Before revision:  But finite-dimensional embeddings are prone to miss a lot of information about persistence diagrams , while kernel methods require the full computation of the kernel matrix. We introduce PersLay: a simple, highly modular layer of learning architecture for persistence diagrams that allows to exploit the full capacities of neural networks on topological information from any dataset. This layer encompasses most of the vectorization methods of the literature.
After revision:  In this work, we focus on persistence diagrams built on top of graphs. Relying on extended persistence theory and the so-called heat kernel signature, we show how graphs can be encoded by (extended) persistence diagrams in a provably stable way. We then propose a general and versatile framework for learning vectorizations of persistence diagrams, which encompasses most of the vectorization methods of the literature.