Cover trees for nearest neighbor

  • Authors:
  • Alina Beygelzimer;Sham Kakade;John Langford

  • Affiliations:
  • IBM Thomas J. Watson Research Center, Hawthorne, NY;TTI-Chicago, Chicago, IL;TTI-Chicago, Chicago, IL

  • Venue:
  • ICML '06 Proceedings of the 23rd international conference on Machine learning
  • Year:
  • 2006

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Abstract

We present a tree data structure for fast nearest neighbor operations in general n-point 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 (c6n log n) time. Furthermore, nearest neighbor queries require time only logarithmic in n, in particular O (c12 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.