seniorPCA
What is the computational complexity of PCA?
Updated May 17, 2026
Short answer
PCA complexity depends on SVD or eigen decomposition, typically O(min(n²p, np²)).
Deep explanation
For data matrix X (n samples, p features), PCA using SVD has complexity O(min(n²p, np²)). Covariance-based methods add overhead of computing p×p matrix. Complexity increases significantly with high dimensionality.
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