用多重尺度流形分析单细胞数据，更好捕捉基因表达的复杂结构。
Multiscale Grassmann Manifolds for Single-Cell Data Analysis
- 将细胞映射到多重尺度的格拉斯曼流形，融合不同几何视角特征。
- 在9个基准数据集上保持稳定聚类效果，小中型数据表现更优。
- 适合研究细胞异质性、需要保留复杂几何结构的单细胞分析场景。
单细胞数据分析旨在基于高维基因表达谱刻画细胞异质性。传统方法将每个细胞表示为欧氏空间中的向量，难以捕捉内在相关性和多尺度几何结构。本文提出一种基于格拉斯曼流形的多尺度框架，结合机器学习与子空间几何，通过在多个表示尺度下生成嵌入，并将其特征从不同几何视角融合至统一的格拉斯曼流形。引入基于幂函数的尺度采样策略，控制尺度选择并平衡跨分辨率信息。在9个基准单细胞RNA-seq数据集上的实验表明，该方法能有效保留有意义的结构，在小至中等规模数据集上表现出稳定的聚类性能。结果表明，格拉斯曼流形为单细胞数据分析提供了连贯且富有信息量的基础。
原文摘要 · Abstract (English)
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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