为 SPD 矩阵保留子空间结构的几何统计

arXiv - STAT - Computation Pub Date : 2024-07-02 DOI:arxiv-2407.03382

Cyrus Mostajeran, Nathaël Da Costa, Graham Van Goffrier, Rodolphe Sepulchre

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引用次数: 0

摘要

我们提出了一个处理 SPD 值数据的几何框架，该框架保留了子空间结构，并以高效计算极端广义特征值为基础。这是通过使用半定锥的汤普森几何来实现的。我们详细探讨了一种特殊的大地空间结构，并建立了与之相关的几个属性。最后，我们回顾了基于这种几何的 SPD 矩阵的一种新颖的归纳平均值。

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Geometric statistics with subspace structure preservation for SPD matrices

We present a geometric framework for the processing of SPD-valued data that preserves subspace structures and is based on the efficient computation of extreme generalized eigenvalues. This is achieved through the use of the Thompson geometry of the semidefinite cone. We explore a particular geodesic space structure in detail and establish several properties associated with it. Finally, we review a novel inductive mean of SPD matrices based on this geometry.

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arXiv - STAT - Computation

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