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arXiv · 2511.11717

Multiscale Grassmann Manifolds for Single-Cell Data Analysis

Xiang Xiang Wang·Sean Cottrell·Guo-Wei Wei
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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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Xiang Xiang Wang, Sean Cottrell, Guo-Wei Wei. 2025-11-12. Multiscale Grassmann Manifolds for Single-Cell Data Analysis. https://arxiv.org/abs/2511.11717

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