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Cited by 337Single-cell and spatial transcriptomicsGene expression and cancer classificationTopological and Geometric Data Analysis

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Interpretable dimensionality reduction of single cell transcriptome data with deep generative models

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Ding, Jiarui, Condon, Anne, Shah, Sohrab P.·2018·Nature Communications
DOI 10.1038/s41467-018-04368-5PMC PMC5962608

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Abstract

Single-cell RNA-sequencing has great potential to discover cell types, identify cell states, trace development lineages, and reconstruct the spatial organization of cells. However, dimension reduction to interpret structure in single-cell sequencing data remains a challenge. Existing algorithms are either not able to uncover the clustering structures in the data or lose global information such as groups of clusters that are close to each other. We present a robust statistical model, scvis, to capture and visualize the low-dimensional structures in single-cell gene expression data. Simulation results demonstrate that low-dimensional representations learned by scvis preserve both the local and global neighbor structures in the data. In addition, scvis is robust to the number of data points and learns a probabilistic parametric mapping function to add new data points to an existing embedding. We then use scvis to analyze four single-cell RNA-sequencing datasets, exemplifying interpretable two-dimensional representations of the high-dimensional single-cell RNA-sequencing data.

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Fig. 1 Overview of the scvis method. a scvis model assumptions: given a low-dimensional point drawn from a simple distribution, e.g., a two-dimensional standard normal distribution, a high-dimensional gene expression vector of a cell can be generated by drawing a sample from the distribution p(x | z, θ). The heatmap represents a cell–gene expression matrix, where each row is a cell and each column is a gene. Color encodes the expression levels of genes in cells. The data-point-specific parameters θ are determined by a model neural network. The model neural network (a feedforward neural network) consists of an input layer, several hidden layers, and an output layer. The output layer outputs the parameters θ of p(x | z, θ). b scvis inference: given a high-dimensional gene expression vector of a cell (a row of the heatmap), scvis obtains its low-dimensional representation by sampling from the conditional distribution q(z | x, ϕ). The data-point-specific parameters ϕ are determined by a variational inference neural network. The inference neural network is also a feedforward neural network and its output layer outputs the parameters ϕ of q(z | x, ϕ). Again, the heatmap represents a cell–gene expression matrix. The scatter plot shows samples drawn from the variational posterior distributions q(z | x, ϕ)
Fig. 1 Overview of the scvis method. a scvis model assumptions: given a low-dimensional point drawn from a simple distribution, e.g., a two-dimensional standard normal distribution, a high-dimensional gene expression vector of a cell can be generated by drawing a sample from the distribution p(x | z, θ). The heatmap represents a cell–gene expression matrix, where each row is a cell and each column is a gene. Color encodes the expression levels of genes in cells. The data-point-specific parameters θ are determined by a model neural network. The model neural network (a feedforward neural network) consists of an input layer, several hidden layers, and an output layer. The output layer outputs the parameters θ of p(x | z, θ). b scvis inference: given a high-dimensional gene expression vector of a cell (a row of the heatmap), scvis obtains its low-dimensional representation by sampling from the conditional distribution q(z | x, ϕ). The data-point-specific parameters ϕ are determined by a variational inference neural network. The inference neural network is also a feedforward neural network and its output layer outputs the parameters ϕ of q(z | x, ϕ). Again, the heatmap represents a cell–gene expression matrix. The scatter plot shows samples drawn from the variational posterior distributions q(z | x, ϕ)CC BY · PubMed Central
Fig. 2 Benchmarking scvis against t-SNE on synthetic data. a The original 2200 two-dimensional synthetic data points (points are colored by cluster labels. The randomly distributed outliers are also colored in a distinct color, same for b, c), b t-SNE results on the transformed nine-dimensional dataset with default perplexity parameter of 30, c scvis results, d coloring points based on their log-likelihoods from scvis, e the kernel density estimates of the scvis results, where the density contours are represented by lines, f average K-nearest neighbor preservations across ten runs for different Ks, and g the average K-nearest neighbor preservations (K = 10) for different numbers of subsampled data points from ten repeated runs. The numbers at the top are the adjusted p-values (FDR, one-sided Welch’s t-test) comparing the average Knn preservations from scvis with those from t-SNE. Boxplots in f, g denote the medians and the interquartile ranges (IQRs). The whiskers of a boxplot are the lowest datum still within 1.5 IQR of the lower quartile and the highest datum still within 1.5 IQR of the upper quartile
Fig. 2 Benchmarking scvis against t-SNE on synthetic data. a The original 2200 two-dimensional synthetic data points (points are colored by cluster labels. The randomly distributed outliers are also colored in a distinct color, same for b, c), b t-SNE results on the transformed nine-dimensional dataset with default perplexity parameter of 30, c scvis results, d coloring points based on their log-likelihoods from scvis, e the kernel density estimates of the scvis results, where the density contours are represented by lines, f average K-nearest neighbor preservations across ten runs for different Ks, and g the average K-nearest neighbor preservations (K = 10) for different numbers of subsampled data points from ten repeated runs. The numbers at the top are the adjusted p-values (FDR, one-sided Welch’s t-test) comparing the average Knn preservations from scvis with those from t-SNE. Boxplots in f, g denote the medians and the interquartile ranges (IQRs). The whiskers of a boxplot are the lowest datum still within 1.5 IQR of the lower quartile and the highest datum still within 1.5 IQR of the upper quartileCC BY · PubMed Central
Fig. 3 Benchmarking scvis against GPLVM, parametric t-SNE, and PCA to embed 22,000 synthetic out-of-sample data. a scvis mapping 22,000 new data points based on the learned probabilistic mapping function from the 2200 training data points, b the estimated log-likelihoods, and c the average K-nearest neighbor classification accuracies for different Ks across 11 runs, the classifiers were trained on the 11 embeddings from the 2200 points. The numbers at the top are the FDR (one-sided Mann–Whitney U-test) comparing the K-nearest neighbor classification accuracy from scvis with those from GPLVM (orange, bottom) and those from parametric t-SNE (golden, top). Notice that, for GPLVM, two runs produced bad results and were not plotted in the figure. Boxplots denote the medians and the interquartile ranges (IQR). The whiskers of a boxplot are the lowest datum still within 1.5 IQR of the lower quartile and the highest datum still within 1.5 IQR of the upper quartile. d scvis results on the larger dataset with the same perplexity parameter as used in Fig. 2; e scvis log-likelihoods on the larger dataset; and f t-SNE results on the larger dataset
Fig. 3 Benchmarking scvis against GPLVM, parametric t-SNE, and PCA to embed 22,000 synthetic out-of-sample data. a scvis mapping 22,000 new data points based on the learned probabilistic mapping function from the 2200 training data points, b the estimated log-likelihoods, and c the average K-nearest neighbor classification accuracies for different Ks across 11 runs, the classifiers were trained on the 11 embeddings from the 2200 points. The numbers at the top are the FDR (one-sided Mann–Whitney U-test) comparing the K-nearest neighbor classification accuracy from scvis with those from GPLVM (orange, bottom) and those from parametric t-SNE (golden, top). Notice that, for GPLVM, two runs produced bad results and were not plotted in the figure. Boxplots denote the medians and the interquartile ranges (IQR). The whiskers of a boxplot are the lowest datum still within 1.5 IQR of the lower quartile and the highest datum still within 1.5 IQR of the upper quartile. d scvis results on the larger dataset with the same perplexity parameter as used in Fig. 2; e scvis log-likelihoods on the larger dataset; and f t-SNE results on the larger datasetCC BY · PubMed Central
Fig. 4 Learning a probabilistic mapping function from the bipolar data and applying the function to the independently generated mouse retina dataset. a scvis learned two-dimensional representations of the bipolar dataset, b coloring each point by the estimated log-likelihood, c the whole mouse retina dataset was directly projected to a two-dimensional space by the probabilistic mapping function learned from the bipolar data, and d coloring each point from the retina dataset by the estimated log-likelihood
Fig. 4 Learning a probabilistic mapping function from the bipolar data and applying the function to the independently generated mouse retina dataset. a scvis learned two-dimensional representations of the bipolar dataset, b coloring each point by the estimated log-likelihood, c the whole mouse retina dataset was directly projected to a two-dimensional space by the probabilistic mapping function learned from the bipolar data, and d coloring each point from the retina dataset by the estimated log-likelihoodCC BY · PubMed Central
Fig. 5 scvis learned low-dimensional representations. a The oligodendroglioma dataset, each cell is colored by its patient of origin, b the oligodendroglioma dataset, each cell is colored by its linage score from Tirosh et al.44, c the melanoma dataset, each cell is colored by its cell type, and d the melanoma dataset, each cell is colored by its patient of origin
Fig. 5 scvis learned low-dimensional representations. a The oligodendroglioma dataset, each cell is colored by its patient of origin, b the oligodendroglioma dataset, each cell is colored by its linage score from Tirosh et al.44, c the melanoma dataset, each cell is colored by its cell type, and d the melanoma dataset, each cell is colored by its patient of originCC BY · PubMed Central
Fig. 6 The scvis directed probabilistic graphical model and the variational approximation of its posterior. Circles represent random variables. Squares represent deterministic parameters. Shaded nodes are observed, and unshaded nodes are hidden. Here we use the plate notation, i.e., nodes inside each box will get repeated when the node is unpacked (the number of repeats is on the bottom right corner of each box). Each node and its parents constitute a family. Given the parents, a random variable is independent of the ancestors. Therefore, the joint distribution of all the random variables is the product of the family conditional distributions. a The generative model to generate data xn, and b the variational approximation q(zn | xn, ϕ) to the posterior p(zn | xn, θ)
Fig. 6 The scvis directed probabilistic graphical model and the variational approximation of its posterior. Circles represent random variables. Squares represent deterministic parameters. Shaded nodes are observed, and unshaded nodes are hidden. Here we use the plate notation, i.e., nodes inside each box will get repeated when the node is unpacked (the number of repeats is on the bottom right corner of each box). Each node and its parents constitute a family. Given the parents, a random variable is independent of the ancestors. Therefore, the joint distribution of all the random variables is the product of the family conditional distributions. a The generative model to generate data xn, and b the variational approximation q(zn | xn, ϕ) to the posterior p(zn | xn, θ)CC BY · PubMed Central

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Research works printed but not linked: 2

  1. Cao, J. et al. Comprehensive single-cell transcriptional profiling of a multicellular organism. Science 357, 661–667 (2017). · DOI · Paper page
  2. Abadi, M. et al. TensorFlow: large-scale machine learning on heterogeneous systems. Preprint at https://static.googleusercontent.com/media/research.google.com/en//pubs/archive/45166.pdf (2015).

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Metadata

Authors
Ding, J., Condon, A., & Shah, S. P.
Affiliations
  • Broad Institute (US)
  • University of British Columbia (CA)
  • BC Cancer Agency (CA)
Corresponding author
  • Ding, Jiarui
  • Shah, Sohrab P.
ORCID
Venue
Nature Communications
Publisher
Springer Science and Business Media LLC
Published
2018-05-21
Volume
9
Issue
1
Pages
2002-2002
ISSN
2041-1723 (ISSN-L)
DOI
10.1038/s41467-018-04368-5
PMC
PMC5962608
OpenAlex
W2949272108
Cited by
337
References
62
Citations by year
2026: 12 · 2025: 32 · 2024: 38 · 2023: 50 · 2022: 48 · 2021: 52 · 2020: 49 · 2019: 47 · 2018: 8
FWCI
13.87
Type
journal article
Language
en
Open access
Licence
Locations
  • Nature Communications (publishedVersion, cc-by)
  • bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by-nc-nd)
  • Europe PMC (PubMed Central) (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • RePEc: Research Papers in Economics (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
Funders
  • Genome Canada
  • Michael Smith Health Research BC
  • Canada Research Chairs
  • Terry Fox Research Institute
  • BC Cancer Foundation
  • Canadian Institutes of Health Research (143246_1, 115170_1)
  • Canadian Cancer Society Research Institute (701584)
  • Natural Sciences and Engineering Research Council of Canada
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 RNA sequencing, dimensionality reduction, scVI, deep generative models, interpretable embeddings, cell clustering, probabilistic embedding, data augmentation, cell type discovery, cell state identification
MeSH terms
Algorithms, Animals, Cells, Humans, RNA, Software, Models, Statistical, Sequence Analysis, RNA, Databases, Nucleic Acid, Mice, Single-Cell Analysis, Transcriptome

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