Abstract
This paper proposes a fast k-means algorithm for graphs based on Elkan’s k-means for vectors. To accelerate the k-means algorithm for graphs without trading computational time against solution quality, we avoid unnecessary graph distance calculations by exploiting the triangle inequality of the underlying distance metric. In experiments we show that the accelerated k-means for graphs is faster than k-means for graphs provided there is a cluster structure in the data.
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Jiang, X., Munger, A., Bunke, H.: On Median Graphs:Properties, Algorithms, and Applications. IEEE Trans. PAMI 23(10), 1144–1151 (2001)
Dosch, P., Valveny, E.: Report on the second symbol recognition contest. In: Liu, W., Lladós, J. (eds.) GREC 2005. LNCS, vol. 3926, pp. 381–397. Springer, Heidelberg (2006)
Elkan, C.: Using the triangle inequality to accelerate k-means. In: ICML 2003 Conference Proceedings, pp. 147–153 (2003)
Ferrer, M.: Theory and algorithms on the median graph. application to graph-based classification and clustering, PhD Thesis, Univ. Autònoma de Barcelona (2007)
Gold, S., Rangarajan, A.: Graduated Assignment Algorithm for Graph Matching. IEEE Trans. PAMI 18, 377–388 (1996)
Hochbaum, D., Shmoys, D.: A best possible heuristic for the k-center problem. Mathematics of Operations Research 10(2), 180–184 (1985)
Indyk, P., Amir, A., Efrat, A., Samet, H.: Efficient algorithms and regular data structures for dilation, location and proximity problems. In: FOCS 1999 Conference Proceedings, pp. 160–170 (1999)
Jain, B., Wysotzki, F.: Central Clustering of Attributed Graphs. Machine Learning 56, 169–207 (2004)
Jain, B., Obermayer, K.: On the sample mean of graphs. In: IJCNN 2008 Conference Proceedings, pp. 993–1000 (2008)
Jain, B., Obermayer, K.: Algorithms for the sample mean of graphs. In: Jiang, X., Petkov, N. (eds.) CAIP 2002. LNCS, vol. 5702, pp. 351–359. Springer, Heidelberg (2009)
Jain, B., Obermayer, K.: Structure Spaces. Journal of Machine Learning Research 10 (2009)
Jain, B., Obermayer, K.: Graph Quantization. arXiv:1001.0921v[1cs.AI] (2010)
Kazius, J., McGuire, R., Bursi, R.: Derivation and validation of toxicophores for mutagenicity prediction. Journal of Medicinal Chemistry 48(1), 312–320 (2005)
Moore, A.: The anchors hierarchy: Using the triangle inequality to survive high dimensional data. In: UAI 2000 Conference Proceedings, pp. 397–405 (2000)
Riesen, K., Bunke, H.: IAM Graph Database Repository for Graph Based Pattern Recognition and Machine Learning. In: SSPR 2008 Conference Proceedings, pp. 287–297 (2008)
Schenker, A., Last, M., Bunke, H., Kandel, A.: Clustering of web documents using a graph model. In: Web Document Analysis: Challenges and Opportunities, pp. 1–16 (2003)
Theodoridis, S., Koutroumbas, K.: Pattern Recognition. Elsevier, Amsterdam (2009)
Watson, C., Wilson, C.: NIST Special Database 4, Fingerprint Database, National Institute of Standards and Technology (1992)
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Jain, B.J., Obermayer, K. (2010). Elkan’s k-Means Algorithm for Graphs. In: Sidorov, G., Hernández Aguirre, A., Reyes García, C.A. (eds) Advances in Soft Computing. MICAI 2010. Lecture Notes in Computer Science(), vol 6438. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16773-7_2
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DOI: https://doi.org/10.1007/978-3-642-16773-7_2
Publisher Name: Springer, Berlin, Heidelberg
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