Graph Embedding Using Dissimilarities with Applications in Classification

The domain of graphs contains only little mathematical structure. That is, most of the basic mathematical operations, actually required by many standard computer vision and pattern recognition algorithms, are not available for graphs. One of the few mathematical concepts that has been successfully transferred from the vector space to the graph domain is distance computation between graphs, commonly referred to as graph matching. Yet, distance-based pattern recognition is basically limited to nearest-neighbor classification. The present chapter reviews a novel approach for graph embedding in vector spaces built upon the concept of graph matching. The key-idea of the proposed embedding method is to use the distances of an input graph to a number of training graphs, termed prototypes, as vectorial description of the graph. That is, all graph matching procedures proposed in the literature during the last decades can be employed in this embedding framework. The rationale for such a graph embedding is to bridge the gap between the high representational power and flexibility of graphs and the large amount of algorithms available for object representations in terms of feature vectors. Hence, the proposed framework can be considered a contribution towards unifying the domains of structural and statistical pattern recognition.