A Topology Layer for Machine Learning
Abstract
Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set filtrations and edge-based filtrations. We present three novel applications: the topological layer can (i) regularize data reconstruction or the weights of machine learning models, (ii) construct a loss on the output of a deep generative network to incorporate topological priors, and (iii) perform topological adversarial attacks on deep networks trained with persistence features. The code (www.github.com/bruel-gabrielsson/TopologyLayer) is publicly available and we hope its availability will facilitate the use of persistent homology in deep learning and other gradient based applications.
Cite
@article{arxiv.1905.12200,
title = {A Topology Layer for Machine Learning},
author = {Rickard Brüel-Gabrielsson and Bradley J. Nelson and Anjan Dwaraknath and Primoz Skraba and Leonidas J. Guibas and Gunnar Carlsson},
journal= {arXiv preprint arXiv:1905.12200},
year = {2020}
}