A subspace clustering method for satisfying stoimetric constraints in scRNA -seq

With the advent of single-cell RNA-sequencing, researchers now have the ability to define cell types from large amounts of transcriptome information. Over the years, various clustering algorithms have been designed. Currently, most clustering algorithms measure cell-to-cell similarities using distance metrics based on the assumption that each cluster is comprised of “nearby” neighbors. In effect, clusters are a collection of similar cells in the embedded metric. Here, we propose that biological clusters should be comprised of sets of cells that satisfy a set of stochiometric constraints, whose intersections define a cell type. We propose to model each cell population with a single affine subspace, where all cells of the same type share a common set of linear constraints. We present an algorithm that leverages this subspace structure and learns a cell-to-cell affinity matrix based on notions of subspace similarity. We simulate scRNA-seq data according to the subspace model and benchmark our algorithm against preexisting methods. We further test our algorithm on an in-house C. elegans dataset and show recovery of information on both cell type and developmental time.