Statistics > Machine Learning
arXiv:2307.04056 (stat)
[Submitted on 8 Jul 2023 (v1), last revised 7 Jan 2025 (this version, v4)]
Title:Manifold Filter-Combine Networks
Authors:David R. Johnson,Joyce A. Chew,Edward De Brouwer,Smita Krishnaswamy,Deanna Needell,Michael Perlmutter
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View PDFHTML (experimental)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.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG); Signal Processing (eess.SP); Numerical Analysis (math.NA) |
| Cite as: | arXiv:2307.04056 [stat.ML] |
| (orarXiv:2307.04056v4 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2307.04056 arXiv-issued DOI via DataCite |
Submission history
From: Michael Perlmutter [view email][v1] Sat, 8 Jul 2023 23:19:53 UTC (1,293 KB)
[v2] Tue, 25 Jul 2023 23:49:11 UTC (1,298 KB)
[v3] Tue, 5 Sep 2023 18:14:55 UTC (1,831 KB)
[v4] Tue, 7 Jan 2025 22:36:21 UTC (1,792 KB)
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View a PDF of the paper titled Manifold Filter-Combine Networks, by David R. Johnson and Joyce A. Chew and Edward De Brouwer and Smita Krishnaswamy and Deanna Needell and Michael Perlmutter
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