Optimisation of Spectral Wavelets for Persistence-based Graph Classification
This work provides an incremental improvement for researchers working on persistence-based graph classification by optimizing wavelet selection.
This paper proposes a framework to optimize the choice of spectral wavelets for graph datasets, generating persistence diagrams that capture features relevant to data science problems. The framework encodes geometric properties of graphs without requiring node attributes and achieves competitive performance in graph classification tasks.
A graph's spectral wavelet signature determines a filtration, and consequently an associated set of extended persistence diagrams. We propose a framework that optimises the choice of wavelet for a dataset of graphs, such that their associated persistence diagrams capture features of the graphs that are best suited to a given data science problem. Since the spectral wavelet signature of a graph is derived from its Laplacian, our framework encodes geometric properties of graphs in their associated persistence diagrams and can be applied to graphs without a priori node attributes. We apply our framework to graph classification problems and obtain performances competitive with other persistence-based architectures. To provide the underlying theoretical foundations, we extend the differentiability result for ordinary persistent homology to extended persistent homology.