Distance-Preserving Graph Embeddings from Random Neural Features

We present Graph Random Neural Features (GRNF), a novel embedding method from graph-structured data to real vectors based on a family of graph neural networks. The embedding naturally deals with graph isomorphism and preserves, in probability, the metric structure of graph domain. In addition to being an explicit embedding method, it also allows to efficiently and effectively approximate graph metric distances (as well as complete kernel functions); a criterion to select the embedding dimension trading off the approximation accuracy with the computational cost is also provided. Derived GRNF can be used within traditional processing methods or as input layer of a larger graph neural network. The theoretical guarantees that accompany GRNF ensure that the considered graph distance is metric, hence allowing to distinguish any pair of non-isomorphic graphs. 1 Introduction Inference on graph-structured data is one of the hottest topics in machine learning, thanks to successes achieved in several scientific fields, like neurosciences, chemistry, computational biology and social sciences [1-3]. One of the major research challenges there consists of building a practical solution able to process graphs, yet managing the graph isomorphism problem. A way to address this latter problem passes through metric distances and complete kernels, however, it has been shown to be at least as hard as deciding whether two graphs are isomorphic [4].