Approximate Furthest Neighbor in High Dimensions

  • Rasmus Pagh
  • Francesco Silvestri
  • Johan Sivertsen
  • Matthew SkalaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9371)


Much recent work has been devoted to approximate nearest neighbor queries. Motivated by applications in recommender systems, we consider approximate furthest neighbor (AFN) queries. We present a simple, fast, and highly practical data structure for answering AFN queries in high-dimensional Euclidean space. We build on the technique of Indyk (SODA 2003), storing random projections to provide sublinear query time for AFN. However, we introduce a different query algorithm, improving on Indyk’s approximation factor and reducing the running time by a logarithmic factor. We also present a variation based on a query-independent ordering of the database points; while this does not have the provable approximation factor of the query-dependent data structure, it offers significant improvement in time and space complexity. We give a theoretical analysis, and experimental results.


Recommender System Query Time Approximation Factor Random Projection Neighbor Query 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Rasmus Pagh
    • 1
  • Francesco Silvestri
    • 1
  • Johan Sivertsen
    • 1
  • Matthew Skala
    • 1
    Email author
  1. 1.IT University of CopenhagenCopenhagenDenmark

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