We convert a PD to a finite-dimensional vector representation which we call a persistence image (PI), and prove the stability of this transformation with respect to small perturbations in the inputs.
SOTA for Graph Classification on NEURON-MULTI
In order to exploit topological information from graph data, we show how graph structures can be encoded in the so-called extended persistence diagrams computed with the heat kernel signatures of the graphs.
The Weisfeiler–Lehman graph kernel exhibits competitive performance in many graph classification tasks.
#24 best model for Graph Classification on PROTEINS
Understanding how neural networks learn remains one of the central challenges in machine learning research.
This paper concerns itself with one popular topological feature, which is the number of $d-$dimensional holes in the dataset, also known as the Betti$-d$ number.
With the rapid adoption of machine learning techniques for large-scale applications in science and engineering comes the convergence of two grand challenges in visualization.
While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data.
Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs).