Dimensionality reduction for visualisation

Reduction of high-dimensional datasets to 2D for visualization & interpretation

Description

Dimensionality reduction is one of the key challenges in single-cell data representation. Routine single-cell RNA sequencing (scRNA-seq) experiments measure cells in roughly 20,000-30,000 dimensions (i.e., features - mostly gene transcripts but also other functional elements encoded in mRNA such as lncRNAs). Since its inception, scRNA-seq experiments have been growing in terms of the number of cells measured. Originally, cutting-edge SmartSeq experiments would yield a few hundred cells, at best. Now, it is not uncommon to see experiments that yield over 100,000 cells or even > 1 million cells.

Each feature in a dataset functions as a single dimension. While each of the ~30,000 dimensions measured in each cell contribute to an underlying data structure, the overall structure of the data is challenging to display in few dimensions due to data sparsity and the “curse of dimensionality” (distances in high dimensional data don’t distinguish data points well). Thus, we need to find a way to dimensionally reduce the data for visualization and interpretation.

Summary

viewof color_by_rank = Inputs.toggle({label: "Color by rank"})
viewof scale_column = Inputs.toggle({label: "Rescale per column"})

funkyheatmap(
    funky_heatmap_args.data,
    funky_heatmap_args.columns,
    funky_heatmap_args.column_info,
    funky_heatmap_args.column_groups,
    funky_heatmap_args.palettes,
    funky_heatmap_args.expand,
    funky_heatmap_args.col_annot_offset,
    funky_heatmap_args.add_abc,
    scale_column,
    {
        fontSize: 14,
        rowHeight: 26,
        rootStyle: 'max-width: none',
        colorByRank: color_by_rank
    }
);

Figure 1: Overview of the results per method. This figures shows the mean of the scaled scores (group Overall), the mean scores per dataset (group Dataset) and the mean scores per metric (group Metric).

funkyheatmap = (await require('d3@7').then(d3 => {
  window.d3 = d3;
  return import('https://unpkg.com/funkyheatmap-js@0.1.7');
})).default;

Metrics

• continuity¹: Continuity measures error of hard extrusions based on nearest neighbor coranking.

• Density preservation²: Similarity between local densities in the high-dimensional data and the reduced data.

• Distance correlation³: Spearman correlation between all pairwise Euclidean distances in the original and dimension-reduced data.

• Distance correlation (spectral)⁴: Spearman correlation between all pairwise diffusion distances in the original and dimension-reduced data.

• local continuity meta criterion¹: The local continuity meta criterion is the co-KNN size with baseline removal which favors locality.

• global property¹: The global property metric is a summary of the global co-KNN.

• local property¹: The local property metric is a summary of the local co-KNN.

• co-KNN size¹: co-KNN size counts how many points are in both k-nearest neighbors before and after the dimensionality reduction.

• co-KNN AUC¹: co-KNN AUC is area under the co-KNN curve.

• trustworthiness⁵: a measurement of similarity between the rank of each point’s nearest neighbors in the high-dimensional data and the reduced data.

Results

Results table of the scores per method, dataset and metric (after scaling). Use the filters to make a custom subselection of methods and datasets. The “Overall mean” dataset is the mean value across all datasets.

Details

Methods

• densMAP (logCP10k)²: densMAP is a modification of UMAP that adds an extra cost term in order to preserve information about the relative local density of the data. It is performed on the same inputs as UMAP. Links: Docs.

• densMAP (logCP10k, 1kHVG)²: densMAP is a modification of UMAP that adds an extra cost term in order to preserve information about the relative local density of the data. It is performed on the same inputs as UMAP. Links: Docs.

• densMAP PCA (logCP10k)²: densMAP is a modification of UMAP that adds an extra cost term in order to preserve information about the relative local density of the data. It is performed on the same inputs as UMAP. Links: Docs.

• densMAP PCA (logCP10k, 1kHVG)²: densMAP is a modification of UMAP that adds an extra cost term in order to preserve information about the relative local density of the data. It is performed on the same inputs as UMAP. Links: Docs.

• Diffusion maps⁴: Diffusion maps uses an affinity matrix to describe the similarity between data points, which is then transformed into a graph Laplacian. The eigenvalue-weighted eigenvectors of the graph Laplacian are then used to create the embedding. Diffusion maps is calculated on the logCPM expression matrix. Links: Docs.

• NeuralEE (CPU) (Default)⁷: NeuralEE is a neural network implementation of elastic embedding. It is a non-linear method that preserves pairwise distances between data points. NeuralEE uses a neural network to optimize an objective function that measures the difference between pairwise distances in the original high-dimensional space and the two-dimensional space. It is computed on both the recommended input from the package authors of 500 HVGs selected from a logged expression matrix (without sequencing depth scaling) and the default logCPM matrix with 1000 HVGs. Links: Docs.

• NeuralEE (CPU) (logCP10k, 1kHVG)⁷: NeuralEE is a neural network implementation of elastic embedding. It is a non-linear method that preserves pairwise distances between data points. NeuralEE uses a neural network to optimize an objective function that measures the difference between pairwise distances in the original high-dimensional space and the two-dimensional space. It is computed on both the recommended input from the package authors of 500 HVGs selected from a logged expression matrix (without sequencing depth scaling) and the default logCPM matrix with 1000 HVGs. Links: Docs.

• PCA (logCP10k)⁶: PCA or “Principal Component Analysis” is a linear method that finds orthogonal directions in the data that capture the most variance. The first two principal components are chosen as the two-dimensional embedding. We select only the first two principal components as the two-dimensional embedding. PCA is calculated on the logCPM expression matrix with and without selecting 1000 HVGs. Links: Docs.

• PCA (logCP10k, 1kHVG)⁶: PCA or “Principal Component Analysis” is a linear method that finds orthogonal directions in the data that capture the most variance. The first two principal components are chosen as the two-dimensional embedding. We select only the first two principal components as the two-dimensional embedding. PCA is calculated on the logCPM expression matrix with and without selecting 1000 HVGs. Links: Docs.

• PHATE (default)¹⁰: PHATE or “Potential of Heat - diffusion for Affinity - based Transition Embedding” uses the potential of heat diffusion to preserve trajectories in a dataset via a diffusion process. It is an affinity - based method that creates an embedding by finding the dominant eigenvalues of a Markov transition matrix. We evaluate several variants including using the recommended square - root transformed CPM matrix as input, this input with the gamma parameter set to zero and the normal logCPM transformed matrix with and without HVG selection. Links: Docs.

• PHATE (logCP10k, 1kHVG)¹⁰: PHATE or “Potential of Heat - diffusion for Affinity - based Transition Embedding” uses the potential of heat diffusion to preserve trajectories in a dataset via a diffusion process. It is an affinity - based method that creates an embedding by finding the dominant eigenvalues of a Markov transition matrix. We evaluate several variants including using the recommended square - root transformed CPM matrix as input, this input with the gamma parameter set to zero and the normal logCPM transformed matrix with and without HVG selection. Links: Docs.

• PHATE (logCP10k)¹⁰: PHATE or “Potential of Heat - diffusion for Affinity - based Transition Embedding” uses the potential of heat diffusion to preserve trajectories in a dataset via a diffusion process. It is an affinity - based method that creates an embedding by finding the dominant eigenvalues of a Markov transition matrix. We evaluate several variants including using the recommended square - root transformed CPM matrix as input, this input with the gamma parameter set to zero and the normal logCPM transformed matrix with and without HVG selection. Links: Docs.

• PHATE (gamma=0)¹⁰: PHATE or “Potential of Heat - diffusion for Affinity - based Transition Embedding” uses the potential of heat diffusion to preserve trajectories in a dataset via a diffusion process. It is an affinity - based method that creates an embedding by finding the dominant eigenvalues of a Markov transition matrix. We evaluate several variants including using the recommended square - root transformed CPM matrix as input, this input with the gamma parameter set to zero and the normal logCPM transformed matrix with and without HVG selection. Links: Docs.

• PyMDE Preserve Distances (logCP10k)⁸: PyMDE is a Python implementation of minimum-distortion embedding. It is a non-linear method that preserves distances between cells or neighborhoods in the high-dimensional space. It is computed with options to preserve distances between cells or neighbourhoods and with the logCPM matrix with and without HVG selection as input. Links: Docs.

• PyMDE Preserve Distances (logCP10k, 1kHVG)⁸: PyMDE is a Python implementation of minimum-distortion embedding. It is a non-linear method that preserves distances between cells or neighborhoods in the high-dimensional space. It is computed with options to preserve distances between cells or neighbourhoods and with the logCPM matrix with and without HVG selection as input. Links: Docs.

• PyMDE Preserve Neighbors (logCP10k)⁸: PyMDE is a Python implementation of minimum-distortion embedding. It is a non-linear method that preserves distances between cells or neighborhoods in the high-dimensional space. It is computed with options to preserve distances between cells or neighbourhoods and with the logCPM matrix with and without HVG selection as input. Links: Docs.

• PyMDE Preserve Neighbors (logCP10k, 1kHVG)⁸: PyMDE is a Python implementation of minimum-distortion embedding. It is a non-linear method that preserves distances between cells or neighborhoods in the high-dimensional space. It is computed with options to preserve distances between cells or neighbourhoods and with the logCPM matrix with and without HVG selection as input. Links: Docs.

• Random Features¹⁶: Randomly generated two-dimensional coordinates from a normal distribution. Links: Docs.

• Spectral Features¹⁶: Use 1000-dimensional diffusions maps as an embedding. Links: Docs.

• True Features¹⁶: Use of the original feature inputs as the ‘embedding’. Links: Docs.

• t-SNE (logCP10k)⁹: t-SNE or t-distributed Stochastic Neighbor Embedding converts similarities between data points to joint probabilities and tries to minimize the Kullback-Leibler divergence between the joint probabilities of the low-dimensional embedding and the high-dimensional data. We use the implementation in the scanpy package with the result of PCA on the logCPM expression matrix (with and without HVG selection). Links: Docs.

• t-SNE (logCP10k, 1kHVG)⁹: t-SNE or t-distributed Stochastic Neighbor Embedding converts similarities between data points to joint probabilities and tries to minimize the Kullback-Leibler divergence between the joint probabilities of the low-dimensional embedding and the high-dimensional data. We use the implementation in the scanpy package with the result of PCA on the logCPM expression matrix (with and without HVG selection). Links: Docs.

• UMAP (logCP10k)¹¹: UMAP or Uniform Manifold Approximation and Projection is an algorithm for dimension reduction based on manifold learning techniques and ideas from topological data analysis. We perform UMAP on the logCPM expression matrix before and after HVG selection and with and without PCA as a pre-processing step. Links: Docs.

• UMAP (logCP10k, 1kHVG)¹¹: UMAP or Uniform Manifold Approximation and Projection is an algorithm for dimension reduction based on manifold learning techniques and ideas from topological data analysis. We perform UMAP on the logCPM expression matrix before and after HVG selection and with and without PCA as a pre-processing step. Links: Docs.

• UMAP PCA (logCP10k)¹¹: UMAP or Uniform Manifold Approximation and Projection is an algorithm for dimension reduction based on manifold learning techniques and ideas from topological data analysis. We perform UMAP on the logCPM expression matrix before and after HVG selection and with and without PCA as a pre-processing step. Links: Docs.

• UMAP PCA (logCP10k, 1kHVG)¹¹: UMAP or Uniform Manifold Approximation and Projection is an algorithm for dimension reduction based on manifold learning techniques and ideas from topological data analysis. We perform UMAP on the logCPM expression matrix before and after HVG selection and with and without PCA as a pre-processing step. Links: Docs.

Baseline methods

• Random Features: Randomly generated two-dimensional coordinates from a normal distribution.

• Spectral Features: Use 1000-dimensional diffusions maps as an embedding.

• True Features: Use of the original feature inputs as the ‘embedding’.

Datasets

• Mouse hematopoietic stem cell differentiation¹⁵: 1.6k hematopoietic stem and progenitor cells from mouse bone marrow. Sequenced by Smart-seq2. 1920 cells x 43258 features with 3 cell type labels.

• Mouse myeloid lineage differentiation¹³: Myeloid lineage differentiation from mouse blood. Sequenced by SMARTseq in 2016 by Olsson et al. 660 cells x 112815 features with 4 cell type labels.

• 5k Peripheral blood mononuclear cells¹⁴: 5k Peripheral Blood Mononuclear Cells (PBMCs) from a healthy donor. Sequenced on 10X v3 chemistry in July 2019 by 10X Genomics. 5247 cells x 20822 features with no cell type labels.

• Zebrafish¹²: 90k cells from zebrafish embryos throughout the first day of development, with and without a knockout of chordin, an important developmental gene. Dimensions: 26022 cells, 25258 genes. 24 cell types (avg. 1084±1156 cells per cell type).

Download raw data

Task info Method info Metric info Dataset info Results Quality control

Quality control results

Category	Name	Value	Condition	Severity
Raw results	Dataset 'zebrafish_labs' %missing	0.60	pct_missing <= .1	✗✗✗
Raw results	Metric 'continuity' %missing	0.25	pct_missing <= .1	✗✗
Raw results	Metric 'lcmc' %missing	0.25	pct_missing <= .1	✗✗
Raw results	Metric 'qglobal' %missing	0.25	pct_missing <= .1	✗✗
Raw results	Metric 'qlocal' %missing	0.25	pct_missing <= .1	✗✗
Raw results	Metric 'qnn_auc' %missing	0.25	pct_missing <= .1	✗✗
Raw results	Metric 'qnn' %missing	0.25	pct_missing <= .1	✗✗
Raw results	Method 'densmap_logCP10k_1kHVG' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'densmap_logCP10k' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'densmap_pca_logCP10k_1kHVG' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'densmap_pca_logCP10k' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'diffusion_map' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'neuralee_default' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'neuralee_logCP10k_1kHVG' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'pca_logCP10k_1kHVG' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'pca_logCP10k' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'phate_default' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'phate_logCP10k_1kHVG' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'phate_logCP10k' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'phate_sqrt' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'pymde_distances_log_cp10k_hvg' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'pymde_distances_log_cp10k' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'pymde_neighbors_log_cp10k_hvg' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'pymde_neighbors_log_cp10k' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'random_features' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'spectral_features' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'true_features' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'tsne_logCP10k_1kHVG' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'tsne_logCP10k' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'umap_logCP10k_1kHVG' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'umap_logCP10k' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'umap_pca_logCP10k_1kHVG' %missing	0.15	pct_missing <= .1	✗
Raw results	Method 'umap_pca_logCP10k' %missing	0.15	pct_missing <= .1	✗

Visualization of raw results

Warning: Removed 1 row(s) containing missing values (geom_path).

Warning: Removed 156 rows containing missing values (geom_point).