Principal Component Analysis on low-dimensional manifolds embedded in 3D
3D Data (drag to rotate)
PCA Projection (2D)
PC1 variance: — PC2 variance: —
Dataset
PCA
PCA finds orthogonal directions of maximum variance. On a Swiss Roll, the top 2 PCs capture global structure but cannot unfurl the manifold — that requires nonlinear methods (t-SNE, UMAP, Isomap).
Drag the 3D view to rotate.
Key insight: PCA is optimal for Gaussian data. Manifold structure requires geodesic distances, not Euclidean.