How does PCA handle numerical stability issues in high-dimensional data?

PCA uses SVD-based decomposition to improve numerical stability in high-dimensional spaces.

In high-dimensional datasets, covariance matrices become ill-conditioned and unstable due to floating-point precision issues. Modern PCA implementations avoid explicit covariance matrix computation and instead use Singular Value Decomposition (SVD). SVD decomposes the centered data matrix directly, ensuring stable computation of principal components even when features far exceed observations.