Multiscale Grassmann Manifolds for Single-Cell Data Analysis
This work addresses cellular heterogeneity analysis for single-cell RNA-seq data, representing an incremental improvement over conventional Euclidean methods.
The authors tackled the problem of single-cell data analysis by proposing a multiscale framework based on Grassmann manifolds to capture intrinsic correlations and geometric structures, demonstrating effective structure preservation and stable clustering performance on nine benchmark datasets.
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.