A Hierarchical Sheaf Spectral Embedding Framework for Single-Cell RNA-seq Analysis

TL;DR

This paper introduces a hierarchical sheaf spectral embedding framework that captures multiscale local structures in single-cell RNA-seq data, providing robust and interpretable features for downstream analysis.

Contribution

The novel HSSE framework constructs cell features using persistent sheaf Laplacian analysis, enabling multiscale, stable, and interpretable representations without additional training.

Findings

HSSE achieves competitive or superior classification performance on twelve datasets.

Spectral descriptors effectively summarize local relational structure across scales.

The approach enhances interpretability and robustness in single-cell RNA-seq analysis.

Abstract

Single-cell RNA-seq data analysis typically requires representations that capture heterogeneous local structure across multiple scales while remaining stable and interpretable. In this work, we propose a hierarchical sheaf spectral embedding (HSSE) framework that constructs informative cell-level features based on persistent sheaf Laplacian analysis. Starting from scale-dependent low-dimensional embeddings, we define cell-centered local neighborhoods at multiple resolutions. For each local neighborhood, we construct a data-driven cellular sheaf that encodes local relationships among cells. We then compute persistent sheaf Laplacians over sampled filtration intervals and extract spectral statistics that summarize the evolution of local relational structure across scales. These spectral descriptors are aggregated into a unified feature vector for each cell and can be directly used in downstream learning tasks without additional model training. We evaluate HSSE on twelve benchmark single-cell RNA-seq datasets covering diverse biological systems and data scales. Under a consistent classification protocol, HSSE achieves competitive or improved performance compared with existing multiscale and classical embedding-based methods across multiple evaluation metrics. The results demonstrate that sheaf spectral representations provide a robust and interpretable approach for single-cell RNA-seq data representation learning.