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Jul, 2024
具有应用于SPD流形的Cholesky流形上的产品几何
Product Geometries on Cholesky Manifolds with Applications to SPD Manifolds
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Ziheng Chen, Yue Song, Xiao-Jun Wu, Nicu Sebe
TL;DR
该论文提出了两种基于Choelsky流形的对称正定流形的新度量方法,分别是对角功率欧几里得度量和对角广义Bures-Wasserstein度量,相较于现有的流形度量,这两种度量方法具有较高的数值稳定性和计算效率。
Abstract
This paper presents two new metrics on the Symmetric Positive Definite (SPD) manifold via the
cholesky manifold
, i.e., the space of lower triangular matrices with positive diagonal elements. We first unveil that the existing popular
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