点集之间的符号距离

Question

Say I have two sets of points X and Y possibly holding a different number of points, and of different dimensionality. We can assume that X and Y are nxm numpy arrays (n points, m dimensions each)

I would like to obtain the distribution (median and std) of sum(yx) distances between the points in Y and X .

Eg if one y point is (2,4) and one x point is (3,5) the sum(yx) distance would be 2-3 + 4-5 = -2 .

How can I do that in Python without looping?

Answer 1

A quick browse through scipy.spatial.distance did not yield any results so you likely need to use broadcasting:

>>> a = np.random.rand(5,3) #(N x M)
>>> b = np.random.rand(4,3) #(K X M)
>>> dists = np.sum(a[:,None,:] - b, axis=-1)
>>> dists
array([[-0.57713957, -1.88996939, -0.13993727, -1.17222018],
       [ 0.89288677, -0.41994304,  1.33008907,  0.29780616],
       [ 0.45866859, -0.85416123,  0.89587088, -0.13641203],
       [ 1.12909228, -0.18373754,  1.56629457,  0.53401166],
       [ 0.64299673, -0.66983308,  1.08019903,  0.04791612]])

Now just grab the median and std:

>>> np.median(dists)
0.17286113728020264
>>> np.std(dists)
0.88228393506243197