Manifold Filter-Combine Networks
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866929664099876864 |
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| author | Johnson, David R. Chew, Joyce A. De Brouwer, Edward Krishnaswamy, Smita Needell, Deanna Perlmutter, Michael |
| author_facet | Johnson, David R. Chew, Joyce A. De Brouwer, Edward Krishnaswamy, Smita Needell, Deanna Perlmutter, Michael |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_04056 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Manifold Filter-Combine Networks Johnson, David R. Chew, Joyce A. De Brouwer, Edward Krishnaswamy, Smita Needell, Deanna Perlmutter, Michael Machine Learning Numerical Analysis Signal Processing 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. |
| title | Manifold Filter-Combine Networks |
| topic | Machine Learning Numerical Analysis Signal Processing |
| url | https://arxiv.org/abs/2307.04056 |