What is the difference between metric and non-metric dimensionality reduction?

Metric methods preserve actual distances, while non-metric methods preserve only rank or neighborhood relationships.

Metric dimensionality reduction techniques (like PCA, Isomap, MDS) aim to preserve exact or approximate pairwise distances between points. Non-metric methods (like t-SNE) focus on preserving relative similarities or neighborhood rankings rather than exact distances. This makes non-metric methods better for visualization but less suitable for downstream tasks requiring geometric fidelity.