Bregman Vantage Point Trees for Efficient Nearest Neighbor Queries

Description

Nearest Neighbor (NN) retrieval is a crucial tool of many computer vision tasks. Since the brute-force naive search is too time consuming for most applications, several tailored data structures have been proposed to improve the efficiency of NN search. Among these, vantage point tree (vp-tree) was introduced for information retrieval in metric spaces. Vptrees have recently shown very good performances for image patch retrieval with respect to the L2 metric. In this paper we generalize the seminal vp-tree construction and search algorithms to the broader class of Bregman divergences. These distorsion measures are preferred in many cases, as they also handle entropic distances (e.g., Kullback-Leibler divergence) besides quadratic distances. We also extend vp-tree to deal with symmetrized Bregman divergences, which are commonplace in applications of content-based multimedia retrieval. We evaluated performances of our Bvp-tree for exact and approximate NN search on two image feature datasets. Our results show good performances of Bvp-tree, specially for symmetrized Bregman NN queries.

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