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

2026-03-27

AI Summary

This study addresses the challenge of balancing local heterogeneity, robustness, and interpretability in single-cell RNA sequencing data analysis. It introduces persistent sheaf theory—a novel application in this domain—and proposes a multiscale embedding method based on the persistent sheaf Laplacian. By constructing dynamic sheaf structures over cellular neighborhoods, the approach tracks the evolution of local relationships across resolutions and aggregates spectral statistics to generate unsupervised cell representations without requiring additional training. Evaluated on twelve benchmark datasets, the method matches or outperforms existing state-of-the-art techniques, demonstrating strong empirical performance, generalization capability, and an interpretable characterization of multiscale topological structures.

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.

Problem

• single-cell RNA-seq
• multiscale representation
• local structure
• data embedding
• interpretability

Innovation

• sheaf Laplacian
• multiscale embedding
• single-cell RNA-seq
• spectral representation
• persistent topology