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.
Chapter PDF
Similar content being viewed by others
Keywords
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
Hastie, T., Tibshirani, R., Friedman, J.: The elements of statistical learning: Data mining, inference, and prediction, 2nd edn. Springer (2009)
Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE TPAMI 22(8), 888–905 (2000)
Ng, A., Jordan, M., Weiss, Y.: On spectral clustering: Analysis and an algorithm. In: NIPS (2001)
Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Computation 15(6), 1373–1396 (2003)
Grady, L., Schwartz, E.: Isoperimetric graph partitioning for image segmentation. IEEE TPAMI 28(3), 469–475 (2006)
Zhang, W., Lin, Z., Tang, X.: Learning semi-Riemannian metrics for semisupervised feature extraction. IEEE TKDE 23(4), 600–611 (2011)
Frey, B., Dueck, D.: Clustering by passing messages between data points. Science 315(5814), 972–976 (2007)
Zhou, D., Huang, J., Schölkopf, B.: Learning from labeled and unlabeled data on a directed graph. In: ICML (2005)
Kleinberg, J.: Authoritative sources in a hyperlinked environment. Journal of the ACM 46(5), 604–632 (1999)
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)
Zelnik-Manor, L., Perona, P.: Self-tuning spectral clustering. In: NIPS (2005)
Wu, M., Schölkopf, B.: A local learning approach for clustering. In: NIPS (2007)
Franti, P., Virmajoki, O., Hautamaki, V.: Fast agglomerative clustering using a k-nearest neighbor graph. IEEE TPAMI 28(11), 1875–1881 (2006)
Cho, M., Lee, J., Lee, K.: Feature correspondence and deformable object matching via agglomerative correspondence clustering. In: ICCV (2009)
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)
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)
Karypis, G., Han, E., Kumar, V.: Chameleon: Hierarchical clustering using dynamic modeling. IEEE Computer 32(8), 68–75 (1999)
Zhao, D., Tang, X.: Cyclizing clusters via zeta function of a graph. In: NIPS (2008)
Felzenszwalb, P., Huttenlocher, D.: Efficient graph-based image segmentation. IJCV 59(2), 167–181 (2004)
Yu, S., Shi, J.: Multiclass spectral clustering. In: ICCV (2003)
Leordeanu, M., Hebert, M.: A spectral technique for correspondence problems using pairwise constraints. In: ICCV (2005)
Liu, H., Yan, S.: Common visual pattern discovery via spatially coherent correspondences. In: CVPR (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhang, W., Wang, X., Zhao, D., Tang, X. (2012). Graph Degree Linkage: Agglomerative Clustering on a Directed Graph. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds) Computer Vision – ECCV 2012. ECCV 2012. Lecture Notes in Computer Science, vol 7572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33718-5_31
Download citation
DOI: https://doi.org/10.1007/978-3-642-33718-5_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33717-8
Online ISBN: 978-3-642-33718-5
eBook Packages: Computer ScienceComputer Science (R0)