Dimensionality Reduction for Visualisation

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.

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.

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.

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.

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.

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.

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.

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.

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).

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.

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.

Randomly generated two-dimensional coordinates from a normal distribution.

Use 1000-dimensional diffusions maps as an embedding

Use of the original feature inputs as the 'embedding'.

co-KNN AUC is area under the co-KNN curve

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

Continuity measures error of hard extrusions based on nearest neighbor coranking

Similarity between local densities in the high-dimensional data and the reduced data.

Spearman correlation between all pairwise Euclidean distances in the original and dimension-reduced data

Spearman correlation between all pairwise diffusion distances in the original and dimension-reduced data

The global property metric is a summary of the global co-KNN

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

The local property metric is a summary of the local co-KNN

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

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

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

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

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).