2020/07/01 by Marc T. Law, Law, Marc T., Jos Stam +1 · 1 citation
Computer Science · Engineering · #3D Shape Modeling and Analysis #FOS: Computer and information sciences #Generative Adversarial Networks and Image Synthesis #Human Pose and Action Recognition #Machine Learning (cs.LG) #Machine Learning (stat.ML)
paper · pdf · doi:10.48550/arxiv.2007.00211
openalex publication_date 2020/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In machine learning, data is usually represented in a (flat) Euclidean space where distances between points are along straight lines. Researchers have recently considered more exotic (non-Euclidean) Riemannian manifolds such as hyperbolic space which is well suited for tree-like data. In this paper, we propose a representation living on a pseudo-Riemannian manifold of constant nonzero curvature. It is a generalization of hyperbolic and spherical geometries where the nondegenerate metric tensor need not be positive definite. We provide the necessary learning tools in this geometry and extend gradient-based optimization techniques. More specifically, we provide closed-form expressions for distances via geodesics and define a descent direction to minimize some objective function. Our novel framework is applied to graph representations.