Optimization of spectral wavelets for persistence-based graph classification

Yim, Ka Man ORCID: https://orcid.org/0000-0003-4736-3151 and Leygonie, Jacob 2021. Optimization of spectral wavelets for persistence-based graph classification. Frontiers in Applied Mathematics and Statistics 7 , 651467. 10.3389/fams.2021.651467

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Abstract

A graph's spectral wavelet signature determines a filtration, and consequently an associated set of extended persistence diagrams. We propose a framework that optimizes 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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Frontiers Media
ISSN:	2297-4687
Date of First Compliant Deposit:	6 October 2023
Date of Acceptance:	24 February 2021
Last Modified:	07 Oct 2023 18:35
URI:	https://orca.cardiff.ac.uk/id/eprint/162644

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