On Graph-Associated Matrices and Their Eigenvalues for Optical Character Recognition Miriam Schmidt, G¨ unther Palm, and Friedhelm Schwenker Institute of Neural Information Processing, University of Ulm, 89069 Ulm, Germany {miriam.k.schmidt,guenther.palm,friedhelm.schwenker}@uni-ulm.de http://www.uni-ulm.de/in/neuroinformatik.html Abstract. In this paper, the classification power of the eigenvalues of six graph-associated matrices is investigated and evaluated on a bench- mark dataset for optical character recognition. The extracted eigenvalues were utilized as feature vectors for multi-class classification using sup- port 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 fea- ture 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 clas- sification performance can be increased by decision fusion, using the sum rule, to 92.4 %. Keywords: graph classification, weighted adjacency matrix, spectrum, support vector machine. 1 Introduction Spectral graph theory is an important branch in the area of graph classification. Matrices associated with graphs, e.g. the adjacency matrices, contain essential information about the graph’s connectivity [1]. This information is also included in the eigenvalues of the adjacency matrix which build the so-called spectrum. The spectrum of a graph exhibits some important properties, which make them ideal candidates for classification tasks [2],[3]. First, the spectrum is invariant with respect to the labeling of the nodes. Two graphs, which only differ in the labeling, are called isomorph to each other and the graph isomorphism problem (the computation, if two graphs are iso- morph) belongs to the NP-complete problems. These problems build a subset of NP problems, which are defined as decision problems whose solutions can be verified in polynomial time, but the time required to solve the problems in- creases quickly [4]. The graph isomorphism problem occurs, if one has to match the nodes of two graphs to calculate, for example, the graph edit distance [5],[6]. N. Mana, F. Schwenker, and E. Trentin (Eds.): ANNPR 2012, LNAI 7477, pp. 104–114, 2012. c  Springer-Verlag Berlin Heidelberg 2012