Ricerc@Sapienza

Graph kernels are one of the mainstream approaches when dealing with measuring similarity between graphs, especially for pattern recognition and machine learning tasks. In turn, graphs gained a lot of attention due to their modeling capabilities for several real-world phenomena ranging from bioinformatics to social network analysis. However, the attention has been recently moved towards hypergraphs, generalization of plain graphs where multi-way relations (other than pairwise relations) can be considered.

This paper investigates a novel graph embedding procedure based on simplicial complexes. Inherited from algebraic topology, simplicial complexes are collections of increasing-order simplices (e.g., points, lines, triangles, tetrahedrons) which can be interpreted as possibly meaningful substructures (i.e., information granules) on the top of which an embedding space can be built by means of symbolic histograms. In the embedding space, any Euclidean pattern recognition system can be used, possibly equipped with feature selection capabilities in order to select the most informative symbols.