Fig. 1. Schematic overview of diffusion maps embedding

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Fig. 1. Schematic overview of diffusion maps embedding Fig. 1. Schematic overview of diffusion maps embedding. (A) The n × G matrix representation of single-cell data consisting of four different cell types. The last column on the right side of the matrix (colour band) indicates the cell type for each cell. (B) Representation of each cell by a Gaussian in the G-dimensional gene space. Diffusion paths (continuous paths with relatively high-probability density) form on the data manifold as a result of interference of the Gaussians. The Probability density function is shown in the heat map. (C) The n × n Markovian transition probability matrix. (D) Data embedding on the first two eigenvectors of the Markovian transition matrix (DC1 and DC2) which correspond to the largest diffusion coefficients of the data manifold. The embedding shows the continuous flow of cells across four cell types; however, it does not suggest the putative time direction From: Diffusion maps for high-dimensional single-cell analysis of differentiation data Bioinformatics. 2015;31(18):2989-2998. doi:10.1093/bioinformatics/btv325 Bioinformatics | © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Fig. 2. (A) Toy model of a differentiation regulatory network consisting of three pairs of antagonistic genes simulated by the Gillespie algorithm. The arrows show activation or inhibition interactions between genes. The toy model employs two classes of gene regulation: (B) G<sub>i</sub> is connected to an inhibitor, its production rate α<sub>i</sub> is proportional to a Hill function of the concentration of the inhibitor Proteini′(C) G<sub>i</sub> is connected to an inhibitor Gi′ and an activator Gi″, its production rate α<sub>i</sub> is proportional to product of an inhibiting and an activating Hill function. The degradation rate γ is constant for all proteins From: Diffusion maps for high-dimensional single-cell analysis of differentiation data Bioinformatics. 2015;31(18):2989-2998. doi:10.1093/bioinformatics/btv325 Bioinformatics | © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Fig. 3. The average dimensionality of the data 〈d〉 as a function of log10(σ) for the balanced and imbalanced toy datasets From: Diffusion maps for high-dimensional single-cell analysis of differentiation data Bioinformatics. 2015;31(18):2989-2998. doi:10.1093/bioinformatics/btv325 Bioinformatics | © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Fig. 8. Visualization of human preimplantation embryos data on (A) the first three eigenvectors of the diffusion map, (B) PCA and (C) t-SNE. Eigenvalues sorted in a decreasing order for (D) the diffusion map and (E) PCA From: Diffusion maps for high-dimensional single-cell analysis of differentiation data Bioinformatics. 2015;31(18):2989-2998. doi:10.1093/bioinformatics/btv325 Bioinformatics | © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Fig. 7 Visualization of mouse embryonic stem cells on (A) the first three eigenvectors of diffusion map, (B) PCA and (C) t-SNE. Eigenvalues sorted in a decreasing order for (D) diffusion map and (E) PCA. (F) The hierarchy of cells for mouse embryonic stem cells From: Diffusion maps for high-dimensional single-cell analysis of differentiation data Bioinformatics. 2015;31(18):2989-2998. doi:10.1093/bioinformatics/btv325 Bioinformatics | © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Fig. 4. Visualization of the balanced toy data on (A) the first three eigenvectors of the diffusion map, (B) PCA and (C) t-SNE. The colours (heat map of blue to red) indicate the maximum expression among all genes. Eigenvalues sorted in decreasing order for (D) diffusion map and (E) PCA From: Diffusion maps for high-dimensional single-cell analysis of differentiation data Bioinformatics. 2015;31(18):2989-2998. doi:10.1093/bioinformatics/btv325 Bioinformatics | © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Fig. 5. Visualization of the imbalanced toy data on (A) the first three eigenvectors of the diffusion map, (B) the first, second and fourth eigenvectors of the diffusion map, (C) the first three components of the PCA (D) the first, second and fourth components of PCA and (E) t-SNE. The colours (heat map of blue to red) indicate the maximum expression among all genes. Eigenvalues sorted in a decreasing order for (F) diffusion map and (G) PCA From: Diffusion maps for high-dimensional single-cell analysis of differentiation data Bioinformatics. 2015;31(18):2989-2998. doi:10.1093/bioinformatics/btv325 Bioinformatics | © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Fig. 6. Visualization of haematopoietic stem cells data on the first three eigenvectors of (A) diffusion map, (B) PCA and (C) t-SNE. Eigenvalues sorted in a decreasing order for (D) diffusion map and (E) PCA. (F) The hierarchy of haematopoietic cell types From: Diffusion maps for high-dimensional single-cell analysis of differentiation data Bioinformatics. 2015;31(18):2989-2998. doi:10.1093/bioinformatics/btv325 Bioinformatics | © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com