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Explained variance of the first principal component · formula reference
Use covariance eigenvalues sorted in descending order and a positive total variance.
Formula
Use covariance eigenvalues sorted in descending order and a positive total variance.
ratio = λ₁ / Σλj
Worked example
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
Prerequisites and checking
Algebra and the topic definitions. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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