Manifold Filter-Combine Networks
Machine Learning
2025-01-09 v4 Machine Learning
Numerical Analysis
Signal Processing
Numerical Analysis
Abstract
In order to better understand manifold neural networks (MNNs), we introduce Manifold Filter-Combine Networks (MFCNs). Our filter-combine framework parallels the popular aggregate-combine paradigm for graph neural networks (GNNs) and naturally suggests many interesting families of MNNs which can be interpreted as manifold analogues of various popular GNNs. We propose a method for implementing MFCNs on high-dimensional point clouds that relies on approximating an underlying manifold by a sparse graph. We then prove that our method is consistent in the sense that it converges to a continuum limit as the number of data points tends to infinity, and we numerically demonstrate its effectiveness on real-world and synthetic data sets.
Cite
@article{arxiv.2307.04056,
title = {Manifold Filter-Combine Networks},
author = {David R. Johnson and Joyce A. Chew and Edward De Brouwer and Smita Krishnaswamy and Deanna Needell and Michael Perlmutter},
journal= {arXiv preprint arXiv:2307.04056},
year = {2025}
}