Optimisation of Spectral Wavelets for Persistence-based Graph Classification

• URL: http://arxiv.org/abs/2101.05201v2
• Date: Mon, 1 Mar 2021 16:43:12 GMT
• Title: Optimisation of Spectral Wavelets for Persistence-based Graph Classification
• Authors: Ka Man Yim, Jacob Leygonie
• Abstract summary: We propose a framework that optimises the choice of wavelet for a dataset of graphs. Our framework encodes geometric properties of graphs in their associated persistence diagrams. We apply our framework to graph classification problems and obtain performances competitive with other persistence-based architectures.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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