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Assessing single-cell transcriptomic variability through density-preserving data visualization


Nonlinear data visualization methods, such as t-distributed stochastic neighbor embedding (t-SNE) and uniform manifold approximation and projection (UMAP), summarize the complex transcriptomic landscape of single cells in two dimensions or three dimensions, but they neglect the local density of data points in the original space, often resulting in misleading visualizations where densely populated subsets of cells are given more visual space than warranted by their transcriptional diversity in the dataset. Here we present den-SNE and densMAP, which are density-preserving visualization tools based on t-SNE and UMAP, respectively, and demonstrate their ability to accurately incorporate information about transcriptomic variability into the visual interpretation of single-cell RNA sequencing data. Applied to recently published datasets, our methods reveal significant changes in transcriptomic variability in a range of biological processes, including heterogeneity in transcriptomic variability of immune cells in blood and tumor, human immune cell specialization and the developmental trajectory of Caenorhabditis elegans. Our methods are readily applicable to visualizing high-dimensional data in other scientific domains.

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Fig. 1: Overview of density-preserving data visualization.
Fig. 2: Density-preserving visualization more accurately captures the true underlying shape of synthetic datasets than existing tools.
Fig. 3: Density-preserving visualization reveals heterogeneity in transcriptomic variability of immune cells in blood and tumor.
Fig. 4: Density-preserving visualization of PBMCs reveals monocyte and DC subsets that differ in transcriptomic variability.
Fig. 5: Density-preserving visualization of C. elegans development reveals temporal dynamics of transcriptomic variability in different developmental lineages.

Data availability

The lung cancer7 and C. elegans9 datasets are available from the Gene Expression Omnibus (GEO) database with accession numbers GSE127465 and GSE126954, respectively. The PBMC dataset8 is available from 10× Genomics at For our validation datasets, the secondary lung cancer dataset17 is available from GEO (GSE99254), and the PBMC2 (ref. 22) and PBMC3 (ref. 23) datasets can be accessed through the Broad Institute’s Single Cell Portal ( with dataset IDs SCP43 and SCP345, respectively. Data access applications for the UK Biobank data can be submitted at The MNIST dataset is available at We also provide our preprocessed data for the main datasets (lung cancer, PBMC and C. elegans) at

Code availability

We provide the software for den-SNE and densMAP in the densVis package available at Our densMAP implementation is also available as part of the Python umap package (


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This work is, in part, supported by NIH U01 CA250554 (to B.B). H.C. is partially supported by Eric and Wendy Schmidt through the Schmidt Fellows Program at the Broad Institute. The authors thank B. Hie, B. DeMeo, E. Zhong and J. Peters for helpful discussions. Our visualization of genotype data was conducted using the UK Biobank Resource under application number 46341 in keeping with the informed consent given by its participants. was used to generate Fig. 4d.

Author information




All authors conceived the method, evaluated results and wrote the manuscript. A.N. and H.C. implemented the software and conducted the experiments. B.B. and H.C. guided the research.

Corresponding authors

Correspondence to Bonnie Berger or Hyunghoon Cho.

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Competing interests

The authors declare no competing interests.

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Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Density-preserving methods more accurately visualize diversity of small subpopulations in UKBB data.

We visualize the genotype profiles of 97,676 UKBB participants (a 20% subsample of the dataset) using a, densMAP, b, UMAP, c, den-SNE and d, t-SNE. For each, in the left plot, points corresponding to white people are colored by five computationally-identified subpopulations (Methods); in the middle plot, non-white people are colored according to their ethnicity; right shows correlation of local radius between the original dataset and the embedding, with points colored by ethnicity and R2 reported. We show the analogous scatter plots using neighborhood count to measure in the visualization in Supplementary Figure 18. As 94% of the the people in the UKB dataset self-identified as white, the UMAP and t-SNE plots give overwhelming visual space to this group, hiding the genetic variability of the other ethnic groups. The density-preserving plots, however, clearly expand the clusters of non-white people as well as certain white subpopulations, more accurately conveying their genetic diversity.

Extended Data Fig. 2 Density-preserving visualization of MNIST handwritten digit image dataset reveals the relative homogeneity of the digit 1.

We visualize the MNIST handwritten digits with a, denSNE and t-SNE and b, densMAP and UMAP, with points colored by digit. Note that the size of the cluster corresponding to the digit 1 shrinks under both density-preserving algorithms. Plots on the right show the correlation of the local radii between the original dataset and the embedding in each algorithm, with points colored by digit and the R2 score reported. The higher R2 for the density-preserving methods illustrates that the digit 1 indeed has higher density than the other digits. We show the analogous scatter plots using neighborhood count to measure local density in Supplementary Figure 19.

Extended Data Fig. 3 den-SNE and densMAP are nearly as efficient as t-SNE and UMAP in runtime and memory.

We compare a, den-SNE and t-SNE and b, densMAP and UMAP with respect to runtime and peak memory usage on all the datasets analyzed in this study. For these tests, we exclude the time taken to compute the local radii of the final embedding, which is used only for evaluation and does not affect the embedding. Left plots running time in seconds at different data sizes (achieved by subsampling the datasets; Methods); middle shows the ratio of the density-preserving algorithm’s runtime to that of the original method; right shows peak memory usage over different data sizes. Although density-preserving methods take longer, the overhead is small (around 30% additional runtime for den-SNE and 20% additional runtime for densMAP both for our largest dataset). Both densMAP and UMAP obtain fast runtimes for large datasets, taking less than ~ 30 minutes for all our datasets. Peak memory usage is the same between t-SNE and den-SNE, and differs by a small constant between UMAP and densMAP.

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Supplementary Figs. 1–20, Supplementary Tables 1–11 and Supplementary Notes 1–4

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Narayan, A., Berger, B. & Cho, H. Assessing single-cell transcriptomic variability through density-preserving data visualization. Nat Biotechnol (2021).

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