How To Create A Distance Matrix In Python

A distance matrix contains the distances computed pairwise between the vectors of matrix/ matrices. scipy.spatial package provides us distance_matrix() method to compute the distance matrix. Generally matrices are in the form of 2-D array and the vectors of the matrix are matrix rows ( 1-D array).

          Syntax:          scipy.spatial.distance_matrix(x, y, p=2)          Parameters:          x : (M, K) Matrix of M vectors, each of dimension K.      y : (N, K) Matrix of N vectors, each of dimension K.      p : float, 1 <= p <= infinity, defines which Minkowski p-norm to use.          Returns:          (M, N) ndarray / matrix containing the distance from every vector in x to every vector in y.

Note: the column dimensions of both x , and y matrices must be same.

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We can use different values for p to apply different types of the distances to compute the distance matrix.

p = 1, Manhattan Distance p = 2, Euclidean Distance p = ∞, Chebychev Distance

Example 1.

We compute the distance matrix for two matrices x , and y . Both matrices have same dimension (3, 2). So the distance matrix has dimension (3,3). Using p=2, the distances are calculated as Minkowski 2-norm (or Euclidean distance).

Python3

import numpy as np

from scipy.spatial import distance_matrix

x = np.array([[ 1 , 2 ],[ 2 , 1 ],[ 2 , 2 ]])

y = np.array([[ 5 , 0 ],[ 1 , 2 ],[ 2 , 0 ]])

print ( "matrix x:\n" , x)

print ( "matrix y:\n" , y)

dist_mat = distance_matrix(x, y, p = 2 )

print ( "Distance Matrix:\n" , dist_mat)

Output:

distance matrix example 1

Example 2.

We compute the distance matrix for two matrices x, and y. Both matrices have different dimensions. Matrix x has dimension (3,2) and matrix y has dimension (5,2). So the distance matrix has dimension (3,5).

Python3

import numpy as np

from scipy.spatial import distance_matrix

x = np.array([[ 1 , 2 ],[ 2 , 1 ],[ 2 , 2 ]])

y = np.array([[ 0 , 0 ],[ 0 , 0 ],[ 1 , 1 ],[ 1 , 1 ],[ 1 , 2 ]])

print ( "matrix x:\n" , x)

print ( "matrix y:\n" , y)

dist_mat = distance_matrix(x, y, p = 2 )

print ( "Distance Matrix:\n" , dist_mat)

Output:

distance matrix example 2

Example 3.

We compute the distance matrix using single matrix ( i.e. x). Matrix x has dimension (3,2). Same matrix x is given as parameter y. The distance matrix has dimension (3,3).

Python3

import numpy as np

from scipy.spatial import distance_matrix

x = np.array([[ 1 , 2 ],[ 2 , 1 ],[ 2 , 2 ]])

print ( "matrix x:\n" , x)

dist_mat = distance_matrix(x, x, p = 2 )

print ( "Distance Matrix:\n" , dist_mat)

output:

distance matrix example 3

Note: Notice that the above distance matrix is a symmetric matrix. When both x, and y matrices are same, the distance matrix is a symmetric matrix.

Example 4.

Python3

import numpy as np

from scipy.spatial import distance_matrix

x = np.array([[ 1 , 2 ],[ 2 , 1 ],[ 2 , 2 ]])

y = np.array([[ 5 , 0 ],[ 1 , 2 ],[ 2 , 0 ]])

print ( "matrix x:\n" , x)

print ( "matrix y:\n" , y)

dist_mat = distance_matrix(x, y, p = 1 )

print ( "Distance Matrix:\n" , dist_mat)

Output:

distance matrix example 4

Example 5.

We compute the distance matrix for two matrices x, and y. Both matrices have dimension (2, 5). So the distance matrix has dimension (3,5). Using p=2, the distances are calculated as Minkowski 2-norm (or Euclidean Distance).

Python3

import numpy as np

from scipy.spatial import distance_matrix

x = np.array([[ 1 , 2 , 3 , 4 , 5 ],[ 2 , 1 , 0 , 3 , 4 ]])

y = np.array([[ 0 , 0 , 0 , 0 , 1 ],[ 1 , 1 , 1 , 1 , 2 ]])

print ( "matrix x:\n" , x)

print ( "matrix y:\n" , y)

dist_mat = distance_matrix(x, y, p = 2 )

print ( "Distance Matrix:\n" , dist_mat)

Output:

distance matrix example 5