Multiscale Grassmann Manifolds for Single-Cell Data Analysis

• URL: http://arxiv.org/abs/2511.11717v1
• Date: Wed, 12 Nov 2025 19:47:10 GMT
• Title: Multiscale Grassmann Manifolds for Single-Cell Data Analysis
• Authors: Xiang Xiang Wang, Sean Cottrell, Guo-Wei Wei,
• Abstract summary: We propose a multiscale framework that integrates machine learning with subspace geometry for single-cell data analysis.<n>A power-based scale sampling function is introduced to control the selection of scales and balance in- formation across resolutions.<n>Experiments on nine benchmark single-cell RNA-seq datasets demonstrate that the proposed approach effectively preserves meaningful structures.
• Score: 3.073258665974412
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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