Abstract
In pattern recognition and related fields, graph based representations offer a versatile alternative to the widely used feature vectors. Therefore, an emerging trend of representing objects by graphs can be observed. This trend is intensified by the development of novel approaches in graph based machine learning, such as graph kernels or graph embedding techniques. These procedures overcome a major drawback of graphs, which consists in a serious lack of algorithms for classification and clustering. The present paper is inspired by the idea of representing graphs by means of dissimilarities and extends previous work to the more general setting of Lipschitz embeddings. In an experimental evaluation we empirically confirm that classifiers relying on the original graph distances can be outperformed by a classification system using the Lipschitz embedded graphs.
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References
Duda, R., Hart, P., Stork, D.: Pattern Classification, 2nd edn. Wiley-Interscience, Chichester (2000)
Conte, D., Foggia, P., Sansone, C., Vento, M.: Thirty years of graph matching in pattern recognition. Int. Journal of Pattern Recognition and Artificial Intelligence 18(3), 265–298 (2004)
Gärtner, T.: A survey of kernels for structured data. SIGKDD Explorations 5(1), 49–58 (2003)
Bourgain, J.: On Lipschitz embedding of finite metric spaces in Hilbert spaces. Israel Journal of Mathematics 52(1-2), 46–52 (1985)
Riesen, K., Neuhaus, M., Bunke, H.: Graph embedding in vector spaces by means of prototype selection. In: Escolano, F., Vento, M. (eds.) GbRPR. LNCS, vol. 4538, pp. 383–393. Springer, Heidelberg (2007)
Duin, R., Pekalska, E.: The Dissimilarity Representations for Pattern Recognition: Foundations and Applications. World Scientific, Singapore (2005)
Hjaltason, G., Samet, H.: Properties of embedding methods for similarity searching in metric spaces. IEEE Trans. on Pattern Analysis ans Machine Intelligence 25(5), 530–549 (2003)
Bunke, H., Allermann, G.: Inexact graph matching for structural pattern recognition. Pattern Recognition Letters 1, 245–253 (1983)
Riesen, K., Neuhaus, M., Bunke, H.: Bipartite graph matching for computing the edit distance of graphs. In: Escolano, F., Vento, M. (eds.) GbRPR. LNCS, vol. 4538, pp. 1–12. Springer, Heidelberg (2007)
Linial, N., London, E., Rabinovich, Y.: The geometry of graphs and some of its algorithmic applications. Combinatorica 15, 215–245 (1995)
Kaufman, L., Rousseeuw, P.: Finding Groups in Data: An Introduction to Cluster Analysis. John Wiley & Sons, Chichester (1990)
Nene, S., Nayar, S., Murase, H.: Columbia Object Image Library: Coil-100. Technical report, Department of Computer Science, Columbia University, New York (1996)
Watson, C., Wilson, C.: NIST Special Database 4, Fingerprint Database. National Institute of Standards and Technology (1992)
DTP, D.T.P.: AIDS antiviral screen (2004), http://dtp.nci.nih.gov/docs/aids/aids_data.html
Schenker, A., Bunke, H., Last, M., Kandel, A.: Graph-Theoretic Techniques for Web Content Mining. World Scientific, Singapore (2005)
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Riesen, K., Bunke, H. (2008). On Lipschitz Embeddings of Graphs. In: Lovrek, I., Howlett, R.J., Jain, L.C. (eds) Knowledge-Based Intelligent Information and Engineering Systems. KES 2008. Lecture Notes in Computer Science(), vol 5177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85563-7_22
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DOI: https://doi.org/10.1007/978-3-540-85563-7_22
Publisher Name: Springer, Berlin, Heidelberg
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