UMAP Visualization

Harvard EPS-210 | Interactive tutorial — Explore Uniform Manifold Approximation and Projection

Original Data (High-D Space)

UMAP Embedding (2D)

ψ(x) = 1 / (1 + a·x²ᵇ)
Smooth approximation to fuzzy membership

Cross-Entropy Loss

k-NN Graph

vⱼ|ᵢ = exp(-(d(xᵢ,xⱼ) - ρᵢ) / σᵢ)
Local connectivity with adaptive σᵢ

UMAP Parameters

15
n_neighbors
0.1
min_dist
n_neighbors 15
min_dist 0.10

n_neighbors: local vs global structure
min_dist: how tightly points cluster

Algorithm

0
Epoch
Ready

Learning Rate

α (alpha) 1.0

Statistics

Points
0
Loss
--
Clusters
0
Edges
0

Quick Examples

How it works: UMAP constructs a fuzzy topological representation using k-NN graphs, then optimizes a low-D embedding to match this structure. Unlike t-SNE, it better preserves global structure and is generally faster.