#covariance

1 articles

01 ·Linear Algebra·FREE·PAPER·11 min read PCA from Scratch — Eigenvectors as the Axes of Your Data A cloud of correlated data has a grain — a direction along which it varies most. Principal component analysis is the machinery that finds that grain. This article builds it from one picture: center the data, ask which direction carries the most variance, and discover that the answer is an eigenvector of the covariance matrix. Eigenvalues turn out to be the variance along each axis, the top few axes give you dimensionality reduction, and the explained-variance ratio tells you what you threw away.