Graph Degree Linkage: Agglomerative Clustering on a Directed Graph

  • Wei Zhang
  • Xiaogang Wang
  • Deli Zhao
  • Xiaoou Tang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7572)

Abstract

This paper proposes a simple but effective graph-based agglomerative algorithm, for clustering high-dimensional data. We explore the different roles of two fundamental concepts in graph theory, indegree and outdegree, in the context of clustering. The average indegree reflects the density near a sample, and the average outdegree characterizes the local geometry around a sample. Based on such insights, we define the affinity measure of clusters via the product of average indegree and average outdegree. The product-based affinity makes our algorithm robust to noise. The algorithm has three main advantages: good performance, easy implementation, and high computational efficiency. We test the algorithm on two fundamental computer vision problems: image clustering and object matching. Extensive experiments demonstrate that it outperforms the state-of-the-arts in both applications.

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References

  1. 1.
    Hastie, T., Tibshirani, R., Friedman, J.: The elements of statistical learning: Data mining, inference, and prediction, 2nd edn. Springer (2009)Google Scholar
  2. 2.
    Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE TPAMI 22(8), 888–905 (2000)CrossRefGoogle Scholar
  3. 3.
    Ng, A., Jordan, M., Weiss, Y.: On spectral clustering: Analysis and an algorithm. In: NIPS (2001)Google Scholar
  4. 4.
    Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation 15(6), 1373–1396 (2003)MATHCrossRefGoogle Scholar
  5. 5.
    Grady, L., Schwartz, E.: Isoperimetric graph partitioning for image segmentation. IEEE TPAMI 28(3), 469–475 (2006)CrossRefGoogle Scholar
  6. 6.
    Zhang, W., Lin, Z., Tang, X.: Learning semi-Riemannian metrics for semisupervised feature extraction. IEEE TKDE 23(4), 600–611 (2011)Google Scholar
  7. 7.
    Frey, B., Dueck, D.: Clustering by passing messages between data points. Science 315(5814), 972–976 (2007)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Zhou, D., Huang, J., Schölkopf, B.: Learning from labeled and unlabeled data on a directed graph. In: ICML (2005)Google Scholar
  9. 9.
    Kleinberg, J.: Authoritative sources in a hyperlinked environment. Journal of the ACM 46(5), 604–632 (1999)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Mislove, A., Marcon, M., Gummadi, K., Druschel, P., Bhattacharjee, B.: Measurement and analysis of online social networks. In: Proc. ACM SIGCOMM Conf. on Internet Measurement (2007)Google Scholar
  11. 11.
    Zelnik-Manor, L., Perona, P.: Self-tuning spectral clustering. In: NIPS (2005)Google Scholar
  12. 12.
    Wu, M., Schölkopf, B.: A local learning approach for clustering. In: NIPS (2007)Google Scholar
  13. 13.
    Franti, P., Virmajoki, O., Hautamaki, V.: Fast agglomerative clustering using a k-nearest neighbor graph. IEEE TPAMI 28(11), 1875–1881 (2006)CrossRefGoogle Scholar
  14. 14.
    Cho, M., Lee, J., Lee, K.: Feature correspondence and deformable object matching via agglomerative correspondence clustering. In: ICCV (2009)Google Scholar
  15. 15.
    Sander, J., Ester, M., Kriegel, H., Xu, X.: Density-based clustering in spatial databases: The algorithm GDBSCAN and its applications. Data Mining and Knowledge Discovery 2(2), 169–194 (1998)CrossRefGoogle Scholar
  16. 16.
    Ertöz, L., Steinbach, M., Kumar, V.: Finding clusters of different sizes, shapes, and densities in noisy, high dimensional data. In: SIAM International Conf. on Data Mining (2003)Google Scholar
  17. 17.
    Karypis, G., Han, E., Kumar, V.: Chameleon: Hierarchical clustering using dynamic modeling. IEEE Computer 32(8), 68–75 (1999)CrossRefGoogle Scholar
  18. 18.
    Zhao, D., Tang, X.: Cyclizing clusters via zeta function of a graph. In: NIPS (2008)Google Scholar
  19. 19.
    Felzenszwalb, P., Huttenlocher, D.: Efficient graph-based image segmentation. IJCV 59(2), 167–181 (2004)CrossRefGoogle Scholar
  20. 20.
    Yu, S., Shi, J.: Multiclass spectral clustering. In: ICCV (2003)Google Scholar
  21. 21.
    Leordeanu, M., Hebert, M.: A spectral technique for correspondence problems using pairwise constraints. In: ICCV (2005)Google Scholar
  22. 22.
    Liu, H., Yan, S.: Common visual pattern discovery via spatially coherent correspondences. In: CVPR (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Wei Zhang
    • 1
  • Xiaogang Wang
    • 2
    • 3
  • Deli Zhao
    • 1
  • Xiaoou Tang
    • 1
    • 3
  1. 1.Department of Information EngineeringThe Chinese University of Hong KongHong Kong
  2. 2.Department of Electronic EngineeringThe Chinese University of Hong KongHong Kong
  3. 3.Shenzhen Institutes of Advanced TechnologyChinese Academy of SciencesChina

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