Data summarization aims at utilizing a small-scale summary to represent massive datasets as a whole, which is useful for visualization and information sipped generation. However, most existing studies of hierarchical summarization only work onone single treeby selecting$k$representative nodes, which neglects an important problem of comparative summarization on two trees. In this paper, given two trees with the same topology structure and different node weights, we aim at finding$k$representative nodes, where$k_{1}$nodes summarize the common relationship between them and$k_{2}$nodes highlight significantly different subtrees meanwhile satisfying$k_{1}+k_{2}=k$. To optimize summarization results, we introduce a scaling coefficient for balancing the summary view between two subtrees in terms of similarity and difference. Additionally, we propose a novel definition based on the Hellinger distance to quantify the node distribution difference between two subtrees. We present a greedy algorithm SVDT to find high-quality results with approximation guaranteed in an efficient way. Furthermore, we explore an extension of our comparative summarization to handle two trees with different structures. Extensive experiments demonstrate the effectiveness and efficiency of our SVDT algorithm against existing summarization competitors.

Community detection is an important topic in network analysis, and recently many community detection methods have been developed on top of the Nonnegative Matrix Factorization (NMF) technique. Most NMF-based community detection methods only utilize the first-order proximity information in the adjacency matrix, which has some limitations. Besides, many NMF-based community detection methods involve sparse regularizations to promote clearer community memberships. However, in most of these regularizations, different nodes are treated equally, which seems unreasonable. To dismiss the above limitations, this article proposes a community detection method based on node centrality under the framework of NMF. Specifically, we design a new similarity measure which considers the proximity of higher-order neighbors to form a more informative graph regularization mechanism, so as to better refine the detected communities. Besides, we introduce the node centrality and Gini impurity to measure the importance of nodes and sparseness of the community memberships, respectively. Then, we propose a novel sparse regularization mechanism which forces nodes with higher node centrality to have smaller Gini impurity. Extensive experimental results on a variety of real-world networks show the superior performance of the proposed method over thirteen state-of-the-art methods.

Recommender system provides personalized suggestions based on users' interests and social connections. However, most existing social recommendation models utilize social relationships in a direct manner, i.e., they only consider the user-user connections, neglecting the clustering nature of social networks. As social information recursively spreads in the social network, the community structure, which contains richer information in contrast to pure user-user relationships, would emerge. To dismiss these limitations, in this paper, we propose a unified recommendation framework named Simultaneous Community detection and Singular Value Decomposition (SCSVD), which utilizes the underlying community structure to regularize user latent preferences. We propose a well-designed iterative optimization algorithm to tackle social recommendation efficiently. In addition, we theoretically analyze the proposed algorithm in terms of convergence, time complexity, and also the unified process of community detection and user embedding learning. Extensive experiments are conducted on three benchmark real-world datasets of product reviews, demonstrating the effectiveness, robustness, and flexibility of SCSVD in both rating prediction and top-N recommendation tasks, compared to fifteen state-of-the-art approaches.

Social recommendation aims at improving recommendation performance by incorporating social information. Most existing social recommender systems only utilize the one-hop interpersonal social information, neglecting the community structure emerged in social networks, which may contain additional conducive information. In this paper, we propose a unified Simultaneous Community detection and Singular Value Decomposition (SCSVD) framework for community-aware social recommendation. An efficient optimization algorithm is also derived to optimize SCSVD, with an analysis of convergence and computational complexity. Comprehensive experimental results on three real-world benchmark datasets demonstrate the effectiveness of SCSVD, over both traditional matrix factorization based recommendation models and advanced neural network based recommendation models.