Towards reliable quantification of cell state velocities
Fig 3
Scaling of gene-wise velocity components.
A. If the gene-wise velocities are incorrectly scaled the high-dimensional velocity vector will change direction (displacement angle θ). B. We propose to use cell densities as a proxy of time. For a same time interval, the displacement in u will be proportional to a gene’s speed. This allows us to relate velocities across genes and solve the scale invariance problem. C. To validate κ-velo, we simulate splicing kinetics scaled by a scaling factor κ and evaluate how well the factors are recovered. D. We compare the κ-velo and scVelo velocities to the true velocities for two genes with different speeds. The high-dimensional velocity vectors are normalised to have equal variance for ease of comparison. E. The high-dimensional vector is projected on the first two principal components to evaluate differences between true velocities and recovered velocities. We return the change in direction (cosine similarity) and length (difference in vector norm) (Note J in S1 Appendix) for κ-velo and scVelo. To make the length comparable, the vectors are variance-normalised. Note the log-scale for frequency.