Principal Component Analysis (PCA)

3-Second Blueprint (English)

1. PCA compresses high-dimensional data into uncorrelated principal components ranked from most to least preserved variance for clear analysis.
2. Maximizing the sum of squared inner-product projections onto a unit vector via Lagrange multipliers yields the dominant axis of variation.
3. Orthogonal eigenvectors of the covariance matrix define component directions while normalized eigenvalues measure variance explained.