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Artificial intelligence · University

Explained variance of the first principal component

Use covariance eigenvalues sorted in descending order and a positive total variance.

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Method and conditions

Use covariance eigenvalues sorted in descending order and a positive total variance.

ratio = λ₁ / Σλj

Worked examples

PCA covariance eigenvalues are 28, 12, 2. Find the fraction of total variance explained by the first component. Round the final result to 4 decimal places if needed.

Divide the largest eigenvalue 28 by their sum 42.

0.6667

PCA covariance eigenvalues are 21, 3, 3. Find the fraction of total variance explained by the first component. Round the final result to 4 decimal places if needed.

Divide the largest eigenvalue 21 by their sum 27.

0.7778

Try it

  1. PCA covariance eigenvalues are 20, 11, 1. Find the fraction of total variance explained by the first component. Round the final result to 4 decimal places if needed.

  2. PCA covariance eigenvalues are 32, 13, 3. Find the fraction of total variance explained by the first component. Round the final result to 4 decimal places if needed.

Check your work

Answers and marking notes
  1. 0.625

    Divide the largest eigenvalue 20 by their sum 32.

  2. 0.6667

    Divide the largest eigenvalue 32 by their sum 48.

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