Principal Component Analysis - Interactive Tutorial

Harvard EPS-210 | Interactive tutorial — Explore dimensionality reduction and variance maximization

Original Data with Principal Components

PC1

PC2

Mean

Projected Data (PC Space)

z = Wᵀ(x - μ)

Project centered data onto eigenvectors

Variance Explained (Scree Plot)

Reconstruction

x̂ = μ + Wz

Reconstruct from k principal components

Data Points

Click on the data canvas to add points

Visualization Options

Show mean point Show PC vectors Show projection lines Show covariance ellipse

Reconstruction

Reconstruction Error 0.00%

Principal Components

Statistics

Points

Total Var

Quick Examples

How it works: PCA finds orthogonal directions (principal components) that maximize variance. PC1 captures the most variance, PC2 the second most (perpendicular to PC1), etc. It's computed via eigendecomposition of the covariance matrix.