Python alternative for calculating pairwise distance between two sets of 2d points [duplicate]

Question

This question already has an answer here:

• Efficient distance calculation between N points and a reference in numpy/scipy 6 answers
• Minimum Euclidean distance between points in two different Numpy arrays, not within 5 answers

In Matlab there exists the pdist2 command. Given the matrix mx2 and the matrix nx2, each row of matrices represents a 2d point. Now I want to create a mxn matrix such that (i,j) element represents the distance from ith point of mx2 matrix to jth point of nx2 matrix. I simply call the command pdist2(M,N).

I am looking for an alternative to this in python. I can of course write 2 for loops but since I am working with 2 numpy arrays, using for loops is not always the best choice. Is there an optimized command for this in the python universe? Basically I am asking for python alternative to MATLAB's pdist2.

Answer 1

You're looking for the cdist scipy function. It will calculate the pair-wise distances (euclidean by default) between two sets of n-dimensional matrices.

from scipy.spatial.distance import cdist
import numpy as np

X = np.arange(10).reshape(-1,2)
Y = np.arange(10).reshape(-1,2)

cdist(X, Y)

[[  0.           2.82842712   5.65685425   8.48528137  11.3137085 ]
 [  2.82842712   0.           2.82842712   5.65685425   8.48528137]
 [  5.65685425   2.82842712   0.           2.82842712   5.65685425]
 [  8.48528137   5.65685425   2.82842712   0.           2.82842712]
 [ 11.3137085    8.48528137   5.65685425   2.82842712   0.        ]]

Answer 2

You should check the pairwise_distances method of the scikit-learn package.

sklearn.metrics.pairwise.pairwise_distances(X, Y=None, metric='euclidean', n_jobs=1, **kwds)

More information in http://scikit-learn.org/stable/modules/generated/sklearn.metrics.pairwise.pairwise_distances.html

Answer 3

If your matrix is not too big, this should do without using other libs. If the matrix is big, this method will be a bit slow and memory intensive.

mx2 = np.random.randint(1,9,5)    
nx2 = np.random.randint(1,9,3)    
mx2
Out[308]: array([2, 3, 4, 8, 7])    
nx2
Out[309]: array([3, 2, 2])    
mx2[:,None]-nx2
Out[310]: 
array([[-1,  0,  0],
       [ 0,  1,  1],
       [ 1,  2,  2],
       [ 5,  6,  6],
       [ 4,  5,  5]])