Nearest neighbors can be found efficiently if the dimension is small relative to the input size

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2572, Issue , 2003, Pages 440-454

  Hagedoorn, Michiel ^a  

^a MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DATA STRUCTURES; DIRECTED GRAPHS; GEOMETRY; GRAPH THEORY; NEAREST NEIGHBOR SEARCH; QUERY PROCESSING;

DEPENDENT FACTORS; DIRECTED ACYCLIC GRAPH (DAG); DISTANCE FUNCTIONS; NEAREST NEIGHBORS; SECONDARY MEMORY; SUPER-EXPONENTIAL; UNIFORM DISTRIBUTION; VARIABLE-DIMENSION;

DIGITAL STORAGE;

EID: 35248844008     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-36285-1_29     Document Type: Article

References (23)

1. P. K. Agarwal and J. Erickson. Geometric range searching and its relatives. In B. Chazelle, J. E. Goodman, and R. Pollack, editors, Advances in Discrete and Computational Geometry, volume 223 of Contemporary Mathematics, pages 1-56. American Mathematical Society, 1999.
2. ∞ nearest neighbor search in high dimensions. In Proceedings of the 17th ACM Symposium on Computational Geometry, pages 157-163, 2001.
3. S. Arya and D. M. Mount. Algorithms for fast vector quantization. In Proceedings of the 1993 IEEE Data Compression Conference, pages 381-390, 1993.
4. S. Arya, D. M. Mount, N. S. Netanyahu, R. Silverman, and A. Y. Wu. An optimal algorithm for approximate nearest neighbor searching in fixed dimensions. Journal of the ACM, 45:891-923, 1998.
5. K. Beyer, J. Goldstein, R. Ramakrishnan, and U. Shaft. When is "Nearest Neighbor" meaningful. In Proceedings of the 7th International Conference on Database Theory, pages 217-235, 1999.
6. T. M. Chan. Closest-point problems simplified on the RAM. In Proceedings of the 13th ACM-SIAM Symposium on Discrete Algorithms, 2002.
7. K. L. Clarkson. A randomized algorithm for closest-point queries. SIAM Journal on Computing, 17(4):830-847, 1988.
8. S. Dasgupta and A. Gupta. An elementary proof of the Johnson-Lindenstrauss lemma. Technical Report TR-99-006, International Computer Science Institute, 1999.
9. R. O. Duda, P. E. Hart, and D. G. Stork. Pattern classification. Wiley, 2000.
10. R. A. Dwyer. The expected number of k-faces of a Voronoi diagram. Computers and Mathematics with Applications, 26(5):13-19, 1993.
11. C. Faloutsos and K.-I. Lin. FastMap: a fast algorithm for indexing, data-mining, and visualization of traditional and multimedia databases. In Proceedings of the 1995 ACM-SIGMOD International Conference on Management of Data, pages 163-173, 1995.
12. J. Goldstein and R. Ramakrishnan. Contrast plots and p-sphere trees: Space vs. time in nearest neighbor searches. In Proceedings of the 26th International Conference on Very Large Data Bases, pages 429-440, 2000.
13. S. Har-Peled. A replacement for voronoi diagrams of near linear size. In Proceedings of the 42th IEEE Symposium on the Foundations of Computer Science, pages 94-103, 2001.
14. P. Indyk and R. Motwani. Approximate nearest neighbors: Towards removing the curse of dimensionality. In Proceedings of the 30th ACM Symposium on the Theory of Computing, pages 604-613, 1998.
15. F. Korn, N. Sidiropoulos, C. Faloutsos, E. Siegel, and Z. Protopapas. Fast nearest neighbor search in medical image databases. In The International Journal on Very Large Data Bases, pages 215-226, 1996.
16. E. Kushilevitz, R. Ostrovsky, and Y. Rabani. Efficient search for approximate nearest neighbor in high dimensional spaces. In Proceedings of the 30th ACM Symposium on the Theory of Computing, pages 614-623, 1998.
17. S. Meiser. Point location in arrangements of hyperplanes. Information and Computation, 106(2):286-303, 1993.
18. R. Motwani and P. Raghavan. Randomized Algorithms. Cambridge University, 1995.
19. K. Mulmuley. Computational Geometry: An introduction through randomized algorithms. Prentice Hall, 1994.
20. B.-U. Pagel, F. Korn, and C. Faloutsos. Deflating the dimensionality curse using multiple fractal dimensions. In Proceedings of the 16th International Conference on Data Engineering, pages 589-598, 2000.
21. A. Pentland, R. W. Picard, and S. Sclaroff. Photobook: tools for content-based manipulation of image databases. International Journal of Computer Vision, 18(3):233-254, 1996.
22. H. Samet. Applications of Spatial Data Structures: Computer Graphics, Image Processing, and GIS. Addison-Wesley, 1990.
23. J. Vleugels and R. C. Veltkamp. Efficient image retrieval through vantage objects. In Proceedings of the 3rd International Conference on Visual Information Systems, pages 575-584, 1999.