Cover Trees for Nearest Neighbor

We present a tree data structure for fast nearest neighbor operations in general n- point metric spaces (where the data set con- sists of n points). The data structure re- quires O(n) space regardless of the met- ric's structure yet maintains all performance properties of a navigating net [KL04a]. If the point set has a bounded expansion con- stant c, which is a measure of the intrinsic dimensionality (as defined in [KR02]), the cover tree data structure can be constructed in O(c^6 n log n) time. Furthermore, nearest neighbor queries require time only logarith- mic in n, in particular O(c^{12} log n) time. Our experimental results show speedups over the brute force search varying between one and several orders of magnitude on nat- ural machine learning datasets.

• Type: Conference
• Year: 2006
• Where: ICML
• Authors: Alina Beygelzimer, Sham Kakade, John Langford
• Keywords: Cover Tree, Nearest Neighbour