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In the rASR matlab implementation, the geometric median is euclidean.
For now, python RASR uses also the euclidean geometric median (with the different optimization method though).
We might want to implement a riemannian Geometric Median.
Advantage:
Fisher metric instead of euclidean metric is better suited for covariance matrices
therefore we might expect better overall performance of the rASR
Disadvantage:
doesn't handle non-positive definite matrices (but we could compensate by using robust cov estimator or regularization)
slower (but it should be a problem as the median is only required during calibration)
we need to find a way to optimize the cost function (e.g. we can compute analytically the gradien, use pymanopt or with a handmade gradien descent)
Right-now, the advantage is not clear so it is not a priority.
The text was updated successfully, but these errors were encountered:
Florent Bouchard proposed us to give the gradien and hessian so we can find the riemannian geometric median using pymanopt TrustRegions() and/or we can simply ask autograd to find them (the cost function is very simple).
In the rASR matlab implementation, the geometric median is euclidean.
For now, python RASR uses also the euclidean geometric median (with the different optimization method though).
We might want to implement a riemannian Geometric Median.
Advantage:
Disadvantage:
Right-now, the advantage is not clear so it is not a priority.
The text was updated successfully, but these errors were encountered: