Densest subgraph in streaming and MapReduce
Proceedings of the VLDB Endowment
A general collaborative filtering framework based on matrix bordered block diagonal forms
Proceedings of the 24th ACM Conference on Hypertext and Social Media
Improve collaborative filtering through bordered block diagonal form matrices
Proceedings of the 36th international ACM SIGIR conference on Research and development in information retrieval
Localized matrix factorization for recommendation based on matrix block diagonal forms
Proceedings of the 22nd international conference on World Wide Web
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This paper presents a method for identifying a set of dense subgraphs of a given sparse graph. Within the main applications of this “dense subgraph problem,” the dense subgraphs are interpreted as communities, as in, e.g., social networks. The problem of identifying dense subgraphs helps analyze graph structures and complex networks and it is known to be challenging. It bears some similarities with the problem of reordering/blocking matrices in sparse matrix techniques. We exploit this link and adapt the idea of recognizing matrix column similarities, in order to compute a partial clustering of the vertices in a graph, where each cluster represents a dense subgraph. In contrast to existing subgraph extraction techniques which are based on a complete clustering of the graph nodes, the proposed algorithm takes into account the fact that not every participating node in the network needs to belong to a community. Another advantage is that the method does not require to specify the number of clusters; this number is usually not known in advance and is difficult to estimate. The computational process is very efficient, and the effectiveness of the proposed method is demonstrated in a few real-life examples.