Geometric Deep Learning on Graphs and Manifolds Using Mixture Model CNNs
Abstract
Deep learning has achieved a remarkable performance breakthrough in several fields, most notably in speech recognition, natural language processing, and computer vision. In particular, convolutional neural network (CNN) architectures currently produce state-of-the-art performance on a variety of image analysis tasks such as object detection and recognition. Most of deep learning research has so far focused on dealing with 1D, 2D, or 3D Euclidean-structured data such as acoustic signals, images, or videos. Recently, there has been an increasing interest in geometric deep learning, attempting to generalize deep learning methods to non-Euclidean structured data such as graphs and manifolds, with a variety of applications from the domains of network analysis, computational social science, or computer graphics. In this paper, we propose a unified framework allowing to generalize CNN architectures to non-Euclidean domains (graphs and manifolds) and learn local, stationary, and compositional task-specific features. We show that various non-Euclidean CNN methods previously proposed in the literature can be considered as particular instances of our framework. We test the proposed method on standard tasks from the realms of image-, graph-and 3D shape analysis and show that it consistently outperforms previous approaches.
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Under the MoNet framework, several existing approaches for manifolds and graphs can be generalized as special instances of MoNet by constructing nonparametric weight functions.
“Under the MoNet framework, several existing approaches for manifolds such as Geodesic CNN (GCNN) [90], Anisotropic CNN (ACNN) [91], Spline CNN [92], and for graphs such as GCN [22], DCNN [25] can be generalized as special instances of MoNet by constructing nonparametric weight functions.”
From A Comprehensive Survey on Graph Neural Networks (2021) · cites this paper as [44]
MoNet introduces node pseudo-coordinates to determine the relative position between a node and its neighbor.
“Mixture Model Network (MoNet) [44] adopts a different approach to assign different weights to a node's neighbors. It introduces node pseudo-coordinates to determine the relative position between a node and its neighbor.”
From A Comprehensive Survey on Graph Neural Networks (2021) · cites this paper as [44]
MoNet achieved a classification accuracy of 81.69 on the Cora data set.
“MoNet (2017) | 81.69 | - | 78.81 | - | -”
From A Comprehensive Survey on Graph Neural Networks (2021) · cites this paper as [44]
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“[106] Monti F, Boscaini D, Masci J, Rodola E, Svoboda J, Bronstein MM.”
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“spectral representations [Boscaini et al. 2016; Bronstein et al. 2017; Monti et al. 2017; Yi et al. 2017].”
Background
- Authors
- Monti, F., Boscaini, D., Masci, J., Rodola, E., Svoboda, J., & Bronstein, M. M.
- Affiliations
- Università della Svizzera italiana (CH)
- Intel (United States) (US)
- Venue
- 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
- Publisher
- IEEE
- Published
- 2017-07
- Pages
- 5425-5434
- ISSN
- 1063-6919 (ISSN-L)
- OpenAlex
- W2558460151
- Cited by
- 1,820
- References
- 7
- Citations by year
- 2026: 56 · 2025: 108 · 2024: 172 · 2023: 244 · 2022: 269 · 2021: 352 · 2020: 282 · 2019: 213 · 2018: 99 · 2017: 25
- FWCI
- 77.33
- Type
- conference paper
- Language
- en
- Open access
- closed
- Locations
- IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings (publishedVersion)
- IRIS Research product catalog (Sapienza University of Rome) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Advanced Graph Neural Networks
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
- Physical Sciences › Engineering › Computational Mechanics › 3D Shape Modeling and Analysis
- Keywords
- geometric deep learning, graph neural networks, manifold learning, non-Euclidean data, compositional features, 3D shape analysis, image analysis, network analysis
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