XplainTDA: Explaining the topological structure of single-cell multi-omics data through perturbation

Single-cell experiments have improved our ability to study biological systems by profiling thousands of cells simultaneously. The data can be viewed as a point cloud in a proper experimental space, whose shape is defined by the gene regulatory network. Persistent homology has been proposed as a method for studying the intrinsic structure of data and has shown the potential to reveal novel insights. Existing approaches focus on detecting topological features or groups of cells, without a focus on explainability and interpretability. Here, we introduce an explainable topological data analysis framework for single-cell data (XplainTDA) that identifies molecular determinants underlying the topological structure of the data via a perturbation-based approach. Across omics and data sets, we show that the method is stable, reproducible, and interpretable, extending persistent homology from topological description to molecular interpretation.