Mahalanobis Distance (Diagonal Covariance)

Problem

Compute the Mahalanobis distance between x and y under a diagonal covariance with variances given per dimension:

d = sqrt(sum((x[i] - y[i])^2 / variances[i]))

Assume all variances are positive.

Hint

Scaling each axis by its standard deviation turns this into a Euclidean distance.

case 1

in: [[1,2],[2,4],[1,1]]

expected: 2.23606797749979

case 2

in: [[1,2],[2,4],[1,4]]

expected: 1.4142135623730951

case 3

in: [[1,1],[1,1],[1,1]]

expected: 0

case 4

in: [[0,0],[3,4],[9,16]]

expected: 1.4142135623730951

Starter codePython

def mahalanobis_diagonal(x, y, variances):
    # Your code here
    pass

4 test cases · run your code against them in the editor