Geometric deep learning on graphs and manifolds using mixture model CNNs
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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CIFAR-10
MNIST
Cora
ZINC
FAUST
| Task | Dataset | Model | Metric Name | Metric Value | Global Rank | Benchmark |
|---|---|---|---|---|---|---|
| Superpixel Image Classification | 75 Superpixel MNIST | Monet | Classification Error | 8.89 | # 6 | |
| Graph Classification | CIFAR10 100k | MoNet | Accuracy (%) | 53.42 | # 13 | |
| Node Classification | PATTERN 100k | MoNet | Accuracy (%) | 85.482 | # 6 | |
| Graph Regression | ZINC 100k | MoNet | MAE | 0.407 | # 7 | |
| Graph Regression | ZINC-500k | MoNet | MAE | 0.292 | # 25 |
