Persistence-based operators in machine learning
Machine Learning
2022-12-29 v1 Algebraic Topology
Abstract
Artificial neural networks can learn complex, salient data features to achieve a given task. On the opposite end of the spectrum, mathematically grounded methods such as topological data analysis allow users to design analysis pipelines fully aware of data constraints and symmetries. We introduce a class of persistence-based neural network layers. Persistence-based layers allow the users to easily inject knowledge about symmetries (equivariance) respected by the data, are equipped with learnable weights, and can be composed with state-of-the-art neural architectures.
Cite
@article{arxiv.2212.13985,
title = {Persistence-based operators in machine learning},
author = {Mattia G. Bergomi and Massimo Ferri and Alessandro Mella and Pietro Vertechi},
journal= {arXiv preprint arXiv:2212.13985},
year = {2022}
}