Is there a Python function to compute minimal L2 norm between 2 matrices up to column permutation?

Question

I have two sets of column vectors X = (X_1 ... X_n), Y = (Y_1 ... Y_n) of same shape.

I would like to compute something like this:

i.e the minimal L2 norm between X and Y up to column permutation. Is it possible to do it in less than O(n!)? Is it already implemented in Numpy for instance? Thank you in advance.

Answer 1

Apply scipy.optimize.linear_sum_assignment to the matrix A where A_ij = ‖X_i − Y_j‖.