PCA explained variance ratio

How much variance does each component keep?

Before choosing how many principal components to keep, you need to know how much of the data's variance each one explains. Implement explained_variance_ratio(X).

1. Center X by subtracting the column means.
2. Compute the singular values of the centered matrix with np.linalg.svd.
3. The variance along component i is s_i² / (n − 1). The ratio for component i is its variance divided by the total.
4. Return the ratios as a 1-D array sorted in descending order. They must sum to 1.

Constraints

• X must have at least 2 rows, otherwise raise ValueError.
• If all columns are constant, return a zero array of length min(n, d).
• Do not modify X.

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