Ranking on Data Manifold with Sink Points

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Ranking is an important problem in various applications, such as Information Retrieval (IR), natural language processing, computational biology, and social sciences. Many ranking approaches have been proposed to rank objects according to their degrees of relevance or importance. Beyond these two goals, diversity has also been recognized as a crucial criterion in ranking. Top ranked results are expected to convey as little redundant information as possible, and cover as many aspects as possible. However, existing ranking approaches either take no account of diversity, or handle it separately with some heuristics. In this paper, we introduce a novel approach, Manifold Ranking with Sink Points (MRSPs), to address diversity as well as relevance and importance in ranking. Specifically, our approach uses a manifold ranking process over the data manifold, which can naturally find the most relevant and important data objects. Meanwhile, by turning ranked objects into sink points on data manifold, we can effectively prevent redundant objects from receiving a high rank. MRSP not only shows a nice convergence property, but also has an interesting and satisfying optimization explanation. We applied MRSP on two application tasks, update summarization and query recommendation, where diversity is of great concern in ranking. Experimental results on both tasks present a strong empirical performance of MRSP as compared to existing ranking approaches.