论文标题
超纤维体表示学习
Ultrahyperbolic Representation Learning
论文作者
论文摘要
在机器学习中，数据通常在（平坦的）欧几里得空间中表示，其中点之间的距离沿直线沿线。研究人员最近考虑了更奇特的（非欧几里得）riemannian歧管，例如双曲线空间，非常适合类似树状的数据。在本文中，我们提出了一个生活在恒定非零曲率的伪里人歧管上的表示。这是双曲线和面质几何形状的概括，其中非排效度张量不必是正定的。我们在此几何形状中提供必要的学习工具，并扩展基于梯度的优化技术。更具体地说，我们通过测量学为距离提供封闭形式的表达式，并定义下降方向以最小化某些目标函数。我们的新框架应用于图表。
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.
