Geometric Deep Learning on Graphs and Manifolds Using Mixture Model CNNs

• Published in: 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) pp. 5425 - 5434
• Main Authors: Monti, Federico, Boscaini, Davide, Masci, Jonathan, Rodola, Emanuele, Svoboda, Jan, Bronstein, Michael M.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.07.2017
• Subjects: Computational modeling; Convolution; Laplace equations; Machine learning; Manifolds; Shape; Three-dimensional displays
• ISSN: 1063-6919; 1063-6919
• DOI: 10.1109/CVPR.2017.576

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.