PAC Nearest Neighbor Queries: Using the Distance Distribution for Searching in High-Dimensional Metric Spaces

In this paper we introduce a new paradigm for similarity search, called PAC-NN (probably approximately correct nearest neighbor) queries, aiming to break the “dimensionality curse” which inhibits current approaches to be applied in high-dimensional spaces. PAC-NN queries return, with probability at least 1− δ, a (1+ )-approximate NN – an object whose distance from the query q is less than (1 + ) times the distance between q and its NN. We describe how the distance distribution of the query object can be used to determine a suitable stopping condition with probabilistic guarantees on the quality of the result, and then analyze performance of both sequential and index-based PAC-NN algorithms. This shows that PAC-NN queries can be efficiently processed even on very high-dimensional spaces and that control can be exerted in order to tradeoff between the accuracy of the result and the cost.