CIM: Categorical influence maximization

Influence maximization is an interesting and well-motivated problem in social networks study. The traditional influence maximization problem is defined as finding the most "influential" vertices without considering the vertex attribute. Though it is useful, in practice, there exist different attributes for vertices, e.g., mobile phone social networks. So, it is more important and useful to capture the vertices having the maximum influence in different search categories, which is exactly the problem that we study in this work. Thus, we name this new problem as Categorical Influence Maximization (CIM). Compare with identifying maximum influence vertices in a single category social network, CIM is much harder because we have to deal with large scale complex data. In this work, based on the observations from real mobile phone social network data, we propose a Probability Distribution based Search method (PDS) to tackle the CIM problem. Specifically, the PDS method consists of three steps. First, we propose a probability distribution based parameter free method (PD-max) to identify the maximum influential vertex set for the specified category by studying the categorical influential distribution within a time interval. Second, among these detected influential vertices, we design a probability distribution based minimizing method (PD-minmax) to find the minimum number of vertices in each category having the maximum influences. We test our solutions with real data sets, which were collected for one year in a city in China. The extensive experiment results show that our methods outperform the existing ones.