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Finding typical instances is an effective approach to understand and analyze large data sets. In this paper, we apply the idea of typicality analysis from psychology and cognitive science to database query answering, and study the novel problem of answering top-k typicality queries. We model typicality in large data sets systematically. Three types of top-k typicality queries are formulated. To answer questions like "Who are the top-k most typical NBA players?", the measure of simple typicality is developed. To answer questions like "Who are the top-k most typical guards distinguishing guards from other players?", the notion of discriminative typicality is proposed. Moreover, to answer questions like "Who are the best k typical guards in whole representing different types of guards?", the notion of representative typicality is used. Computing the exact answer to a top-k typicality query requires quadratic time which is often too costly for online query answering on large databases. We develop a series of approximation methods for various situations: (1) the randomized tournament algorithm has linear complexity though it does not provide a theoretical guarantee on the quality of the answers; (2) the direct local typicality approximation using VP-trees provides an approximation quality guarantee; (3) a local typicality tree data structure can be exploited to index a large set of objects. Then, typicality queries can be answered efficiently with quality guarantees by a tournament method based on a Local Typicality Tree. An extensive performance study using two real data sets and a series of synthetic data sets clearly shows that top-k typicality queries are meaningful and our methods are practical.

Top-k typicality queries and efficient query answering methods on large databases