What is PCA mathematically based on?
Updated May 16, 2026
Short answer
PCA is based on eigen decomposition of covariance matrix or SVD.
Deep explanation
PCA solves an optimization problem maximizing variance under orthogonality constraints. This leads to eigen decomposition or singular value decomposition of centered data matrix.
Real-world example
Used in compressing high-dimensional sensor data.
Common mistakes
- Ignoring centering of data before PCA.
Follow-up questions
- Why must data be centered?
- What optimization does PCA solve?