What is the difference between global and local structure preservation in dimensionality reduction?

Global methods preserve overall geometry, while local methods preserve neighborhood relationships.

Global structure preservation focuses on maintaining large-scale distances and overall geometry of the dataset (e.g., PCA, classical MDS). Local structure preservation focuses on keeping nearest neighbors intact, even if global distances are distorted (e.g., t-SNE, UMAP). This trade-off exists because preserving both perfectly is often mathematically impossible in lower dimensions. Many modern methods prioritize local structure because it better reflects clustering and manifold geometry.