{"ID":2842987,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.11717","arxiv_id":"2511.11717","title":"Multiscale Grassmann Manifolds for Single-Cell Data Analysis","abstract":"Single-cell data analysis seeks to characterize cellular heterogeneity based on high-dimensional gene expression profiles. Conventional approaches represent each cell as a vector in Euclidean space, which limits their ability to capture intrinsic correlations and multiscale geometric structures. We propose a multiscale framework based on Grassmann manifolds that integrates machine learning with subspace geometry for single-cell data analysis. By generating embeddings under multiple representation scales, the framework combines their features from different geometric views into a unified Grassmann manifold. A power-based scale sampling function is introduced to control the selection of scales and balance in- formation across resolutions. Experiments on nine benchmark single-cell RNA-seq datasets demonstrate that the proposed approach effectively preserves meaningful structures and provides stable clustering performance, particularly for small to medium-sized datasets. These results suggest that Grassmann manifolds offer a coherent and informative foundation for analyzing single cell data.","short_abstract":"Single-cell data analysis seeks to characterize cellular heterogeneity based on high-dimensional gene expression profiles. Conventional approaches represent each cell as a vector in Euclidean space, which limits their ability to capture intrinsic correlations and multiscale geometric structures. We propose a multiscale...","url_abs":"https://arxiv.org/abs/2511.11717","url_pdf":"https://arxiv.org/pdf/2511.11717v1","authors":"[\"Xiang Xiang Wang\",\"Sean Cottrell\",\"Guo-Wei Wei\"]","published":"2025-11-12T19:47:10Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"q-bio.GN\"]","methods":"[]","has_code":false}