Figure 2

Difference between PCA and Time-ordered linear model. Vector $\overrightarrow{AB}$ and $\overrightarrow{BC}$ existing in a 2-D space, represent a cell departed form state A, bypassing state B, finally reached to state C. Left: Principal component analysis generates two features, PC1 corresponds to a line that passes through the mean and minimizes sum squared error; PC2 is perpendicular to PC1. On PC1 and PC2, the order of two vectors may be lost. Right: Time-ordered linear model generates one cell state line $\overrightarrow{e_{all}}$. On this line, the order of two vectors are preserved perfectly, meanwhile, the distance ratio is also preserved: $\overrightarrow{AB\text{'}}:\overrightarrow{B\text{'}C\text{'}}=\overrightarrow{AB}:\overrightarrow{BC}$.