Non-linear Transformations of Vector Space Embedded Graphs

In pattern recognition and related areas an emerging trend of representing objects by graphs can be observed. As a matter of fact, graph based representation offers a powerful and flexible alternative to the widely used feature vectors. However, the space of graphs contains almost no mathematical structure, and consequently, there is a lack of suitable algorithms for graph classification, clustering, and analysis. Recently, a general approach to transforming graphs into n-dimensional real vectors has been proposed. In the present paper we use this method, which can also be regarded as a novel graph kernel, and investigate the application of kernel principal component analysis (kPCA) on the resulting vector space embedded graphs. To this end we consider the common task of object classification, and show that kPCA in conjunction with the novel graph kernel outperforms different reference systems on several graph data sets of diverse nature.