Geometric machine learning: research and applications

Over the last decade, deep learning has revolutionized many traditional machine learning tasks, ranging from computer vision to natural language processing. Although deep learning has achieved excellent performance, it does not perform as well as expected on geometric (non-Euclidean domain) data. Recently, many studies on extending deep learning approaches for graphs and manifolds have merged. In this article, we aim to provide a comprehensive overview of geometric deep learning and comparative methods. First, we introduce the related work and history of the geometric deep learning field and the theoretical background. Next, we summarize the evaluation of the methods of graph and manifold. We further discuss the applications and benchmark datasets of these methods across various research domains. Finally, we propose potential research directions and challenges in this rapidly growing field.