论文标题
不同维度的子空间的整个硕士上的不对称指标
Asymmetric Metrics on the Full Grassmannian of Subspaces of Different Dimensions
论文作者
论文摘要
格拉斯曼尼亚人的指标有各种各样的应用：机器学习，无线通信，计算机视觉等。但是，不同维度的子空间之间的可用距离存在问题，以及子空间的维度不对称，要求使用非对称度量标准。我们将Fubini-study指标扩展为具有有用特性的不对称角度，并且与Grassmann和Clifford几何代数的关系使其易于计算。我们还描述了提供额外信息的相关角度，以及一种将其他格拉曼尼亚指标扩展到全格拉曼尼亚人的非对称指标的方法。
Metrics on Grassmannians have a wide array of applications: machine learning, wireless communication, computer vision, etc. But the available distances between subspaces of distinct dimensions present problems, and the dimensional asymmetry of the subspaces calls for the use of asymmetric metrics. We extend the Fubini-Study metric as an asymmetric angle with useful properties, and whose relations to products of Grassmann and Clifford geometric algebras make it easy to compute. We also describe related angles that provide extra information, and a method to extend other Grassmannian metrics to asymmetric metrics on the full Grassmannian.
