Significant Geo-Social Group Discovery over Location-Based Social Network ^†

Geo-social community detection over location-based social networks combining both location and social factors to generate useful computational results has attracted increasing interest from both industrial and academic communities. In this paper, we formulate a novel community model, termed geo-social group (GSG), to enforce both spatial and social factors to generate significant computational patterns and to investigate the problem of community detection over location-based social networks. Specifically, GSG detection aims to extract all group-venue clusters, where users are similar to each other in the same group and they are located in a minimum covering circle (MCC) for which the radius is no greater than a distance threshold $\gamma$. Then, we present a GSGD algorithm following a three-step paradigm to enumerate all qualified GSGs in a large network. We propose effective optimization techniques to efficiently enumerate all communities in a network. Furthermore, we extend a significant GSG detection problem to top-k geo-social group (TkGSG) mining. Rather than extracting all qualified GSGs in a network, TkGSG aims to return k feasibility groups to guarantee the diversity. We prove the hardness of computing the TkGSGs. Nevertheless, we propose the effective greedy approach with a guaranteed approximation ratio of $1-1/e$. Extensive empirical studies on real and synthetic networks show the superiority of our algorithm when compared with existing methods and demonstrate the effectiveness of our new community model and the efficiency of our optimization techniques.