What is the difference between deterministic and stochastic dimensionality reduction?

Deterministic methods always produce same output; stochastic methods involve randomness.

Deterministic methods like PCA produce identical results for the same input due to closed-form solutions. Stochastic methods like t-SNE or UMAP involve random initialization or sampling, leading to variability in results unless controlled with seeds. Stochasticity can help escape poor local minima but reduces reproducibility.