When data owners are only interested in the community containing a given node, it is unnecessary and computationally expensive for multiple networks to interact with each other to mine all communities. Moreover, data owners who are specifically looking for a community typically prefer to provide less data than the global algorithms require. Therefore, we propose the Local Collaborative Community Detection problem (LCCD). It exploits information from multiple networks to jointly detect the local community containing a given node without directly sharing edges between networks. To address the LCCD problem, we present a method developed from M method, called colM, to detect the local community in multiple networks. This method adopts secure multiparty computation protocols to protect each network’s private information. Our experiments were conducted on real-world and synthetic datasets. Experimental results show that colM method could effectively identify community structures and outperform comparison algorithms.

Owing to the lack of a universal definition of communities, some semi-supervised community detection approaches learn the concept of community structures from known communities, and then dig out communities using learned concepts of communities. In some cases, users are only interested in the community containing a given node. However, communities detected by these semi-supervised approaches may not contain a given node. Besides, these methods traverse the entire network to detect many communities and cost more resources than a local algorithm. Therefore, it is necessary and meaningful to find the local community that contains a given node with prior information on the local network around the given node. We call this a Semi-supervised Local Community Detection (SLCD) problem. In this paper, prior information refers to certain known communities. To address the SLCD problem, we propose the Semi-supervised Local community detection with the Structural Similarity algorithm, called SLSS, which uses some known communities instead of all known communities. The idea of SLSS is to use the structural similarity between the known communities and the detected community, calculated by the graph kernel, to guide the expansion of the community. Experimental results show that SLSS outperforms other algorithms on six real-world datasets.

The identification of the local community structure in geo-social networks has been gaining increasing attention. The structure of geo-social networks evolves over time with the addition/deletion of edges/nodes and the update of node locations, which has motivated recent studies to mine local communities in dynamic geo-social networks. Mining communities in evolving geo-social networks is essential for understanding the evolution of group behaviors. However, in most previous studies on the community mining in dynamic networks, local spatial-aware communities were not identified in evolving geo-social networks. Therefore, in this study, the problem of determining local spatial-aware communities in evolving geo-social networks is proposed. To address this problem, we propose a parameter-free algorithm, called LSADEN. Specifically, LSADEN involves two main steps: i) selecting candidate nodes, where LSADEN defines the community dominance relation under dynamic environments to obtain candidate nodes that improve the community in terms of the community quality or the smoothness between communities at adjacent time stamps; ii) community expansion, where LSADEN designs the Manhattan distance of communities to add some candidate nodes to the local community. Experimental results on six real-world datasets and one synthetic dataset show that LSADEN performs well both in terms of the quality of communities and the smoothness between communities at adjacent time stamps.

In real-world social networks, global information (e.g., the number of nodes and the connections between them) is incomplete or expensive to acquire; therefore, local community detection becomes especially important. Local community detection is used to identify the local community to which the given starting node belongs according to local information. For a given node, most existing local community detection methods can only find single scale local communities but not those of variable sizes. However, local communities with different scales are often required. Therefore, it is necessary and meaningful to find local communities of the given starting node with different scales; we call this multiscale local community detection. In this paper, we propose a new local modularity inspired by the global modularity and prove the equivalence of the proposed local modularity with two other typical local modularities. Furthermore, to detect local communities with different scales, we present a method based on the proposed local modularity. We test this method on several synthetic and real datasets, and the experimental results indicate that the detected community is meaningful and its scale can be changed reasonably.

Local community detection refers to finding the community that contains the given node based on local information, which becomes very meaningful when global information about the network is unavailable or expensive to acquire. Most studies on local community detection focus on finding non-overlapping communities. However, many real-world networks contain overlapping communities like social networks. Given an overlapping node that belongs to multiple communities, the problem is to find communities to which it belongs according to local information. We propose a framework for local overlapping community detection. The framework has three steps. First, find nodes in multiple communities to which the given node belongs. Second, select representative nodes from nodes obtained above, which tends to be in different communities. Third, discover the communities to which these representative nodes belong. In addition, to demonstrate the effectiveness of the framework, we implement six versions of this framework. Experimental results demonstrate that the six implementation versions outperform the other algorithms.

Clustering is a classical unsupervised learning task, which is aimed to divide a data set into several groups with similar objects. Clustering problem has been studied for many years, and many excellent clustering algorithms have been proposed. In this paper, we propose a novel clustering method based on density, which is simple but effective. The primary idea of the proposed method is given as follows. Firstly, the point with the largest local density in a cluster is considered as the cluster center. The local density of each point is estimated based on the distance (called radius) between the point and its k-th nearest neighbor. The point with a smaller radius indicates a larger local density. Secondly, the difference of the local densities between each two internal points should be small, while the difference between the density of a border point and the density of an internal point should be relatively large. Thirdly, if the intersection of k nearest neighbors of two points is small, they should be assigned to different clusters. The proposed algorithm has been compared with a typical clustering algorithm named FDPCluster, and the experimental results show that our algorithm has better clustering quality.