Figure 1.

Overview of DTFLOW algorithm

A. Pre-process a single-cell dataset into a gene expression matrix X_N×D with N cells and D genes. B. Compute the $k$ nearest neighbors for each cell, get a nearest neighbor graph structure, and then transform the dataset into a Markov transition matrix $M$. C. Use the random walk with restart method to get a diffusion matrix S, in which each cell is represented by a discrete distribution vector. D. Construct a Bhattacharyya kernel matrix $G$ and a matrix $\log G$ based on the properties of the kernel method. E. Perform singular value decomposition on $\log G$ to get the low-dimensional embedding $Y$. F. Calculate the new distance metric $D_{\mathit{ri}}$ based on the row of the matrix $\log G$ corresponding to the root cell $r$, and unitize it to get the pseudotime distances $T$. G. Identify the multi-branches of cellular differentiation by reverse searching based on the nearest neighbor graph structure.