Optimization of Spectral Wavelets for Persistence-Based Graph Classification

A graph's spectral wavelet signature determines a filtration, and consequently an associated set of extended persistence diagrams. We propose framework that optimises the choice for dataset graphs, such their diagrams capture features graphs are best suited to given data science problem. Since graph is derived from its Laplacian, our encodes geometric properties in can be applied without priori node attributes. apply classification problems obtain performances competitive with other persistence-based architectures. To provide underlying theoretical foundations, we extend differentiability result ordinary persistent homology homology.