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

Question

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.

[`scipy pdist`](https://docs.scipy.org/doc/scipy-0.13.0/reference/generated/scipy.spatial.distance.pdist.html)? — andrew_reece, Apr 27 '17 at 07:19
it calculates pairwise distances between points in the same matrix. — user_1_1_1, Apr 27 '17 at 07:22
Sorry, it's been awhile. [`cdist`](https://docs.scipy.org/doc/scipy-0.13.0/reference/generated/scipy.spatial.distance.cdist.html#scipy.spatial.distance.cdist) should do it. — andrew_reece, Apr 27 '17 at 07:25

Duncan WP · Accepted Answer · 2017-04-27T07:29:43.833

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.        ]]

score 0 · Answer 2 · answered Apr 27 '17 at 07:22

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

score 0 · Answer 3 · answered Apr 27 '17 at 07:31

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]])

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

3 Answers3

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