Distances and data dimensionality. (A) A set of single cells expressing 3 genes arranged along a curved shape has been simulated. There are 2 measures of distance between the blue and red cells. Whereas D₁ represents the shortest possible distance between the 2 cells, D₂ is the distance between the cells through the structure of the data (manifold). The two arms of the curved shape may represent continuous transition processes (eg, cell differentiation); therefore, distance D₂ is the important distance measure. A dimensionality reduction technique (here tSNE) should capture such features. (B) Excessive reduction in dimensionality causes important information to be lost. In this case, a 2-dimensional representation of the data incorrectly suggests that the green cell is farther from the yellow cell than the orange cell, because information has been lost about axis 2. (C) To infer cellular trajectories from scRNA-seq data, dimensionality reduction is used to learn the structure of the data (learned data), which captures the important distances between cells in a suitable number of dimensions, typically 10 to 100. Trajectory inference can then be attempted from this learned data. For visualization, the dimensionality of the data needs to be reduced to either 2 or 3, but this will inevitably result in the loss of some of the important biological information, rendering data unsuitable for trajectory inference.