ArticleiScience2021
Hyperbolic geometry of gene expression.
Article in iScience, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 15 papers.
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
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Who cites it
15 citing papers in PubMed, 41 citations in OpenAlex.
- Multiscale hyperbolic embedding reveals hierarchical structure in complex biological systems.NPJ systems biology and applications · 2026Article
- The cell as a token: high-dimensional geometry in language models and cell embeddings.Bioinformatics (Oxford, England) · 2025Review
- Multiscale Cell-Cell Interactive Spatial Transcriptomics Analysis.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2025Article
- Multiscale Hyperbolic Embedding for Cell Hierarchies in Large-Scale Bioinformatics Data.bioRxiv : the preprint server for biology · 2025Article
- scE2EGAE: enhancing single-cell RNA-Seq data analysis through an end-to-end cell-graph-learnable graph autoencoder with differentiable edge sampling.Biology direct · 2025Article
- Unveiling the role of IL7R in metabolism-associated fatty liver disease leading to hepatocellular carcinoma through transcriptomic and machine learning approaches.Discover oncology · 2025Article
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- Dimensionality reduction for visualizing spatially resolved profiling data using SpaSNE.GigaScience · 2025Article
- ImAge quantitates aging and rejuvenation.Nature aging · 2024Article
- Charting cellular differentiation trajectories with Ricci flow.Nature communications · 2024Article
- Multiscale differential geometry learning of networks with applications to single-cell RNA sequencing data.Computers in biology and medicine · 2024Article
- Principal Component Analysis in Space Forms.IEEE transactions on signal processing : a publication of the IEEE Signal Processing Society · 2024Article
- Imaging-based chromatin and epigenetic age, ImAge, quantitates aging and rejuvenation.Research square · 2023Article
- The San Diego Nathan Shock Center: tackling the heterogeneity of aging.GeroScience · 2021Article
- Computing the Riemannian curvature of image patch and single-cell RNA sequencing data manifolds using extrinsic differential geometry.Proceedings of the National Academy of Sciences of the United States of America · 2021Article
Corrections and comments
PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.
Authors and funding
2 authors at 1 institution in 1 country.
Funding
Abstract
Patterns of gene expressions play a key role in determining cell state. Although correlations in gene expressions have been well documented, most of the current methods treat them as independent variables. One way to take into account gene correlations is to find a low-dimensional curved geometry that describes variation in the data. Here we develop such a method and find that gene expression across multiple cell types exhibits a low-dimensional hyperbolic structure. When more genes are taken into account, hyperbolic effects become stronger but representation remains low dimensional. The size of the hyperbolic map, which indicates the hierarchical depth of the data, was the largest for human cells, the smallest for mouse embryonic cells, and intermediate in differentiated cells from different mouse organs. We also describe how hyperbolic metric can be incorporated into the t-SNE method to improve visualizations compared with leading methods.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.