Matrix regression with manopt

[ernst.s...@gmail.com]

Hi!

I'm thinking about (no work done yet, so this is all very vague) of doing least squares regression on matrices, eg. finding a function f(t) = M_t where M_t is a (rotation) matrix, given samples (M_i...k t_i...k).
That's something that should be doable with manopt, am I right?

thanks a lot,
Ernst

[Nicolas Boumal]

Hello Ernst,

I do not understand the problem. Could you explain what the data and the unknowns are, in particular specifying to what space each object belongs?

Thanks,

Nicolas

[ernst.s...@gmail.com]

well, like I said, this is more of an idea and I haven't thought this through completely, but the general setting is I have a series of point clouds p and time points 1 ... t and rotation matrices R_tt' from 1 to 2, 2 to 3, etc. now, going from 1 to 3 would of course be R_32*R_21*p(1).
now, what I want is a regression R(t) that approximates each (R_tt-1 * ... * R_21) under *some* smoothness constraint. I hope I'm clear - and thanks for the extremely fast reply ;)

[Nicolas Boumal]

Hello again,

Yes, this does absolutely sound like something you could do with Manopt.

If I may, here are two short conference papers of mine that bear significant resemblance with the situation you describe:

N. Boumal, A. Singer and P.-A. Absil,
Robust estimation of rotations from relative measurements by maximum likelihood,
in the proceedings of the 52nd Conference on Decision and Control (CDC), 2013.

N. Boumal,
Interpolation and regression of rotation matrices,
in the proceedings of Geometric Science of Information (GSI), 2013.

For both papers, I used Manopt, so definitely doable.

Cheers,

Nicolas

[ernst.s...@gmail.com]

haha, thanks - this looks spot on! merci bcps!