Finding stable clusterings of single-cell RNA-seq data
Run a UMI count matrix through a pipeline to obtain n cell clusters. Suppose that counts for an equal number of additional cells from the same experiment become available. Would including them change the result? Form the matrix containing both sets of counts, obtain n clusters, restrict this clustering to the initial cells and compare it with the initial clustering. If they are not consistent, conclude that the initial clustering is unstable. This is unrealistic, but reverse the perspective: given a clustering, process samples of half of the cells. If their clusters are consistent with those of all cells restricted to the samples, conclude that the clustering is stable. We use divisive hierarchical spectral clustering and define what may be a novel mapping of the dendrogram to nested clusterings. Counts are transformed to points in low-dimensional Euclidean space. Positive affinities are defined for points that are k-nearest neighbors. The affinity equals the inverse of the distance between points. Ng, Jordan, and Weiss algorithm divides the points into two clusters. The normalized cut measures the clusters separation. Recursion generates a dendrogram. Set the length of the branch between a node and its daughters to the normalized cut. Nodes distances from the root define the mapping to nested clusterings. Analysis is performed for all cells and for multiple pairs of complementary samples of cells. For a given number of clusters, each samples clustering and clusters are compared with those of the full data set (restricted to the sample). This provides measures of the stability of the clustering and its clusters. For three large data sets, this yielded clusterings compatible with published results, though with fewer clusters. Clusterings of two were judged to be stable. We conclude that it is feasible to identify stable clusterings of as many as 100,000 cells. Future research should explore using differential expression for validation.