midPCA
How does PCA reduce dimensionality mathematically?
Updated May 17, 2026
Short answer
PCA projects data onto top-k eigenvectors of covariance matrix.
Deep explanation
PCA computes covariance matrix, performs eigen decomposition, selects top-k eigenvectors, and projects data onto this reduced basis. This minimizes reconstruction error in least squares sense.
Real-world example
Compressing image features for faster classification.
Common mistakes
- Thinking PCA removes rows instead of transforming features.
Follow-up questions
- What is reconstruction error?
- Why top-k eigenvectors?