I'm a statistician working on a research project dealing with metrics on SPD matrices, specifically the log-Euclidean $d_{LE}(X, Y) = \|\log(X) - \log(Y)\|$ and the Riemannian metric $d_{R}(X, Y) = \|\log(Y^{-1/2}XY^{-1/2})\|$, where the norm is the Frobenius norm.

I understand that the two metrics are closely related, and that the LE metric is something like a linearization of the Riemannian metric, but I haven't been able to find a reference that makes this precise. Any comments or suggestions are appreciated.

For some references, [1] is a good intro to different metrics for SPD matrices, and [2] gives some more details on the context I'm working in.

  • $\begingroup$ I imagine that a linearisation of $d_R$ is a straightforward expansion in a Taylor series. Did you check matrix analysis texts? $\endgroup$ – Dima Pasechnik Dec 1 '18 at 10:13

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.