JuniorTheoryCommon

What does this program print?

Python

import numpy as np

X = np.array([[-2, 0], [0, 1], [2, 0], [0, -1]])
Xc = X - X.mean(axis=0)
_, s, Vt = np.linalg.svd(Xc)
print(round(s[0] ** 2 / (s ** 2).sum(), 2))

0.8

Expecting 0.67, the value of s[0] / s.sum(): variance grows with the square of s, and the squares are 8 and 2, so the share is 8 / 10 = 0.8.
Expecting 0.2: svd returns s in decreasing order, so s[0] belongs to the component with the largest variance.

What share of the variance does the second component carry here?
Why must the data be centered before calling np.linalg.svd?

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JuniorTheoryCommon

What does this program print?

Python

import numpy as np

X = np.array([[-2, 0], [0, 1], [2, 0], [0, -1]])
Xc = X - X.mean(axis=0)
_, s, Vt = np.linalg.svd(Xc)
print(round(s[0] ** 2 / (s ** 2).sum(), 2))

0.8

Expecting 0.67, the value of s[0] / s.sum(): variance grows with the square of s, and the squares are 8 and 2, so the share is 8 / 10 = 0.8.
Expecting 0.2: svd returns s in decreasing order, so s[0] belongs to the component with the largest variance.

What share of the variance does the second component carry here?
Why must the data be centered before calling np.linalg.svd?

Back to questions Open topic in roadmap →Answer it yourself — Quiz