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.

翻译：本文提出了一种处理SPD值数据的几何框架，该框架能保持子空间结构，并基于广义特征值极值的高效计算。这一框架通过利用半定锥的Thompson几何实现。我们详细探讨了一种特定的测地空间结构，并建立了与之相关的若干性质。最后，我们基于此几何结构综述了一种新颖的SPD矩阵归纳均值方法。