Abstract The rapid expansion of biological and computational datasets demands scalable methods that support both visualization and quantitative interpretation. Hyperbolic embeddings are well-suited to represent hierarchical structure, but existing approaches are limited by fixed curvature assumptions or poor scalability to large datasets. We introduce MuH-MDS , a multiscale hyperbolic multidimensional scaling algorithm that employs an adiabatic optimization strategy : local positions are iteratively refined while cluster centroids are temporarily fixed. This strategy accelerates computation by 10 3 and enables scaling to datasets with over 80,000 samples. Applied to diverse benchmarks, including C. elegans embryogenesis scRNA-seq data, MuH-MDS uncovers intrinsic hierarchical organization and improves both pseudotime inference and lineage reconstruction relative to UMAP and other standard methods. In contrast to UMAP and t-SNE, which prioritize local neighborhoods at the expense of global coherence and metric fidelity, MuH-MDS preserves both local detail and global hierarchy, providing a metrically faithful framework for multiscale analysis of complex biological systems.
Yao et al. (Tue,) studied this question.