Fractional Order Total Variation Low-Rank Representation on Single-Cell RNA Sequencing Clustering.

Traditional bulk RNA sequencing often masks cell-to-cell variability, leading to a loss of individual heterogeneity information. Single-cell RNA sequencing (scRNA-seq) preserves cellular heterogeneity by reverse-transcribing, amplifying, as well as sequencing mRNA molecules from individual cells, enabling in-depth studies of cell development, differentiation, and disease mechanisms. However, scRNA-seq data are inherently high-dimensional and noisy with prevalent dropout events, posing challenges for accurate clustering and subtype identification. To address these issues, this study proposes an Adaptive Fractional-Order Total Variation Regularised Low-Rank Representation (AFTV-LRR) model that integrates adaptive fractional-order total variation into the low-rank representation framework. The proposed method reconstructs low-rank subspace structures to learn cell similarities while preserving fine-grained cellular features through fractional-order gradient learning. The optimisation problem is efficiently solved using the Alternating Direction Method of Multipliers (ADMM), and spectral clustering is applied to the learnt similarity matrix for accurate cell type identification. Extensive experiments on 11 publicly available scRNA-seq datasets demonstrate that AFTV-LRR achieves competitive and often superior performance compared with eight representative single-cell clustering algorithms in terms of Adjusted Rand Index (ARI) and Normalised Mutual Information (NMI). Visualisation with t-SNE further confirms that the proposed model yields clearer inter-cluster separations and higher intra-cluster compactness. Moreover, marker gene analysis using the mouse embryo dataset supports the biological interpretability and robustness of the clustering results. Overall, this work provides an adaptive computational framework for improving the accuracy and reliability of single-cell clustering analysis.