No abstract

The graph edit distance (GED) is a widely used distance measure for attributed graphs. It has recently been shown that the problem of computing GED, which is a NPhard optimization problem, can be formulated as a quadratic assignment problem (QAP). This formulation is useful, since it allows to derive well performing approximative heuristics for GED from existing techniques for QAP. In this paper, we focus on the case where the edit costs that underlie GED are quasimetric. This is the case in many applications of GED. We show that, for quasimetric edit costs, it is possible to reduce the size of the corresponding QAP formulation. An empirical evaluation shows that this reduction significantly speeds up the QAP-based approximative heuristics for GED.

Convolutional neural networks (CNN) have deeply impacted the field of machine learning. These networks, designed to process objects with a fixed topology, can readily be applied to images, videos and sounds but cannot be easily extended to structures with an arbitrary topology such as graphs. Examples of applications of machine learning to graphs include the prediction of the properties molecular graphs, or the classification of 3D meshes. Within the chemical graphs framework, we propose a method to extend networks based on a fixed topology to input graphs with an arbitrary topology. We also propose an enriched feature vector attached to each node of a chemical graph and a new layer interfacing graphs with arbitrary topologies with a full connected layer.