Geometric Deep Learning on Graphs and Manifolds Using Mixture Model CNNs

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 Euclideanstructured 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-, graphand 3D shape analysis and show that it consistently outperforms previous approaches.

GraphDTA: Predicting drug–target binding affinity with graph neural networks

“…Compared to the spectralbased methods which handle the whole graph simultaneously, the spatial approaches can instead process graph nodes in batches thus can be scalable to large graphs. Recent works on this approach include [21,23,12,37,36,40].…”

“…Compared to the spectral-based methods which handle the whole graph simultaneously, the spatial approaches can instead process graph nodes in batches thus can be scalable to large graphs. Recent works on this approach include [21,23,12,37,36,40] GCNs have been used in computational drug discovery [34], including quantitative structure activity/property relationship prediction, interaction prediction, synthesis prediction, and de novo molecular design. The problem we explore in this paper, prediction of drug-target binding affinity, belongs to the task of interaction prediction, where the interactions could be among drugs, among proteins, or between drugs and proteins.…”

Toward Data‐Driven Weather and Climate Forecasting: Approximating a Simple General Circulation Model With Deep Learning

“…In terms of neural network development it would also be interesting to attempt developing a special convolutional network architecture that operates on the native model grid (not projected on a regular grid), for example, following the work of Monti et al (2017). Additionally, one could assess in detail how the dimensionality reduction in the autoencoder-like network used in this study affects the results and also whether adding recurrent elements to the network can lead to improved predictions.…”

Graph-Based Method for Anomaly Detection in Functional Brain Network using Variational Autoencoder

“…As our approach focuses on completing graph and prediction defective parts of graph with obtained feature of network embedding, we consider some of related fields. In additional, we used a combination of graph convolution VAE to address both recovery and learning problems which can be performed in spectral [8,9] or spatial domain [10]. D. Xu and et al in [11] construct a graph from a set of object proposals, provide initial embedding to each node and edge while used message passing to obtain a consistent prediction.…”

“…Graph Convolutional Neural Network (G-CNN): for apply convolution-like operators over irregular local supports, as graphs where nodes can have a varying number of neighbors which can be used as layers in deep networks, for node classification or recommendation, link prediction and etc. in this process we involved with three challenges, a) defining translation structure on graphs to allow parameters sharing, b) designing compactly supported filters on graphs, c) aggregating multi-scale information, the proposed strategies broadly fall into two domains, there is one spatial operation directly perform the convolution by aggregating the neighbor nodes' information in a certain batch of the graph, where weights can be easily shared across different structures [21,22] and other one is spectral operation relies on the Eigen-decomposition of the Laplacian matrix that apply in whole graph at the same time [23,24,25,26], spectral-based decomposition is often unstable making the generalization across different graphs difficult [10], that cannot preserve both the local and global network structures also require large memory and computation. On the other hand, local filtering approaches [27] rely on possibly suboptimal hardcoded local pseudo-coordinates over graph to define filters.…”