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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Results from the Paper

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 # 11
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 # 19

Results from Other Papers

Task Dataset Model Metric Name Metric Value Rank Source Paper Compare
Document Classification Cora MoNet Accuracy 81.7% # 4