Multiscale hyperbolic embedding reveals hierarchical structure in complex biological systems.

Area of Science:

• Computational Biology
• Data Visualization
• Bioinformatics

Background:

• Biological and computational datasets are rapidly expanding, requiring scalable visualization and interpretation methods.
• Hyperbolic embeddings excel at representing hierarchical data, but current methods lack scalability and flexibility.
• Existing techniques like UMAP and t-SNE often sacrifice global structure for local detail.

Purpose of the Study:

• To introduce MuH-MDS, a novel multiscale hyperbolic multidimensional scaling algorithm.
• To address the limitations of existing hyperbolic embedding methods in terms of scalability and curvature assumptions.
• To provide a robust framework for analyzing large-scale biological datasets with intrinsic hierarchies.

Main Methods:

• MuH-MDS utilizes an adiabatic optimization strategy, iteratively refining local positions while temporarily fixing cluster centroids.
• This approach significantly accelerates computation, enabling analysis of datasets with over 80,000 samples.
• The algorithm is applied to diverse benchmarks, including single-cell RNA sequencing data from C. elegans embryogenesis.

Main Results:

• MuH-MDS demonstrates a computational speedup of up to 1000x compared to existing methods.
• It successfully uncovers intrinsic hierarchical organization in complex biological datasets.
• The method improves pseudotime inference and lineage reconstruction accuracy.

Conclusions:

• MuH-MDS offers a scalable and metrically faithful framework for multiscale analysis of complex biological systems.
• It preserves both local detail and global hierarchy, outperforming UMAP and t-SNE in preserving metric fidelity.
• This algorithm enhances the quantitative interpretation and visualization of large, hierarchical biological data.