Graph Classification Based on Dissimilarity Space Embedding
Abstract
Recently, an emerging trend of representing objects by graphs can be observed. In fact, graphs offer a powerful alternative to feature vectors in pattern recognition, machine learning, and related fields. However, the domain of graphs contains very little mathematical structure, and consequently, there is only a limited amount of classification algorithms available. In this paper we survey recent work on graph embedding using dissimilarity representations. Once a population of graphs has been mapped to a vector space by means of this embedding procedure, all classification methods developed in statistical pattern recognition become directly available. In an experimental evaluation we show that the proposedmethodology of first embedding graphs in vector spaces and then applying a statistical classifier has significant potential to outperform classifiers that directly operate in the graph domain. Additionally, the proposed framework can be considered a contribution towards unifying the domains of structural and statistical pattern recognition.
Keywords
Linear Discriminant Analysis Edit Distance Statistical Pattern Recognition Graph Domain Graph EmbeddingReferences
- 1.Duda, R., Hart, P., Stork, D.: Pattern Classification, 2nd edn. Wiley-Interscience, Hoboken (2000)MATHGoogle Scholar
- 2.Pekalska, E., Duin, R.: The Dissimilarity Representation for Pattern Recognition: Foundations and Applications. World Scientific, Singapore (2005)CrossRefMATHGoogle Scholar
- 3.Spillmann, B., Neuhaus, M., Bunke, H., Pekalska, E., Duin, R.: Transforming strings to vector spaces using prototype selection. In: Yeung, D.-Y., Kwok, J.T., Fred, A., Roli, F., de Ridder, D. (eds.) SSPR 2006 and SPR 2006. LNCS, vol. 4109, pp. 287–296. Springer, Heidelberg (2006)CrossRefGoogle Scholar
- 4.Riesen, K., Neuhaus, M., Bunke, H.: Graph embedding in vector spaces by means of prototype selection. In: Escolano, F., Vento, M. (eds.) GbRPR 2007. LNCS, vol. 4538, pp. 383–393. Springer, Heidelberg (2007)CrossRefGoogle Scholar
- 5.Riesen, K., Bunke, H.: Classifier ensembles for vector space embedding of graphs. In: Haindl, M., Kittler, J., Roli, F. (eds.) MCS 2007. LNCS, vol. 4472, pp. 220–230. Springer, Heidelberg (2007)CrossRefGoogle Scholar
- 6.Riesen, K., Bunke, H.: Reducing the dimensionality of dissimilarity space embedding graph kernels. Engineering Applications of Artificial Intelligence Engineering Applications of Artificial Intelligence (accepted, 2008)Google Scholar
- 7.Riesen, K., Bunke, H.: Non-linear transformations of vector space embedded graphs. In: 8th International Workshop on Pattern Recognition in Information Systems (accepted, 2008)Google Scholar
- 8.Riesen, K., Bunke, H.: On Lipschitz embeddings of graphs. In: 12th International Conference on Knowledge-Based and Intelligent Information & Engineering Systems (accepted, 2008)Google Scholar
- 9.Riesen, K., Bunke, H.: Dissimilarity based vector space embedding of graphs using prototype reduction schemes (submitted)Google Scholar
- 10.Bunke, H., Dickinson, P., Kraetzl, M.: Theoretical and algorithmic framework for hypergraph matching. In: Roli, F., Vitulano, S. (eds.) ICIAP 2005. LNCS, vol. 3617, pp. 463–470. Springer, Heidelberg (2005)CrossRefGoogle Scholar
- 11.Luo, B., Wilson, R., Hancock, E.: Spectral embedding of graphs. Pattern Recognition 36(10), 2213–2223 (2003)CrossRefMATHGoogle Scholar
- 12.Wilson, R., Hancock, E., Luo, B.: Pattern vectors from algebraic graph theory. IEEE Trans. on Pattern Analysis ans Machine Intelligence 27(7), 1112–1124 (2005)CrossRefGoogle Scholar
- 13.Robles-Kelly, A., Hancock, E.: A Riemannian approach to graph embedding. Pattern Recognition 40, 1024–1056 (2007)CrossRefMATHGoogle Scholar
- 14.Bunke, H., Allermann, G.: Inexact graph matching for structural pattern recognition. Pattern Recognition Letters 1, 245–253 (1983)CrossRefMATHGoogle Scholar
- 15.Riesen, K., Bunke, H.: Approximate graph edit distance computation by means of bipartite graph matching. Image and Vision Computing (accepted, 2008)Google Scholar
- 16.Gärtner, T., Lloyd, J., Flach, P.: Kernels and distances for structured data. Machine Learning 57(3), 205–232 (2004)CrossRefMATHGoogle Scholar
- 17.Shawe-Taylor, J., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, Cambridge (2004)CrossRefMATHGoogle Scholar
- 18.Bezdek, J., Kuncheva, L.: Nearest prototype classifier designs: An experimental study. Int. Journal of Intelligent Systems 16(12), 1445–1473 (2001)CrossRefMATHGoogle Scholar
- 19.Kim, S., Oommen, B.: A brief taxonomy and ranking of creative prototype reduction schemes. Pattern Analysis and Applications 6, 232–244 (2003)MathSciNetCrossRefGoogle Scholar
- 20.Schölkopf, B., Smola, A., Müller, K.R.: Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation 10, 1299–1319 (1998)CrossRefGoogle Scholar
- 21.Bourgain, J.: On Lipschitz embedding of finite metric spaces in Hilbert spaces. Israel Journal of Mathematics 52(1-2), 46–52 (1985)MathSciNetCrossRefMATHGoogle Scholar
- 22.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)CrossRefGoogle Scholar
- 23.Kuncheva, L.: Combining Pattern Classifiers: Methods and Algorithms. John Wiley, Chichester (2004)CrossRefMATHGoogle Scholar
- 24.Breiman, L.: Bagging predictors. Machine Learning 24, 123–140 (1996)MATHGoogle Scholar
- 25.Freund, Y., Shapire, R.: A decision theoretic generalization of online learning and application to boosting. Journal of Computer and Systems Sciences 55, 119–139 (1997)CrossRefGoogle Scholar
- 26.Watson, C., Wilson, C.: NIST Special Database 4, Fingerprint Database. National Institute of Standards and Technology (1992)Google Scholar
- 27.DTP, AIDS antiviral screen (2004), http://dtp.nci.nih.gov/docs/aids/aids_data.html
- 28.Schenker, A., Bunke, H., Last, M., Kandel, A.: Graph-Theoretic Techniques for Web Content Mining. World Scientific, Singapore (2005)CrossRefMATHGoogle Scholar
- 29.Neuhaus, M., Bunke, H.: Bridging the Gap Between Graph Edit Distance and Kernel Machines. World Scientific, Singapore (2007)CrossRefMATHGoogle Scholar