PCA & Eigenvalue Decomposition

Visualize how PCA decomposes data into principal components — with covariance matrix and eigenspectrum

Data space + PC axes (drag to add points)

Dataset

N points: 200 Correlation ρ: 0.80

Reconstruction

PCs to keep: 2

Eigenspectrum

Covariance Matrix

PCA = eigendecomposition of the covariance matrix Σ.
Columns of V are principal components (eigenvectors).
Eigenvalues λᵢ = variance explained by PCᵢ.

Truncated reconstruction: x̂ = μ + Σᵢ⁻ᵏ(xᵀvᵢ)vᵢ

Click on the data canvas (custom mode) to add points.