Advertisement

Boruvka Meets Nearest Neighbors

  • Mariano Tepper
  • Pablo Musé
  • Andrés Almansa
  • Marta Mejail
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8259)

Abstract

Computing the minimum spanning tree (MST) is a common task in the pattern recognition and the computer vision fields. However, little work has been done on efficient general methods for solving the problem on large datasets where graphs are complete and edge weights are given implicitly by a distance between vertex attributes. In this work we propose a generic algorithm that extends the classical Boruvka’s algorithm by using nearest neighbors search structures to significantly reduce time and memory consumption. The algorithm can also compute in a straightforward way approximate MSTs thus further improving speed. Experiments show that the proposed method outperforms classical algorithms on large low-dimensional datasets by several orders of magnitude.

Keywords

Delaunay Triangulation Distance Computation Priority Queue Classical Algorithm Hilbert Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Graham, R., Hell, P.: On the history of the minimum spanning tree problem. Annals of the History of Computing 7(1), 43–57 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Jain, A.K., Dubes, R.C.: Algorithms for clustering data. Prentice-Hall, Inc., Upper Saddle River (1988)zbMATHGoogle Scholar
  3. 3.
    Zahn, C.T.: Graph-Theoretical Methods for Detecting and Describing Gestalt Clusters. Transactions on Computers C-20(1), 68–86 (1971)CrossRefGoogle Scholar
  4. 4.
    Carreira-Perpiñán, M., Zemel, R.: Proximity graphs for clustering and manifold learning. In: NIPS (2005)Google Scholar
  5. 5.
    Felzenszwalb, P., Huttenlocher, D.: Efficient Graph-Based Image Segmentation. International Journal of Computer Vision 59(2), 167–181 (2004)CrossRefGoogle Scholar
  6. 6.
    Lai, C., Rafa, T., Nelson, D.: Approximate minimum spanning tree clustering in high-dimensional space. Intelligent Data Analysis 13(4), 575–597 (2009)Google Scholar
  7. 7.
    Eddy, W., Mockus, A., Oue, S.: Approximate single linkage cluster analysis of large data sets in high-dimensional spaces. Computational Statistics & Data Analysis 23(1), 29–43 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Bentley, J., Friedman, J.: Fast Algorithms for Constructing Minimal Spanning Trees in Coordinate Spaces. Transactions on Computers 27(2), 97–105 (1978)CrossRefzbMATHGoogle Scholar
  9. 9.
    Leibe, B., Mikolajczyk, K., Schiele, B.: Efficient Clustering and Matching for Object Class Recognition. In: BMVC (2006)Google Scholar
  10. 10.
    Frank, A., Asuncion, A.: UCI machine learning repository (2010)Google Scholar
  11. 11.
    Tepper, M., Musé, P., Almansa, A., Mejail, M.: Boruvka Meets Nearest Neighbors. Technical report, HAL: hal-00583120 (2011)Google Scholar
  12. 12.
    Toyama, J., Kudo, M., Imai, H.: Probably correct k-nearest neighbor search in high dimensions. Pattern Recognition 43(4), 1361–1372 (2010)CrossRefzbMATHGoogle Scholar
  13. 13.
    Chavez, E., Navarro, G.: An Effective Clustering Algorithm to Index High Dimensional Metric Spaces. In: SPIRE (2000)Google Scholar
  14. 14.
    Chávez, E., Navarro, G.: A compact space decomposition for effective metric indexing. Pattern Recognition Letters 26(9), 1363–1376 (2005)CrossRefGoogle Scholar
  15. 15.
    Samet, H.: Depth-First K-Nearest Neighbor Finding Using the MaxNearestDist Estimator. In: ICIAP (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Mariano Tepper
    • 1
  • Pablo Musé
    • 2
  • Andrés Almansa
    • 3
  • Marta Mejail
    • 4
  1. 1.Department of Electrical and Computer EngineeringDuke UniversityUSA
  2. 2.Instituto de Ingeniería Eléctrica, Facultad de IngenieríaUniversidad de la RepúblicaUruguay
  3. 3.CNRS - LTCI UMR5141Telecom ParisTechFrance
  4. 4.Departamento de Computación, Facultad de Ciencias Exactas y NaturalesUniversidad de Buenos AiresArgentina

Personalised recommendations