However, such a cell type might not be known a priori. To alleviate this problem, scCODA offers an automatic reference selection that aims at selecting a cell type that is mostly unchanged in relative abundance, implying that the abundance of the reference cell type is stable over all samples. This is achieved by selecting the cell type that has the least dispersion of relative abundance over all samples, while being present in at least a fraction t of the samples:13\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{array}{c}{K}_{ref}={{{{{\rm{argmi}}}}}}{{{{{{\rm{n}}}}}}}_{k\in \{1\ldots K\}}{{{{{\rm{Disp}}}}}}({Y}_{.,k}^{{\prime} })\; {{{{{\rm{s.t.}}}}}}\; \frac{|\{n:{Y}_{n,k} > 0\}|}{N}\ge t.\end{array}$$\end{document}Kref=argmink∈{1…K}Disp(Y.,k′)s.t.∣{n:Yn,k>0}∣N≥t.
