Principal-component shrinkage by ridge regression
= Principal-component shrinkage by ridge regression
For $X^TX=V\Lambda V^T$, <ridge regression> multiplies the fitted response along the $i$th <normalized sample principal component> by the shrinkage factor $\Lambda_{ii}/(\Lambda_{ii}+\lambda)$. Directions with variance much larger than $\lambda$ are nearly retained, while directions with variance much smaller than $\lambda$ are nearly removed.