Abstract
In this paper, the classification power of the eigenvalues of six graph-associated matrices is investigated and evaluated on a benchmark dataset for optical character recognition. The extracted eigenvalues were utilized as feature vectors for multi-class classification using support vector machines. Each graph-associated matrix contains a certain type of geometric/spacial information, which may be important for the classification process. Classification results are presented for all six feature types, as well as for classifier combinations at decision level. For the decision level combination probabilistic output support vector machines have been applied. The eigenvalues of the weighted adjacency matrix provided the best classification rate of 89.9 %. Here, almost half of the misclassified letters are confusion pairs, such as I-L and N-Z. This classification performance can be increased by decision fusion, using the sum rule, to 92.4 %.
Chapter PDF
Similar content being viewed by others
References
Cvetković, D.M., Doob, M., Sachs, H.: Spectra of Graphs: Theory and Applications, 3rd edn. Vch Verlagsgesellschaft Mbh (1998)
Chung, F.R.K.: Spectral Graph Theory. CBMS Regional Conference Series in Mathematics, vol. 92. Oxford University Press (1997)
Brouwer, A.E., Haermers, W.H.: Spectra of Graphs. Universitext. Springer (2012)
Garey, M.R., Johnson, D.S.: Computers and Intractability; A Guide to the Theory of NP-Completeness. W. H. Freeman & Co. (1990)
Sanfeliu, A., Fu, K.S.: A distance measure between attributed relational graphs for pattern recognition. IEEE Transactions on Systems, Man, and Cybernetics 13(3), 353–362 (1983)
Bunke, H., Shearer, K.: A graph distance metric based on the maximal common subgraph. Pattern Recognition Letters 19(3-4), 255–259 (1998)
Luo, B., Wilson, R.C., Hancock, E.R.: Spectral embedding of graphs. Pattern Recognition 36(10), 2213–2230 (2003)
Wilson, R.C., Hancock, E.R., Luo, B.: Pattern vectors from algebraic graph theory. IEEE Trans. Pattern Anal. Mach. Intell. 27(7), 1112–1124 (2005)
Schmidt, M., Schwenker, F.: Classification of Graph Sequences Utilizing the Eigenvalues of the Distance Matrices and Hidden Markov Models. In: Jiang, X., Ferrer, M., Torsello, A. (eds.) GbRPR 2011. LNCS, vol. 6658, pp. 325–334. Springer, Heidelberg (2011)
Umeyama, S.: An eigendecomposition approach to weighted graph matching problems. IEEE Transactions on Pattern Analysis and Machine Intelligence 10(5), 695–703 (1988)
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)
Diestel, R.: Graph Theory, 3rd edn. Graduate Texts in Mathematics, vol. 173. Springer (2005)
Bollobás, B.: Modern Graph Theory, 2nd edn. Graduate Texts in Mathematics. Springer (2002)
Vapnik, V.N.: The nature of statistical learning theory, 2nd edn. Statistics for Engineering and Information Science. Springer (1999)
Bishop, C.M.: Pattern Recognition and Machine Learning (Information Science and Statistics). Springer (2007)
Scholkopf, B., Smola, A.J.: Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. Adaptive Computation and Machine Learning. MIT Press (2002)
Riesen, K., Bunke, H.: IAM Graph Database Repository for Graph Based Pattern Recognition and Machine Learning. In: da Vitoria Lobo, N., Kasparis, T., Roli, F., Kwok, J.T., Georgiopoulos, M., Anagnostopoulos, G.C., Loog, M. (eds.) SSPR&SPR 2008. LNCS, vol. 5342, pp. 287–297. Springer, Heidelberg (2008)
Riesen, K., Neuhaus, M., Bunke, H.: Bipartite Graph Matching for Computing the Edit Distance of Graphs. In: Escolano, F., Vento, M. (eds.) GbRPR 2007. LNCS, vol. 4538, pp. 1–12. Springer, Heidelberg (2007)
Bunke, H., Allermann, G.: Inexact graph matching for structural pattern recognition. Pattern Recognition Letters 1(4), 245–253 (1983)
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schmidt, M., Palm, G., Schwenker, F. (2012). On Graph-Associated Matrices and Their Eigenvalues for Optical Character Recognition. In: Mana, N., Schwenker, F., Trentin, E. (eds) Artificial Neural Networks in Pattern Recognition. ANNPR 2012. Lecture Notes in Computer Science(), vol 7477. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33212-8_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-33212-8_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33211-1
Online ISBN: 978-3-642-33212-8
eBook Packages: Computer ScienceComputer Science (R0)Springer Nature Proceedings Computer Science
