Covariance Matrix from Data

Problem

Compute the sample covariance matrix of data, given as a list of samples (rows) with one feature per column, using the unbiased denominator n - 1:

C[i][j] = sum_k (x[k][i] - mean_i) * (x[k][j] - mean_j) / (n - 1)

Assume at least two samples.

Hint

Subtract column means first, then average outer products over n - 1.

case 1

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

expected: [[4,4],[4,4]]

case 2

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

expected: [[1,2],[2,4]]

case 3

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

expected: [[0.5,-0.5],[-0.5,0.5]]

case 4

in: [[[1,1],[2,2],[3,3]]]

expected: [[1,1],[1,1]]

Starter codePython

def covariance_matrix(data):
    # Your code here
    pass

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