Expected distances on manifolds of partially oriented flags
Expected distances on manifolds of partially oriented flags
复制标题
部分定向标志流形上的预期距离
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
C. Shonkwiler
中科院分区：
文献类型：
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作者：
Brenden Balch;C. Peterson;C. Shonkwiler
标志流形是射影空间和其他Grassmannians的推广：它们将标志参数化，标志是给定向量空间中的子空间的嵌套序列。它们是代数和微分几何中的重要对象，但也越来越多地被用于数据科学，在数据科学中，许多类型的数据被正确地理解为子空间而不是向量。在这篇文章中，我们讨论了部分定向的标志流形，它将一些子空间可以赋予方向的标志参数化。我们在一些低维的例子中计算随机点之间的期望距离，我们将其视为比较来自几何或数据的特定部分定向标志之间的距离的统计基线。
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.