论文标题
部分面向标志的多种流形上的预期距离
Expected Distances on Manifolds of Partially Oriented Flags
论文作者
论文摘要
标志歧管是投射空间和其他司曼尼人的概括：它们参数化标志，它们是给定向量空间中子空间的嵌套序列。这些是代数和差异几何形状中的重要对象，但在数据科学中也越来越多地使用，在数据科学中，许多类型的数据被正确理解为子空间而不是向量。在本文中，我们讨论了部分定向的标志歧管，该标志歧管的标志参数化某些子空间可以赋予方向。我们在一些低维示例上计算随机点之间的预期距离，我们认为这是一个统计基线，可以比较来自几何或数据的特定部分方向的标志之间的距离。
Flag manifolds are generalizations of projective spaces and other Grassmannians: they parametrize flags, which are nested sequences of subspaces in a given vector space. These are important objects in algebraic and differential geometry, but are also increasingly being used in data science, where many types of data are properly understood as subspaces rather than vectors. In this paper we discuss partially oriented flag manifolds, which parametrize flags in which some of the subspaces may be endowed with an orientation. We compute the expected distance between random points on some low-dimensional examples, which we view as a statistical baseline against which to compare the distances between particular partially oriented flags coming from geometry or data.
