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Persistence diagrams, the most common descriptors of Topological DataAnalysis, encode topological properties of data and have already proved pivotalin many different applications of data science. However, since the (metric)space of persistence diagrams is not Hilbert, they end up being difficultinputs for most Machine Learning techniques. To address this concern, severalvectorization methods have been put forward that embed persistence diagramsinto either finite-dimensional Euclidean space or (implicit) infinitedimensional Hilbert space with kernels. In this work, we focus on persistencediagrams built on top of graphs. Relying on extended persistence theory and theso-called heat kernel signature, we show how graphs can be encoded by(extended) persistence diagrams in a provably stable way. We then propose ageneral and versatile framework for learning vectorizations of persistencediagrams, which encompasses most of the vectorization techniques used in theliterature. We finally showcase the experimental strength of our setup byachieving competitive scores on classification tasks on real-life graphdatasets.

PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures