PCA First Component Variance

Problem

Compute the variance explained by the first principal component of a two-column data matrix, using the population covariance. For the 2x2 covariance matrix with entries a, b, b, c, return the largest eigenvalue: (a + c) / 2 + sqrt(((a - c) / 2)^2 + b^2).

Return 0.0 for an empty matrix. Each row of data is one observation of two series.

Hint

The first PC variance is the largest eigenvalue of the covariance matrix.

Test cases

case 1

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

expected: 1.3333333333333333

case 2

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

expected: 3.333333333333333

case 3

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

expected: 0.5

case 4

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

expected: 3.333333333333333

Starter codePython

def pca_first_component_variance(data):
    # Your code here
    pass

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