Improving vector space embedding of graphs through feature selection algorithms

Graph based pattern representation offers a versatile alternative to vectorial data structures. Therefore, a growing interest in graphs can be observed in various fields. However, a serious limitation in the use of graphs is the lack of elementary mathematical operations in the graph domain, actually required in many pattern recognition algorithms. In order to overcome this limitation, the present paper proposes an embedding of a given graph population in a vector space RnRn. The key idea of this embedding approach is to interpret the distances of a graph g to a number of prototype graphs as numerical features of g. In previous works, the prototypes were selected beforehand with heuristic selection algorithms. In the present paper we take a more fundamental approach and regard the problem of prototype selection as a feature selection or dimensionality reduction problem, for which many methods are available. With several experiments we show the feasibility of graph embedding based on prototypes obtained from such feature selection algorithms and demonstrate their potential to outperform previous approaches.