Explained Variance Ratio

Problem

Compute the explained variance ratio of a unit principal component v: the population variance of the projected (mean-centered) data divided by the total variance, which is the sum of the per-feature population variances.

If the total variance is 0, return 0.0. Empty X returns 0.0.

Hint

Ratio = variance of projected coordinates / sum of per-feature variances.

Test cases

case 1

in: [[[1,2],[3,4],[5,6]],[0.7071067811865476,0.7071067811865476]]

expected: 1.0000000000000004

case 2

in: [[[1,2],[3,4],[5,6]],[0.7071067811865476,-0.7071067811865476]]

expected: 0

case 3

in: [[[2,0],[0,1],[-2,0],[0,-1]],[1,0]]

expected: 0.8

case 4

in: [[[5,5],[5,5]],[1,0]]

expected: 0

Starter codePython

def explained_variance_ratio(X, v):
    # Your code here
    pass

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