arXiv:2603.26858cs.LGmath.SP2026-03

用层叠的同调谱方法,从单细胞数据中提取稳定可解释的特征。

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

  • 基于持续同调拉普拉斯算子构建多尺度细胞邻域关系
  • 在12个数据集上分类表现优于或持平现有方法
  • 无需额外训练,直接用于下游任务,适合生物机制研究

单细胞RNA测序数据分析需要能捕捉多尺度异质局部结构且保持稳定可解释的表示。本文提出层次化同调谱嵌入(HSSE)框架,通过持续同调拉普拉斯分析构建细胞级特征。从多尺度低维嵌入出发,定义细胞为中心的多分辨率局部邻域,为每个邻域构建数据驱动的细胞同调,计算采样滤波区间上的持续同调拉普拉斯,并提取谱统计量以总结局部关系结构随尺度的变化。这些谱描述符聚合为每个细胞的统一特征向量,可直接用于下游学习任务而无需额外模型训练。我们在覆盖多种生物系统和数据规模的12个基准单细胞RNA-seq数据集上评估了HSSE,采用一致分类协议,在多个评估指标上表现竞争力或更优。结果表明,同调谱表示为单细胞数据表征学习提供了鲁棒且可解释的方法。

原文摘要 · Abstract (English)

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.

单细胞分析同调学习谱嵌入多尺度建模

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