Multiscale Grassmann Manifolds for Single-Cell Data Analysis

TL;DR

This paper introduces a multiscale Grassmann manifold framework for single-cell data analysis, capturing intrinsic geometric structures and improving clustering stability across various dataset sizes.

Contribution

It presents a novel multiscale approach using Grassmann manifolds that integrates multiple geometric views for enhanced single-cell data analysis.

Findings

Effective preservation of meaningful structures in single-cell data

Stable clustering performance across datasets of different sizes

Superior to conventional Euclidean-based methods

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.