Geometric deep learning on graphs and manifolds using mixture model CNNs

TL;DR

This paper introduces a unified geometric deep learning framework using mixture model CNNs that generalizes traditional CNNs to non-Euclidean data like graphs and manifolds, achieving superior results.

Contribution

It presents a novel framework that unifies various non-Euclidean CNN methods and extends deep learning to graphs and manifolds for improved task-specific feature learning.

Findings

Outperforms previous methods on image, graph, and 3D shape analysis tasks

Unifies existing non-Euclidean CNN approaches within a single framework

Effectively learns local, stationary, and compositional features

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.