Manifold Filter-Combine Networks

David R. Johnson; Joyce A. Chew; Edward De Brouwer; Smita Krishnaswamy; Deanna Needell; Michael Perlmutter

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arXiv · 2307.04056

Manifold Filter-Combine Networks

David R. Johnson·Joyce A. Chew·Edward De Brouwer·Smita Krishnaswamy·Deanna Needell·Michael Perlmutter

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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.

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BibTeX RIS

David R. Johnson, Joyce A. Chew, Edward De Brouwer, Smita Krishnaswamy, Deanna Needell, Michael Perlmutter. 2023-07-08. Manifold Filter-Combine Networks. https://arxiv.org/abs/2307.04056

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