# Multiscale Grassmann Manifolds for Single-Cell Data Analysis

arXiv: https://arxiv.org/abs/2511.11717 · HTML: https://mlsanity.com/paper/2511.11717/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 46 references that are in the map.
- First posted on arXiv 12 Nov 2025.

## Builds on (most cited first, 5 of 5)

- [Analyzing Single Cell RNA Sequencing with Topological Nonnegative Matrix Factorization](https://mlsanity.com/paper/2310.15744/) (2023)
- [Geometric structure guided model and algorithms for complete deconvolution of gene expression data](https://mlsanity.com/paper/2202.08733/) (2022)
- [Analyzing scRNA-seq data by CCP-assisted UMAP and t-SNE](https://mlsanity.com/paper/2306.13750/) (2023)
- [K-Nearest-Neighbors Induced Topological PCA for scRNA Sequence Data Analysis](https://mlsanity.com/paper/2310.14521/) (2023)
- [Multi-view Spectral Clustering on the Grassmannian Manifold With Hypergraph Representation](https://mlsanity.com/paper/2503.06066/) (2025)

## Built on by (most cited first, 1 of 1)

- [A Hierarchical Sheaf Spectral Embedding Framework for Single-Cell RNA-seq Analysis](https://mlsanity.com/paper/2603.26858/) (2026)

## Abstract (arXiv)

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.