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This tutorial will show you how to find the Mahalanobis distance between two NumPy arrays in Python.

Use the function scipy.spatial.distancein the Python library cdist()to calculate the Mahalanobis distance

The Mahalanobis distance is a measure of the distance between a point and a distribution. If we want to find the Mahalanobis distance between two arrays, we can use the function scipy.spatial.distancefrom the library in Python cdist(). cdist()The function calculates the distance between two sets. We can specify in the input parameter mahalanobisto find the Mahalanobis distance. Refer to the following code example.

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

x = np.array([[[1, 2, 3], [3, 4, 5], [5, 6, 7]], [[5, 6, 7], [7, 8, 9], [9, 0, 1]]])

i, j, k = x.shape

xx = x.reshape(i, j * k).T


y = np.array([[[8, 7, 6], [6, 5, 4], [4, 3, 2]], [[4, 3, 2], [2, 1, 0], [0, 1, 2]]])


yy = y.reshape(i, j * k).T

results = cdist(xx, yy, "mahalanobis")

results = np.diag(results)
print(results)

Output:

[3.63263583 2.59094773 1.97370848 1.97370848 2.177978   3.04256456
 3.04256456 1.54080605 2.58298363]

cdist()We computed and stored the Mahalanobis distance between arrays xand using the function in the code above . We first created two arrays using the function. We then reshaped both arrays and saved the transpose in new arrays and . We then passed these new arrays to the function, specifying in the parameter using .ynp.array()xxyycdist()cdist(xx,yy,'mahalanobis')mahalanobis

numpy.einsum()Calculate Mahalanobis distance in Python using the method

We can also calculate the Mahalanobis distance between two arrays using numpy.einsum()the methodnumpy.einsum() . The method is used to evaluate the Einstein summation convention for the input arguments.

import numpy as np

x = np.array([[[1, 2, 3], [3, 4, 5], [5, 6, 7]], [[5, 6, 7], [7, 8, 9], [9, 0, 1]]])
i, j, k = x.shape

xx = x.reshape(i, j * k).T


y = np.array([[[8, 7, 6], [6, 5, 4], [4, 3, 2]], [[4, 3, 2], [2, 1, 0], [0, 1, 2]]])


yy = y.reshape(i, j * k).T

X = np.vstack([xx, yy])
V = np.cov(X.T)
VI = np.linalg.inv(V)
delta = xx - yy
results = np.sqrt(np.einsum("nj,jk,nk->n", delta, VI, delta))
print(results)

Output:

[3.63263583 2.59094773 1.97370848 1.97370848 2.177978   3.04256456
 3.04256456 1.54080605 2.58298363]

We passed the array to np.vstack()the function and stored the values ​​in X. After that, we passed Xthe transpose of to np.cov()the function and stored the result in V. Then we calculated Vthe multiplicative inverse of the matrix and stored the result in VI. We calculated the difference between xxand yyand stored the result in delta. Finally, we results = np.sqrt(np.einsum('nj,jk,nk->n', delta, VI, delta))calculated and stored the Mahalanobis distance between xand using .y