On Lipschitz embeddings of graphs

Abstract

In pattern recognition and related fields, graph based representations offer a versatile alternative to the widely used feature vectors. Therefore, an emerging trend of representing objects by graphs can be observed. This trend is intensified by the development of novel approaches in graph based machine learning, such as graph kernels or graph embedding techniques. These procedures overcome a major drawback of graphs, which consists in a serious lack of algorithms for classification and clustering. The present paper is inspired by the idea of representing graphs by means of dissimilarities and extends previous work to the more general setting of Lipschitz embeddings. In an experimental evaluation we empirically confirm that classifiers relying on the original graph distances can be outperformed by a classification system using the Lipschitz embedded graphs. © 2008 Springer-Verlag Berlin Heidelberg.