PCA 2D demo: components, reconstruction, and vector sum for a selected point

Dataset

Samples:

Noise:

Seed:

Reconstruction components

Include PC1

Include PC2

Click a point to select it. You will see its decomposition: x = μ + z1·u1 + z2·u2, and the reconstruction using selected PCs.

View

Show PC axes

Link x to x̂

Show vector sum (selected point)

Numbers

λ1: λ2: Explained var PC1: Explained var PC2: MSE(x, x̂):

Original points x

Reconstructed points x̂ from selected PCs

PC1 axis (u1)

PC2 axis (u2)

Selected point decomposition

click a point

z1 = u1ᵀ(x-μ)

z2 = u2ᵀ(x-μ)

z1·u1

z2·u2

x̂ (selected PCs)

residual r = x - x̂

||r||²

Tip: After selecting a point, toggle PC1/PC2 and watch how x̂ changes as a sum of vectors from the mean.

PCA in 2D: choose components, see reconstruction and per-point vector sum