We present a tree data structure for fast nearest neighbor operations in general npoint metric spaces (where the data set consists of n points). The data structure requires O(n) space regardless of the metric's structure yet maintains all performance properties of a navigating net (Krauthgamer & Lee, 2004b) . If the point set has a bounded expansion constant c, which is a measure of the intrinsic dimensionality, as defined in (Karger & Ruhl, 2002) , the cover tree data structure can be constructed in O c 6 n log n time. Furthermore, nearest neighbor queries require time only logarithmic 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 natural machine learning datasets.
The Cover-Tree REF also constructs a tree data structure for NNS.
Cover trees for nearest neighbor
ICML '06
Mathematics Computer Science