Geometric Deep Learning on Graphs and Manifolds Using Mixture Model CNNs

TLDR

Deep learning, especially CNNs, has dominated image, speech, and language tasks but has largely been limited to Euclidean data, prompting growing interest in extending these methods to non‑Euclidean structures such as graphs and manifolds. The authors propose a unified framework to generalize CNNs to non‑Euclidean domains and learn local, stationary, compositional features. The framework employs mixture‑model CNNs that learn local, stationary, and compositional features on graphs and manifolds. The framework subsumes prior non‑Euclidean CNNs and, on image, graph, and 3D shape benchmarks, consistently outperforms existing methods.

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.