Communities are prevalent in social networks, knowledge graphs, and biological networks. Recently, the topic of community search (CS), extracting a dense subgraph containing a query vertex q from a graph, has received great attention. However, existing CS solutions are designed for undirected graphs, and overlook directions of edges which potentially lose useful information carried on directions. In many applications (e.g., Twitter), users' relationships are often modeled as directed graphs (e.g., if a user a follows another user b, then there is an edge from a to b). In this paper, we study the problem of CS on directed graph. Given a vertex q of a graph G, we aim to find a densely connected subgraph containing q from G, in which vertices have strong interactions and high similarities, by using the minimum in/out-degrees metric. We first develop a baseline algorithm based on the concept of D-core. We further propose three index structures and corresponding query algorithms. Our experimental results on seven real graphs show that our solutions are very effective and efficient. For example, on a graph with over 1 billion of edges, we only need around 40mins to index it and $1\sim 2$ sec to answer a query.

Twitter is widely used all over the world, and a huge number of hot topics are generated by Twitter users in real time. These topics are able to reflect almost every aspect of people’s daily lives. Therefore, the detection of topics in Twitter can be used in many real applications, such as monitoring public opinion, hot product recommendation and incidence detection. However, the performance of traditional topic detection methods is still far from perfect largely owing to the tweets’ features, such as their limited length and arbitrary abbreviations. To address these problems, we propose a novel framework (MVTD) for Twitter topic detection using multiview clustering, which can integrate multirelations among tweets, such as semantic relations, social tag relations and temporal relations. We also propose some methods for measuring relations among tweets. In particular, to better measure the semantic similarity of tweets, we propose a new document similarity measure based on a suffix tree (STVSM). In addition, a new keyword extraction method based on a suffix tree is proposed. Experiments on real datasets show that the performance of MVTD is much better than that of a single view, and it is useful for detecting topics from Twitter.

Clustering of customer transaction data is an important procedure to analyze customer behaviors in retail and e-commerce companies. Note that products from companies are often organized as a product tree, in which the leaf nodes are goods to sell, and the internal nodes (except root node) could be multiple product categories. Based on this tree, we present a “personalized product tree“, named purchase tree, to represent a customer's transaction records. So the customers' transaction data set can be compressed into a set of purchase trees. We propose a partitional clustering algorithm, named PurTreeClust, for fast clustering of purchase trees. A new distance metric is proposed to effectively compute the distance between two purchase trees. To cluster the purchase tree data, we first rank the purchase trees as candidate representative trees with a novel separate density, and then select the top k customers as the representatives of k customer groups. Finally, the clustering results are obtained by assigning each customer to the nearest representative. We also propose a gap statistic based method to evaluate the number of clusters. A series of experiments were conducted on ten real-life transaction data sets, and experimental results show the superior performance of the proposed method.

Communities are prevalent in social networks, knowledge graphs, and biological networks. Recently, the topic of community search (CS) has received plenty of attention. The CS problem aims to look for a dense subgraph that contains a query vertex. Existing CS solutions do not consider the spatial extent of a community. They can yield communities whose locations of vertices span large areas. In applications that facilitate setting social events (e.g., finding conference attendees to join a dinner), it is important to find groups of people who are physically close to each other, so it is desirable to have a spatial-aware community (or SAC), whose vertices are close structurally and spatially. Given a graph G and a query vertex q, we develop an exact solution to find the SAC containing q, but it cannot scale to large datasets, so we design three approximation algorithms. We further study the problem of continuous SAC search on a "dynamic spatial graph", whose vertices' locations change with time, and propose three fast solutions. We evaluate the solutions on both real and synthetic datasets, and the results show that SACs are better than communities returned by existing solutions. Moreover, our approximation solutions perform accurately and efficiently.