Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field

Deep Tree Transductions - A Short Survey

The paper surveys recent extensions of the Long-Short Term Memory networks to handle tree structures from the perspective of learning non-trivial forms of isomorph structured transductions. It provides a discussion of modern TreeLSTM models, showing the effect of the bias induced by the direction of tree processing. An empirical analysis is performed on real-world benchmarks, highlighting how there is no single model adequate to effectively approach all transduction problems.Comment: To appear in the Proceedings of the 2019 INNS Big Data and Deep Learning (INNSBDDL 2019). arXiv admin note: text overlap with arXiv:1809.0909

Network Representation Learning: From Traditional Feature Learning to Deep Learning

Network representation learning (NRL) is an effective graph analytics technique and promotes users to deeply understand the hidden characteristics of graph data. It has been successfully applied in many real-world tasks related to network science, such as social network data processing, biological information processing, and recommender systems. Deep Learning is a powerful tool to learn data features. However, it is non-trivial to generalize deep learning to graph-structured data since it is different from the regular data such as pictures having spatial information and sounds having temporal information. Recently, researchers proposed many deep learning-based methods in the area of NRL. In this survey, we investigate classical NRL from traditional feature learning method to the deep learning-based model, analyze relationships between them, and summarize the latest progress. Finally, we discuss open issues considering NRL and point out the future directions in this field

A Review of Graph Neural Networks and Their Applications in Power Systems

Deep neural networks have revolutionized many machine learning tasks in power systems, ranging from pattern recognition to signal processing. The data in these tasks is typically represented in Euclidean domains. Nevertheless, there is an increasing number of applications in power systems, where data are collected from non-Euclidean domains and represented as graph-structured data with high dimensional features and interdependency among nodes. The complexity of graph-structured data has brought significant challenges to the existing deep neural networks defined in Euclidean domains. Recently, many publications generalizing deep neural networks for graph-structured data in power systems have emerged. In this paper, a comprehensive overview of graph neural networks (GNNs) in power systems is proposed. Specifically, several classical paradigms of GNNs structures (e.g., graph convolutional networks) are summarized, and key applications in power systems, such as fault scenario application, time series prediction, power flow calculation, and data generation are reviewed in detail. Furthermore, main issues and some research trends about the applications of GNNs in power systems are discussed