MarkovHC: Markov hierarchical clustering for the topological structure of high-dimensional single-cell omics data with transition pathway and critical point detection.

Clustering cells and depicting the lineage relationship among cell subpopulations are fundamental tasks in single-cell omics studies. However, existing analytical methods face challenges in stratifying cells, tracking cellular trajectories, and identifying critical points of cell transitions. To overcome these, we proposed a novel Markov hierarchical clustering algorithm (MarkovHC), a topological clustering method that leverages the metastability of exponentially perturbed Markov chains for systematically reconstructing the cellular landscape. Briefly, MarkovHC starts with local connectivity and density derived from the input and outputs a hierarchical structure for the data. We firstly benchmarked MarkovHC on five simulated datasets and ten public single-cell datasets with known labels. Then, we used MarkovHC to investigate the multi-level architectures and transition processes during human embryo preimplantation development and gastric cancer procession. MarkovHC found heterogeneous cell states and sub-cell types in lineage-specific progenitor cells and revealed the most possible transition paths and critical points in the cellular processes. These results demonstrated MarkovHC's effectiveness in facilitating the stratification of cells, identification of cell populations, and characterization of cellular trajectories and critical points.