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.
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
# Python program to compute distance matrix# import important librariesimport numpy as npfrom scipy.spatial import distance_matrix # Create the matricesx = np.array([[1,2],[2,1],[2,2]])y = np.array([[5,0],[1,2],[2,0]])# Display the matricesprint("matrix x:\n", x)print("matrix y:\n", y)# compute the distance matrixdist_mat = distance_matrix(x, y, p=2)# display distance matrixprint("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
# Python program to compute distance matrix# import important librariesimport numpy as npfrom scipy.spatial import distance_matrix # Create the matricesx = np.array([[1,2],[2,1],[2,2]])y = np.array([[0,0],[0,0],[1,1],[1,1],[1,2]])# Display the matricesprint("matrix x:\n", x)print("matrix y:\n", y)# compute the distance matrixdist_mat = distance_matrix(x, y, p=2)# display distance matrixprint("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
# Python program to compute distance matrix# import important librariesimport numpy as npfrom scipy.spatial import distance_matrix # Create the matrixx = np.array([[1,2],[2,1],[2,2]])# Display the matrixprint("matrix x:\n", x)# compute the distance matrixdist_mat = distance_matrix(x, x, p=2)# display distance matrixprint("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.
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). Using p=1, the distances are calculated as Minkowski 1-norm (or Manhattan Distance).
Python3
# Python program to compute distance matrix# import important librariesimport numpy as npfrom scipy.spatial import distance_matrix # Create the matricesx = np.array([[1,2],[2,1],[2,2]])y = np.array([[5,0],[1,2],[2,0]])# Display the matricesprint("matrix x:\n", x)print("matrix y:\n", y)# compute the distance matrixdist_mat = distance_matrix(x, y, p=1)# display distance matrixprint("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
# Python program to compute distance matrix# import important librariesimport numpy as npfrom scipy.spatial import distance_matrix # Create the matricesx = 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]])# Display the matricesprint("matrix x:\n", x)print("matrix y:\n", y)# compute the distance matrixdist_mat = distance_matrix(x, y, p=2)# display distance matrixprint("Distance Matrix:\n", dist_mat) |
Output:
distance matrix example 5
