Modified and adapted from Luecken et al, 2020
The silhouette width measures the relationship between the within-cluster distances of a cell and the between-cluster distances of that cell to the closest cluster. Averaging over all silhouette widths yields the asw, which ranges between -1 and 1. Originally, Asw was used to determine the separation of clusters where 1 represents dense and well-separated clusters. Furthermore, an asw of 0 or -1 corresponds to overlapping clusters (caused by equal between- and within-cluster variability) or strong misclassification, respectively. Here we use asw to describe the mixing of batches within cell clusters, so basically the incoherence of clustering by batch. In this usage, an asw of 0 indicates that batches are well-mixed. Relative to the usual silhouette width it is calculated like \(asw = 1 − abs(asw)\).