Diversified Top-k Similarity Search in Large Attributed Networks

Given a large network and a query node, finding its top-k similar nodes is a primitive operation in many graph-based applications. Recently enhancing search results with diversification have received much attention. In this paper, we explore an novel problem of searching for top-k diversified similar nodes in attributed networks, with the motivation that modeling diversification in an attributed network should consider both the emergence of network links and the attribute features of nodes such as user profile information. We formulate this practical problem as two optimization problems: the Attributed Coverage Diversification (ACD) problem and the r-Dissimilar Attributed Coverage Diversification (r-DACD) problem. Based on the submodularity and the monotonicity of ACD, we propose an efficient greedy algorithm achieving a tight approximation guarantee of 1-1/e. Unlike the expension based methods only considering nodes' neighborhood, ACD generalize the definition of diversification to nodes' own features. To capture diversification in topological structure of networks, the r-DACD problem introduce a dissimilarity constraint. We refer to this problem as the Dissimilarity Constrained Non-monotone Submodular Maximization (DCNSM) problem. We prove that there is no constant-factor approximation for DCNSM, and also present an efficient greedy algorithms achieving $1/\rho$ approximation, where $\rho\le\Delta$, $\Delta$ is the maximum degree of its dissimilarity based graph. To the best of our knowledge, it is the first approximation algorithm for the Submodular Maximization problem with a distance constraint. The experimental results on real-world attributed network datasets demonstrate the effectiveness of our methods, and confirm that adding dissimilarity constraint can significantly enhance the performance of diversification.