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Two algorithms for nearest-neighbor search in high dimensions

Published:04 May 1997Publication History
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References

  1. 1.M. Adler, P. Gemmell, M. Harchol, R.M. Karp, C. Kenyon, "Selection in the presence of noise: the design of playoff systems,' Proc. 5th ACM-SIAM SODA, 1994. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. 2.P.K. Agarwal, J. Matousek, "Ray shooting and parametric search," Proc. 24th ACM STOC, 1992. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. 3.N. AIon, J. Spencer, The Probabilistic Method, Wiley, 1992.Google ScholarGoogle Scholar
  4. 4.S. Arya, Nearest Neighbor Searching and Applications, PhD thesis, University of Maryland technical report CS-TR-3490, June 1995. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. 5.S. Arya, D. Mount, N. Netanyahu, R. Silvennan, A. Wu, "An optimal algorithm for approximate nearest neighbor searching in fixed dimensions;' Proc. 5th ACM-SIAM SODA, 1994. Extended version appears as University of Maryland technical report CS-TR-3568, December 1995. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. 6.J.L. Bentley, "Multidimensional binary search trees used for associative searching," Comm. ACM, 18( 1975), pp. 509-517. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. 7.M.W. Berry, S.T. Dumais, A.T. Shippy, "A case study of latent semantic indexing," U.T. Knoxville technical report CS- 95-271, January 1995. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. 8.C. Buckley, A. Singhal, M. Mitra, and G. Salton, "New Retrieval Approaches Using SMART: TREC 4," Proceedings of the Fourth Text Retrieval Conference, National Institute of Standards and Technology, 1995.Google ScholarGoogle Scholar
  9. 9.P.B. Callahan, S.R. Kosaraju, "A decomposition of multidimensional point sets with applications to k-nearestneighbors and n-body potential fields," Proc. 24th ACM STOC, 1992. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. 10.B. Chor, M. Sudan, "A geometric approach to betweenness," Proc. 3rd European Symposium on Algorithms, 1995. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. 11.K. Clarkson, "A randomized algorithm for closest-point queries," SIAM J. Computing, 17(1988), pp. 830-847. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. 12.K. Clarkson, "An algorithm for approximate closest.point queries;' Proc. lOth ACM Symp. on Computational Geometry, 1994. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. 13.E. Cohen, D. Lewis, "Approximating matrix multiplication for pattern recognition tasks," Proc. 8th ACM-SIAM SODA, 1997. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. 14.T.M. Cover, P.E. Hart, "Nearest neighbor pattern classification;' IEEE Transactions on information Theory, 13(1967), pp. 21-27.Google ScholarGoogle ScholarCross RefCross Ref
  15. 15.S. Deerwester, S. Dumais, T. Landauer, G. Furnas, R. Harshman, "Indexing by latent semantic analysis," J. Soc. Info. Sci., 41 ( 1990), pp. 391-407.Google ScholarGoogle ScholarCross RefCross Ref
  16. 16.L. Devroye, T.J. Wagner, "Nearest neighbor methods in discrimination;' Handbook of Statistics, vol. 2, P.R. Krishnaiah, L.N. Kanal, eds., North-Holland, 1982.Google ScholarGoogle Scholar
  17. 17.D. Dobkin, R. Lipton, "Multidimensional search problems," SIAM J. Computing, 5(1976), pp. 181-186.Google ScholarGoogle ScholarCross RefCross Ref
  18. 18.R.O. Duda, P.E. Hart, Pattern Classification and Scene Analysis, Wiley, 1973. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. 19.R.M. Dudley, "Central limit theorems for empirical measures;' Annals of Prob., 6(1978), pp. 899-929.Google ScholarGoogle Scholar
  20. 20.H. Edelsbrunner, Algorithms in Combinatorial Geometry, Springer, 1987. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. 21.U. Feige, D. Peleg, P. Raghavan, E. Upfal, "Computing with unreliable information," Proc. 22nd ACM STOC, 1990. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. 22.R.A. Finkel, J.L. Bentley, "Quad trees - a data structure for retrieval on composite keys," Acta Inform. 4(1974), pp. 1-9.Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. 23.M. Flickner, H. Sawhney, W. Niblack, J. Ashley, Q. Huang, B. Dom, M. Gorkani, J. Hafner, D. Lee, D. Petkovic, D. Steele, P. Yanker "Query by image and video content: the QBIC system,'' IEEE Computer 28(1995), pp. 23-32. Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. 24.P. Frankl, H. Maehara, "The Johnson-Lindenstrauss lemma and the sphericity of some graphs," J. Combinatorial Theory Set. B, 44(1988), pp. 355-362. Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. 25.M.L. Fredman, R.E. Tarjan, "Fibonacci heaps and their uses in improved network optimization algorithms," Journal of the ACM 34(i 987), pp. 596-615, Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. 26.J.K. Friedman, J.L. Bentley, R.A. Finkel, "An algorithm for finding best matches in logarithmic expected time," ACM Trans. on Math. Software, 3(1977), pp. 209-226. Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. 27.A. Gersho, R.M. Gray, Vector Quantization and Signal Compression, Kluwer Academic, 199 i. Google ScholarGoogle ScholarDigital LibraryDigital Library
  28. 28.M. Goemans, D.P. Williamson, "Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming;' Journal of the ACM, 42(1995), pp. 1115-1145. Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. 29.H. Hotelling, "Analysis of a complex of statistical variables into principal components," J. Educational Psychology, 27(1933), pp. 417-441.Google ScholarGoogle ScholarCross RefCross Ref
  30. 30.W.B. Johnson, J. Lindenstrauss, "Extensions of Lipschitz mappings into Hilbert space;' Contemporary Mathematics 26(1984), pp. 189-206.Google ScholarGoogle Scholar
  31. 31.D. Karger, R. Motwani and M. Sudan, "Approximate graph coloring by semidefinite programming," Proc. 35th IEEE Symposium on Foundations of Computer Science, 1994, pp. 2-I 3.Google ScholarGoogle ScholarDigital LibraryDigital Library
  32. 32.J. Matousek, "Reporting points in halfspaces," Proc. 32nd IEEE FOCS, 1991. Google ScholarGoogle ScholarDigital LibraryDigital Library
  33. 33.S. Meiser, "Point location in arrangements of hyperplanes," Information and Computation, 106(1993), pp. 286-303. Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. 34.R. Motwani, P. Raghavan, Randomized Algorithms, Cambridge University Press, 1995. Google ScholarGoogle ScholarDigital LibraryDigital Library
  35. 35.Panel on Discriminant Analysis and Clustering, National Research Council, Discriminant Analysis and Clustering, National Academy Press, 1988.Google ScholarGoogle Scholar
  36. 36.A. Pentland, R.W. Picard, and S. Sclaroff, "Photobook: tools for content-based manipulation of image databases;' Proceedings of the SPiE Conference on Storage and Retrieval of lmage and Video Databases II, 1994.Google ScholarGoogle Scholar
  37. 37.C.J. van Rijsbergen, Information Retrieval, Butterworths, 1979. Google ScholarGoogle ScholarDigital LibraryDigital Library
  38. 38.G. Salton. Automatic Text Processing. Addison-Wesley, Reading, MA, i 989. Google ScholarGoogle ScholarDigital LibraryDigital Library
  39. 39.H. Samet. The Design and Analysis of Spatial Data Structures. Addison-Wesley, Reading, MA, 1989. Google ScholarGoogle ScholarDigital LibraryDigital Library
  40. 40.A.W.M. Smeulders and R. Jain, editors. Image Databases and Multi-media Search. Proceedings of the First International Workshop, IDB-MMS '96, Amsterdam. Amsterdam University Press, 1996.Google ScholarGoogle Scholar
  41. 41.V.N. Vapnik, A.Y. Chervonenkis, "On the uniform convergence of relative frequencies of events to their probabilities;' Theory of Prob. App., 16(1971 ), pp. 264-280.Google ScholarGoogle Scholar
  42. 42.A.C. Yao, EF. Yao, "A general approach to d-dimensional geometric queries;' Proc. 17th ACM STOC, 1985. Google ScholarGoogle ScholarDigital LibraryDigital Library

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            cover image ACM Conferences
            STOC '97: Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
            May 1997
            752 pages
            ISBN:0897918886
            DOI:10.1145/258533

            Copyright © 1997 ACM

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            • Published: 4 May 1997

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            STOC '97 Paper Acceptance Rate75of211submissions,36%Overall Acceptance Rate1,469of4,586submissions,32%

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