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PreprintCited by 379Single-cell and spatial transcriptomicsGene expression and cancer classificationTopological and Geometric Data Analysis

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The Specious Art of Single-Cell Genomics

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Chari, Tara, Pachter, Lior·2021·PLoS Computational Biology
DOI 10.1101/2021.08.25.457696PMC PMC10434946
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Abstract

Dimensionality reduction is standard practice for filtering noise and identifying relevant features in large-scale data analyses. In biology, single-cell genomics studies typically begin with reduction to two or three dimensions to produce ‘all-in-one’ visuals of the data that are amenable to the human eye, and these are subsequently used for qualitative and quantitative exploratory analysis. However, there is little theoretical support for this practice, and we show that extreme dimension reduction, from hundreds or thousands of dimensions to two, inevitably induces significant distortion of high-dimensional datasets. We therefore examine the practical implications of low-dimensional embedding of single-cell data, and find that extensive distortions and inconsistent practices make such embeddings counter-productive for exploratory, biological analyses. In lieu of this, we discuss alternative approaches for conducting targeted embedding and feature exploration, to enable hypothesis-driven biological discovery.

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Figures

Fig 1 Necessary properties for embedding applications. Application rows denote biological tasks, and columns denote which properties are necessary, i.e., key geometric properties whose preservation or representation is assumed in the task.
Fig 1 Necessary properties for embedding applications. Application rows denote biological tasks, and columns denote which properties are necessary, i.e., key geometric properties whose preservation or representation is assumed in the task.CC BY · PubMed Central
Fig 2 Distortion of necessary properties in embeddings. (a) (i) Distribution of Jaccard distance of cell neighbors in PCA-preprocessed 2D embeddings and the relevant PCA space, as compared to ambient space. (ii) Distribution of Jaccard distance of cell neighbors in PCA-preprocessed 2D embeddings, as compared to the higher dimensional PCA space. (b) (i) Boxplot of correlations of cell type neighbor rankings to ambient space for the PCA-preprocessed 2D embeddings and the relevant PCA space. (ii) Boxplot of correlations of cell type neighbor rankings to the relevant higher dimensional PCA space for the PCA-preprocessed 2D embeddings. Embeddings generated n = 3 times. (c) Selection of equidistant groups with “near” or “far” distances in ambient space. UMAP embedding of the data in gray circles, with orange circles denoting all cells within the previously determined equidistant groups.
Fig 2 Distortion of necessary properties in embeddings. (a) (i) Distribution of Jaccard distance of cell neighbors in PCA-preprocessed 2D embeddings and the relevant PCA space, as compared to ambient space. (ii) Distribution of Jaccard distance of cell neighbors in PCA-preprocessed 2D embeddings, as compared to the higher dimensional PCA space. (b) (i) Boxplot of correlations of cell type neighbor rankings to ambient space for the PCA-preprocessed 2D embeddings and the relevant PCA space. (ii) Boxplot of correlations of cell type neighbor rankings to the relevant higher dimensional PCA space for the PCA-preprocessed 2D embeddings. Embeddings generated n = 3 times. (c) Selection of equidistant groups with “near” or “far” distances in ambient space. UMAP embedding of the data in gray circles, with orange circles denoting all cells within the previously determined equidistant groups.CC BY · PubMed Central
Fig 3 Distortion of mixing patterns. (a) Left plot shows “Log-normalized” ambient (blue) and 2D embedding (orange) distributions of mixing (fraction of cell neighbors in the same condition), where 1.0 is no mixing. Corresponding UMAP shown next to it. Right plot shows “Variance-Stabilized and Scaled” ambient (blue) and 2D embedding (orange) distributions of mixing (fraction of cell neighbors in the same condition). Corresponding UMAP shown next to it. (b) Left plot shows “MNN Integrated” ambient (blue) and 2D embedding (orange) distributions of mixing (fraction of cell neighbors in the same condition) for CEL-Seq cells. Corresponding UMAP shown next to it. Right plot shows “Scanorama Integrated” ambient (blue) and 2D embedding (orange) distributions of mixing (fraction of cell neighbors in the same condition) for CEL-Seq cells. Corresponding UMAP shown next to it.
Fig 3 Distortion of mixing patterns. (a) Left plot shows “Log-normalized” ambient (blue) and 2D embedding (orange) distributions of mixing (fraction of cell neighbors in the same condition), where 1.0 is no mixing. Corresponding UMAP shown next to it. Right plot shows “Variance-Stabilized and Scaled” ambient (blue) and 2D embedding (orange) distributions of mixing (fraction of cell neighbors in the same condition). Corresponding UMAP shown next to it. (b) Left plot shows “MNN Integrated” ambient (blue) and 2D embedding (orange) distributions of mixing (fraction of cell neighbors in the same condition) for CEL-Seq cells. Corresponding UMAP shown next to it. Right plot shows “Scanorama Integrated” ambient (blue) and 2D embedding (orange) distributions of mixing (fraction of cell neighbors in the same condition) for CEL-Seq cells. Corresponding UMAP shown next to it.CC BY · PubMed Central
Fig 4 Distortion in cluster validation and relationships. (a) Prediction of cell label for 30% of the dataset(s) based on the labels of the 50 nearest neighbors. (b) Distributions of cell type inter- and intra-type distances for the ambient or reduced space (bottom). K-S distance shown as measure of separation, where higher values denote greater separation (see Methods in S1 Text).
Fig 4 Distortion in cluster validation and relationships. (a) Prediction of cell label for 30% of the dataset(s) based on the labels of the 50 nearest neighbors. (b) Distributions of cell type inter- and intra-type distances for the ambient or reduced space (bottom). K-S distance shown as measure of separation, where higher values denote greater separation (see Methods in S1 Text).CC BY · PubMed Central
Fig 5 Distortion in density-based visuals and analysis. (a) Top row (left to right) displays UMAP embedding with n_neighbors = 5, embedding contour plot colored by condition, same contour with just in utero cells, same contour with just ex utero cells. Bottom row shows same plots for UMAP embedding with n_neighbors = 50. (b) Top row shows same plots for t-SNE embedding with perplexity of 5. Bottom row shows same plots for t-SNE embedding with perplexity of 50. Numbers denote comparisons between plots, dashed lines denote a difference, and solid lines denote the same appearance.
Fig 5 Distortion in density-based visuals and analysis. (a) Top row (left to right) displays UMAP embedding with n_neighbors = 5, embedding contour plot colored by condition, same contour with just in utero cells, same contour with just ex utero cells. Bottom row shows same plots for UMAP embedding with n_neighbors = 50. (b) Top row shows same plots for t-SNE embedding with perplexity of 5. Bottom row shows same plots for t-SNE embedding with perplexity of 50. Numbers denote comparisons between plots, dashed lines denote a difference, and solid lines denote the same appearance.CC BY · PubMed Central
Fig 6 Distortion in trajectory inference and continuous relationships. (a) Velocyto RNA velocity embeddings for UMAPs made with 17 or 50 n_neighbors. Cell types of interest highlighted in gray. (b) Velocyto RNA velocity embeddings for t-SNEs made with perplexity of 17 or 50.
Fig 6 Distortion in trajectory inference and continuous relationships. (a) Velocyto RNA velocity embeddings for UMAPs made with 17 or 50 n_neighbors. Cell types of interest highlighted in gray. (b) Velocyto RNA velocity embeddings for t-SNEs made with perplexity of 17 or 50.CC BY · PubMed Central
Fig 7 Embedding properties are arbitrary. Elephant-shaped embeddings [62,63] shown on the left, with corresponding correlations of data embeddings to ambient space shown in right-hand plots, for inter- and intra-type distance metrics. Metrics calculated over n = 5 embeddings. Colors denote cell types, delineated in Fig W in S1 Text.
Fig 7 Embedding properties are arbitrary. Elephant-shaped embeddings [62,63] shown on the left, with corresponding correlations of data embeddings to ambient space shown in right-hand plots, for inter- and intra-type distance metrics. Metrics calculated over n = 5 embeddings. Colors denote cell types, delineated in Fig W in S1 Text.CC BY · PubMed Central
Fig 8 Relative contrast of the L1 and L2 metrics. Violin plots display kernel density estimates of the distribution of log2(Relative Contrast) ratio values for each dataset, computed for n = 5 random subsets of 1,000 HVGs selected for each dataset from its top 2,000 HVGs. Relative contrast was calculated as described in Methods in S1 Text and [30], in the ambient (gene) space. Distributions are shown across datasets of increasing sample size (cell number). Box plots are overlaid in black, with the median denoted by the white dot. Whiskers denote 1.5× the interquartile range. HVG, highly variable gene; NSC, neural stem cell; VMH, ventromedial hypothalamus.
Fig 8 Relative contrast of the L1 and L2 metrics. Violin plots display kernel density estimates of the distribution of log2(Relative Contrast) ratio values for each dataset, computed for n = 5 random subsets of 1,000 HVGs selected for each dataset from its top 2,000 HVGs. Relative contrast was calculated as described in Methods in S1 Text and [30], in the ambient (gene) space. Distributions are shown across datasets of increasing sample size (cell number). Box plots are overlaid in black, with the median denoted by the white dot. Whiskers denote 1.5× the interquartile range. HVG, highly variable gene; NSC, neural stem cell; VMH, ventromedial hypothalamus.CC BY · PubMed Central

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Research works printed but not linked: 4

  1. 2005, Approximation algorithms for low-distortion embeddings into low-dimensional spaces in SODA, 5, 119
  2. Tukey, J. W. Exploratory data analysis as part of a larger whole in Proceedings of the 18th conference on design of experiments in army research and development i. Washington, dc 1010 (apps.dtic.mil, 1972).
  3. Goldberger, J. , Roweis, S. , Hinton, G. & Salakhutdinov, R. Neighbourhood components analysis in Proceedings of the 17th International Conference on Neural Information Processing Systems (MIT Press, Vancouver, British Columbia, Canada, Dec. 2004), 513–520.
  4. 2008, SplitsTree 4.0-Computation of phylogenetic trees and networks, Bioinformatics, 14, 68

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Metadata

Authors
Chari, T., & Pachter, L.
Affiliations
California Institute of Technology (US)
Corresponding author
Pachter, Lior
ORCID
Venue
PLoS Computational Biology
Publisher
openRxiv
Published
2021-08-26
Volume
19
Issue
8
Pages
e1011288-e1011288
ISSN
1553-734X (ISSN-L)
DOI
10.1101/2021.08.25.457696
PMC
PMC10434946
OpenAlex
W4385945347
Cited by
379
References
93
Citations by year
2026: 73 · 2025: 97 · 2024: 102 · 2023: 63 · 2022: 40 · 2021: 3
FWCI
29.85
Type
journal article
Language
en
Open access
Licence
cc-by
Locations
  • PLoS Computational Biology (publishedVersion, cc-by)
  • bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by-nc)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • CaltechAUTHORS (California Institute of Technology) (submittedVersion, cc-by-nc)
  • RePEc: Research Papers in Economics (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
Funders
  • California Institute of Technology
  • Resnick Sustainability Institute for Science, Energy and Sustainability, California Institute of Technology
  • National Institutes of Health
  • National Institute of Mental Health (U19MH114830)
Topics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Single-cell and spatial transcriptomics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene expression and cancer classification
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
Keywords
single-cell genomics, dimensionality reduction, embedding distortion, high-dimensional data, exploratory data analysis
MeSH terms
Data Analysis, Humans, Genomics

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