Manifold Filter-Combine Networks
David R. Johnson, Joyce A. Chew, Edward De Brouwer, Smita, Krishnaswamy, Deanna Needell, Michael Perlmutter

TL;DR
This paper introduces Manifold Filter-Combine Networks (MFCNs), a framework for manifold neural networks that extends graph neural network concepts to high-dimensional data, with proven convergence and practical demonstrations.
Contribution
It proposes a novel filter-combine framework for MNNs, including a method for implementation on high-dimensional point clouds with theoretical convergence guarantees.
Findings
Method converges to a continuum limit as data points increase
Effective on real-world and synthetic datasets
Provides a manifold analogue of popular GNNs
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Code & Models
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Graph Neural Networks · Neural Networks and Applications · Stochastic Gradient Optimization Techniques
