Skip to main content

Approximation Techniques to Enable Dimensionality Reduction for Voronoi-Based Nearest Neighbor Search

  • Conference paper
  • 1647 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 3896))

Abstract

Utilizing spatial index structures on secondary memory for nearest neighbor search in high-dimensional data spaces has been the subject of much research. With the potential to host larger indexes in main memory, applications demanding a high query throughput stand to benefit from index structures tailored for that environment. “Index once, query at very high frequency” scenarios on semi-static data require particularly fast responses while allowing for more extensive precalculations. One such precalculation consists of indexing the solution space for nearest neighbor queries as used by the approximate Voronoi cell-based method. A major deficiency of this promising approach is the lack of a way to incorporate effective dimensionality reduction techniques. We propose methods to overcome the difficulties faced for normalized data and present a second reduction step that improves response times through limiting the dimensionality of the Voronoi cell approximations. In addition, we evaluate the suitability of our approach for main memory indexing where speedup factors of up to five can be observed for real world data sets.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berchtold, S., Ertl, B., Keim, D.A., Kriegel, H.P., Seidl, T.: Fast Nearest Neighbor Search in High-Dimensional Spaces. In: ICDE Conf, pp. 209–218 (1998)

    Google Scholar 

  2. Berchtold, S., Keim, D.A., Kriegel, H.P., Seidl, T.: Indexing the Solution Space: A New Technique for Nearest Neighbor Search in High-Dimensional Space. In: IEEE Trans. Knowl. Data Eng, vol. 12, pp. 45–57 (2000)

    Google Scholar 

  3. Dobkin, D., Lipton, R.: Multidimensional Searching Problems. SIAM J. on Computing 5, 181–186 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  4. Weber, R., Schek, H.J., Blott, S.: A Quantitative Analysis and Performance Study for Similarity-Search Methods in High-Dimensional Spaces. In: VLDB Conf, pp. 194–205 (1998)

    Google Scholar 

  5. Guttman, A.: R-Trees: A Dynamic Index Structure for Spatial Searching. In: SIGMOD Conf., pp. 47–57 (1984)

    Google Scholar 

  6. Beckmann, N., Kriegel, H.P., Schneider, R., Seeger, B.: The R*-Tree: An Efficient and Robust Access Method for Points and Rectangles. In: SIGMOD Conf., pp. 322–331 (1990)

    Google Scholar 

  7. Kim, K., Cha, S.K., Kwon, K.: Optimizing Multidimensional Index Trees for Main MemoryAccess. In: SIGMOD Conf, 139–150 (2001)

    Google Scholar 

  8. Berchtold, S., Keim, D.A., Kriegel, H.P.: The X-Tree: An Index Structure for High-Dimensional Data. In: VLDB Conf, 28–39 (1996)

    Google Scholar 

  9. Roussopoulos, N., Kelley, S., Vincent, S.: Nearest Neighbor Queries. In: SIGMOD Conf, 71–79 (1995)

    Google Scholar 

  10. Hjaltason, G.R., Samet, H.: Ranking in Spatial Databases. In: SSD, pp. 83–95 (1995)

    Google Scholar 

  11. Bohannon, P., McIlroy, P., Rastogi, R.: Main-Memory Index Structures with Fixed-Size Partial Keys. In: SIGMOD Conf, pp. 163–174 (2001)

    Google Scholar 

  12. Rao, J., Ross, K.A.: Making B+-Trees Cache Conscious in Main Memory. In: SIGMOD Conf., pp. 475–486 (2000)

    Google Scholar 

  13. Voronoi, G.: Nouvelles applications des parametres continus la theorie des formes quadratiques. J. für die reine und angewandte Mathematik 138, 198–287 (1908)

    Article  Google Scholar 

  14. Aurenhammer, F., Klein, R.: Handbook of Computational Geometry, pp. 201–290. Elsevier Science Publishers, Amsterdam (2000)

    Book  Google Scholar 

  15. Klee, V.: On the Complexity of d-dimensional Voronoi Diagrams. Archiv der Mathematik 34, 75–80 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  16. Seidel, R.: On the Number of Faces in Higher-Dimensional Voronoi Diagrams. In: Symposium on Computational Geometry, pp. 181–185 (1987)

    Google Scholar 

  17. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press, Cambridge (1992)

    Google Scholar 

  18. Kaski, S.: Dimensionality Reduction by Random Mapping: Fast Similarity Computation for Clustering. IJCNN, 413–418 (1998)

    Google Scholar 

  19. Edelsbrunner, H.: Algorithms in Combinatorial Geometry. Springer-Verlag (1987)

    Google Scholar 

  20. Jaffar, J., Maher, M.J., Stuckey, P.J., Yap, R.H.C.: Projecting CLP(R) Constraints. New Generation Computing 11, 449–469 (1993)

    Article  MATH  Google Scholar 

  21. Bradford Barber, C., Dobkin, D., Huhdanpaa, H.: The Quickhull Algorithm for Convex Hulls. ACM Trans. Math. Softw. 22, 469–483 (1996)

    Article  MATH  Google Scholar 

  22. Goldstein, J., Platt, J.C., Burges, C.J.C.: Indexing High Dimensional Rectangles for Fast Multimedia Identification. Technical Report MSR-TR-2003-38, Microsoft Research (2003)

    Google Scholar 

  23. Hafner, J., Sawhney, H.S., Equitz, W., Flickner, M., Niblack, W.: Efficient Color Histogram Indexing for Quadratic Form Distance Functions. IEEE Trans. PAMI 17, 729–736 (1995)

    Google Scholar 

  24. Wahlster, W.: Verbmobil: Foundations of Speech-to-Speech Translation, pp. 537–631. Springer, Heidelberg (2000)

    Google Scholar 

  25. Keogh, E., Folias, T.: The UCR Time Series Data Mining Archive. (2002), http://www.cs.ucr.edu/~eamonn/TSDMA/index.html

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Brochhaus, C., Wichterich, M., Seidl, T. (2006). Approximation Techniques to Enable Dimensionality Reduction for Voronoi-Based Nearest Neighbor Search. In: Ioannidis, Y., et al. Advances in Database Technology - EDBT 2006. EDBT 2006. Lecture Notes in Computer Science, vol 3896. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11687238_15

Download citation

  • DOI: https://doi.org/10.1007/11687238_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32960-2

  • Online ISBN: 978-3-540-32961-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics