Abstract
The field of statistical pattern recognition is characterized by the use of feature vectors for pattern representation, while strings or, more generally, graphs are prevailing in structural pattern recognition. In this paper we aim at bridging the gap between the domain of feature based and graph based object representation. We propose a general approach for transforming graphs into n-dimensional real vector spaces by means of prototype selection and graph edit distance computation. This method establishes the access to the wide range of procedures based on feature vectors without loosing the representational power of graphs. Through various experimental results we show that the proposed method, using graph embedding and classification in a vector space, outperforms the tradional approach based on k-nearest neighbor classification in the graph domain.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bianchini, M., Gori, M., Sarti, L., Scarselli, F.: Recursive processing of cyclic graphs. IEEE Transactions on Neural Networks 17(1), 10–18 (2006)
Pekalska, E., Duin, R., Paclik, P.: Prototype selection for dissimilarity-based classifiers. Pattern Recognition 39(2), 189–208 (2006)
Duin, R., Pekalska, E.: The Dissimilarity Representations for Pattern Recognition: Foundations and Applications. World Scientific, Singapore (2005)
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.) Structural, Syntactic, and Statistical Pattern Recognition. LNCS, vol. 4109, pp. 287–296. Springer, Heidelberg (2006)
Bunke, H., Allermann, G.: Inexact graph matching for structural pattern recognition. Pattern Recognition Letters 1, 245–253 (1983)
Sanfeliu, A., Fu, K.S.: A distance measure between attributed relational graphs for pattern recognition. IEEE Transactions on Systems, Man, and Cybernetics (Part B) 13(3), 353–363 (1983)
Hart, P.E., Nilsson, N.J., Raphael, B.: A formal basis for the heuristic determination of minimum cost paths. IEEE Transactions of Systems, Science, and Cybernetics 4(2), 100–107 (1968)
Wilson, R.C., Hancock, E.R., Luo, B.: Pattern vectors from algebraic graph theory. IEEE Trans. on Pattern Analysis ans Machine Intelligence 27(7), 1112–1124 (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)
Roth, V., Laubm, J., Kawanabe, M., Buhmann, J.: Optimal cluster preserving embedding of nonmetric proximity data. IEEE Trans. on Pattern Analysis ans Machine Intelligence, vol. 15(12) (2003)
MacQueen, J.: Some methods for classification and analysis of multivariant observations. In: Proc. 5th. Berkeley Symp University of California Press 1, pp. 281–297 (1966)
Burges, C.: A tutorial on support vector machines for pattern recognition. Data. Mining and Knowledge Discovery 2(2), 121–167 (1998)
Shawe-Taylor, J., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, Cambridge (2004)
Schölkopf, B., Smola, A.: Learning with Kernels. MIT Press, Cambridge (2002)
Le Saux, B., Bunke, H.: Feature selection for graph-based image classifiers. In: Marques, J.S., Pérez de la Blanca, N., Pina, P. (eds.) IbPRIA 2005. LNCS, vol. 3523, pp. 147–154. Springer, Heidelberg (2005)
Watson, C.I., Wilson, C.L.: NIST special database 4, fingerprint database. National Institute of Standards and Technology (March 1992)
Neuhaus, M., Bunke, H.: A graph matching based approach to fingerprint classification using directional variance. In: Kanade, T., Jain, A., Ratha, N.K. (eds.) AVBPA 2005. LNCS, vol. 3546, pp. 191–200. Springer, Heidelberg (2005)
Development Therapeutics Program DTP. Aids antiviral screen ( 2004), http://dtp.nci.nih.gov/docs/aids/aids_data.html.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Riesen, K., Neuhaus, M., Bunke, H. (2007). Graph Embedding in Vector Spaces by Means of Prototype Selection. In: Escolano, F., Vento, M. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2007. Lecture Notes in Computer Science, vol 4538. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72903-7_35
Download citation
DOI: https://doi.org/10.1007/978-3-540-72903-7_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72902-0
Online ISBN: 978-3-540-72903-7
eBook Packages: Computer ScienceComputer Science (R0)