Rank Cover Trees for Nearest Neighbor Search

Virtually all known distance-based similarity search indexes make use of some form of numerical constraints (triangle inequality, additive distance bounds, . . . ) on similarity values for pruning and selection. The use of such numerical constraints, however, often leads to large variations in the numbers of objects examined in the execution of a query, making it difficult to control the execution costs. We introduce a probabilistic data structure for similarity search, the Rank Cover Tree (Rct), that entirely avoids the use of numerical constraints. All internal selections are made according to the ranks of the objects with respect to the query, allowing much tighter control on the overall execution costs. A rank-based probabilistic analysis shows that with very high probability, the Rct returns a correct query result in time that depends competitively on a measure of the intrinsic dimensionality of the data set.