PDSFLRR: Low-rank representation with projection distance and sparsity constraints for clustering single-cell RNA sequencing data.

Single-cell RNA sequencing (scRNA-seq) has made it possible to dissect cellular heterogeneity at single-cell resolution, and clustering is a key step in this analysis. Because scRNA-seq data are high-dimensional, sparse, and corrupted by dropout effects, clustering them accurately remains challenging. This paper proposes PDSFLRR, a clustering method built upon low-rank representation (LRR). To overcome the limitation of classical LRR models, which fix the dictionary to the raw data matrix, PDSFLRR learns the dictionary adaptively through a projection matrix, imposes an orthonormality constraint, and adds a projection-distance regularization that preserves local structure in the projected space. A sparse constraint is further incorporated so that the global subspace structure and the local neighborhood structure of the data are captured simultaneously. In addition, the nuclear norm is replaced by the Frobenius norm to avoid expensive singular value decomposition (SVD) computations, and the resulting objective is solved efficiently with the Alternating Direction Method of Multipliers (ADMM). Extensive experiments on twelve real scRNA-seq datasets, comparisons with nine popular clustering methods, and an ablation study show that PDSFLRR delivers accurate clustering results, as measured by normalized mutual information (NMI) and adjusted Rand index (ARI).