Dimensionality Reduction: PCA, t-SNE & UMAP

📉 Dimensionality Reduction

Dataset

Method

Perplexity / neighbours: 20

MethodPCA

Status—

Iteration0 / 0

Loss (KL / CE)—

Eigenvalue λ₁—

Eigenvalue λ₂—

Eigenvalue λ₃—

Var. explained PC1—

Var. explained PC2—

Cumulative (PC1+PC2)—

PCA finds the orthogonal directions of maximum variance via eigendecomposition of the covariance matrix — a global, linear projection. t-SNE / UMAP instead try to preserve local neighbourhood structure — which points are close to which — often revealing cluster shape that a straight linear projection misses.

3D point cloud (source)blobs

2D projectionPCA

Drag the left panel to orbit the 3D cloud. The right panel is the live low-dimensional embedding computed by the selected method — for PCA it is an exact linear projection onto the top two eigenvectors; for t-SNE/UMAP-style methods it converges over iterations as the optimisation runs.