#37 · Single-cell

Persistent homology and Grassmann geometry recover multiscale structure in omics data

The common thread is scale-dependent organization in high-dimensional biological data, addressed through topology and geometry rather than a single shared method. PHD-MS applies persistent homology to identify multiscale spatial domains in spatial transcriptomics and reports outperformance over clustering. The multiscale Grassmann manifold framework for single-cell RNA-seq combines embeddings across scales and reports stable clustering. The published comparison The topology of synergy contrasts topological data analysis with multivariate information theory for higher-order interactions, using toy shapes and human fMRI data; it is methodological rather than biological and is not an omics study. What is new is the use of persistent homology and Grassmann geometry to recover multiscale domains and cell-level structure in omics data, although the current evidence base is limited to two preprints and one methodological comparison.