Fig. 3.

The original, as well as the modified versions of the GAP statistic are necessary for the identification of regions of interest in single-cell differentiation trajectories. (A) Toy data were generated by uniform sampling of data-points along three line segments. Two of the segments are held fixed and one of them is positioned at an angle θ. A new dataset is sampled for each value of θ and zero-mean Gaussian noise of standard deviation σ is added. Then, local clustering is performed on centred on three cells, each being in a distinct region: Tip, Intermediate and Branching. The S = 31 (as selected by the proposed heuristic) nearest neighbors of each center-cell define the region used for local clustering. (B) Example of toy data generated for $\theta ={30}^{°}$ and $\sigma =0.5$. The centers of the three regions are highlighted. (C) The original GAP successfully identifies the tip region cell, since ${\text{GAP}}_{K=1}>{\text{GAP}}_{K=3}$ holds for a wide variety of angles. (D)GAP cannot be used to identify branching region cells, since in many cases ${\text{GAP}}_{K=3}>{\text{GAP}}_{K=2}$ holds in the intermediate region. As a result, a large number of intermediate region cells would be false positive branching region cells. (E)$\widetilde{\text{GAP}}$ successfully identifies the branching region cell, since ${\widetilde{\text{GAP}}}_{K=3}>{\widetilde{\text{GAP}}}_{K=2}$ holds for a wide variety of angles. (F)$\widetilde{\text{GAP}}$ cannot be used to identify tip cells. In many cases there is strong overlap between the confidence intervals for ${\widetilde{\text{GAP}}}_{K=1}$ and ${\widetilde{\text{GAP}}}_{K=3}$, which in practice would lead to a large number of branching cells being falsely identified as tip cells. All error bars in the plot correspond to 95% CIs generated using 500 bootstrap datasets