Dimensionality Reduction with Strong Global Structure Preservation

Modern dimensionality reduction (DR) methods, including t-SNE and UMAP, often distort global relationships, limiting the interpretability of embeddings. We introduce two complementary objectives that jointly preserve global geometry and local structure. Landmark Mantel Correlation (LMC) aligns high- and low-dimensional distances with respect to a small set of landmarks, providing an efficient global constraint. Multi-resolution Cluster Supervision (MiCS) promotes local fidelity by encouraging cluster assignments--estimated across multiple resolutions--to remain predictable after projection. Evaluated on 20 biomedical datasets, UMAP+LMC and MiCS+LMC achieve the best overall performance, demonstrating that global and local structure can be optimized simultaneously rather than being inherently conflicting. Our approach consistently outperforms existing methods for global and local structure preservation, yielding more reliable and interpretable visualizations.