On the Complexity of Query Result Diversification

Query result diversification is a bi-criteria optimization problem for ranking query results. Given a database D, a query Q and a positive integer k, it is to find a set of k tuples from Q(D) such that the tuples are as relevant as possible to the query, and at the same time, as diverse as possible to each other. Subsets of Q(D) are ranked by an objective function defined in terms of relevance and diversity. Query result diversification has found a variety of applications in databases, information retrieval and operations research. This paper studies the complexity of result diversification for relational queries. We identify three problems in connection with query result diversification, to determine whether there exists a set of k tuples that is ranked above a bound with respect to relevance and diversity, to assess the rank of a given k-element set, and to count how many k-element sets are ranked above a given bound. We study these problems for a variety of query languages and for three objective functions. We establish the upper and lower bounds of these problems, all matching, for both combined complexity and data complexity. We also investigate several special settings of these problems, identifying tractable cases. 1

Learning to Diversify Web Search Results with a Document Repulsion Model

Search diversification (also called diversity search), is an important approach to tackling the query ambiguity problem in information retrieval. It aims to diversify the search results that are originally ranked according to their probabilities of relevance to a given query, by re-ranking them to cover as many as possible different aspects (or subtopics) of the query. Most existing diversity search models heuristically balance the relevance ranking and the diversity ranking, yet lacking an efficient learning mechanism to reach an optimized parameter setting. To address this problem, we propose a learning-to-diversify approach which can directly optimize the search diversification performance (in term of any effectiveness metric). We first extend the ranking function of a widely used learning-to-rank framework, i.e., LambdaMART, so that the extended ranking function can correlate relevance and diversity indicators. Furthermore, we develop an effective learning algorithm, namely Document Repulsion Model (DRM), to train the ranking function based on a Document Repulsion Theory (DRT). DRT assumes that two result documents covering similar query aspects (i.e., subtopics) should be mutually repulsive, for the purpose of search diversification. Accordingly, the proposed DRM exerts a repulsion force between each pair of similar documents in the learning process, and includes the diversity effectiveness metric to be optimized as part of the loss function. Although there have been existing learning based diversity search methods, they often involve an iterative sequential selection process in the ranking process, which is computationally complex and time consuming for training, while our proposed learning strategy can largely reduce the time cost. Extensive experiments are conducted on the TREC diversity track data (2009, 2010 and 2011). The results demonstrate that our model significantly outperforms a number of baselines in terms of effectiveness and robustness. Further, an efficiency analysis shows that the proposed DRM has a lower computational complexity than the state of the art learning-to-diversify methods

Sparse spatial selection for novelty-based search result diversification

Abstract. Novelty-based diversification approaches aim to produce a diverse ranking by directly comparing the retrieved documents. However, since such approaches are typically greedy, they require O(n 2) documentdocument comparisons in order to diversify a ranking of n documents. In this work, we propose to model novelty-based diversification as a similarity search in a sparse metric space. In particular, we exploit the triangle inequality property of metric spaces in order to drastically reduce the number of required document-document comparisons. Thorough experiments using three TREC test collections show that our approach is at least as effective as existing novelty-based diversification approaches, while improving their efficiency by an order of magnitude.

Efficient Diversification of Web Search Results

In this paper we analyze the efficiency of various search results diversification methods. While efficacy of diversification approaches has been deeply investigated in the past, response time and scalability issues have been rarely addressed. A unified framework for studying performance and feasibility of result diversification solutions is thus proposed. First we define a new methodology for detecting when, and how, query results need to be diversified. To this purpose, we rely on the concept of "query refinement" to estimate the probability of a query to be ambiguous. Then, relying on this novel ambiguity detection method, we deploy and compare on a standard test set, three different diversification methods: IASelect, xQuAD, and OptSelect. While the first two are recent state-of-the-art proposals, the latter is an original algorithm introduced in this paper. We evaluate both the efficiency and the effectiveness of our approach against its competitors by using the standard TREC Web diversification track testbed. Results shown that OptSelect is able to run two orders of magnitude faster than the two other state-of-the-art approaches and to obtain comparable figures in diversification effectiveness.Comment: VLDB201