arXiv:2503.13954cs.LG2025-03

用自适应多尺度方法提升高维数据可视化,更好区分簇内与簇间结构。

Enhanced High-Dimensional Data Visualization through Adaptive Multi-Scale Manifold Embedding

  • 用序数距离替代欧氏距离,克服高维诅咒
  • 两阶段嵌入框架显著增强簇间分离度
  • 适用于单细胞测序等生物数据的深层结构发现

为应对高维流形嵌入中维度灾难与簇内/簇间结构难以分离的双重挑战,本文提出自适应多尺度流形嵌入(AMSME)算法。通过引入序数距离替代传统欧氏距离,理论上证明其可克服高维空间中的维度诅咒,有效区分异质样本。设计自适应邻域调整方法构建相似性图,同时兼顾簇内紧凑性与簇间可分性。进一步提出两阶段嵌入框架:第一阶段利用相似性图实现初步簇分离并保持结构相似簇间的连通性;第二阶段通过标签驱动的距离重加权强化簇间分离。实验表明,AMSME在真实数据集上显著保持簇内拓扑结构并提升簇间分离效果。此外,借助其多分辨率分析能力,成功在小鼠腰段背根神经节单细胞转录组数据集中发现新型神经元亚型,标记基因分析揭示其独特的生物学功能。

原文摘要 · Abstract (English)

To address the dual challenges of the curse of dimensionality and the difficulty in separating intra-cluster and inter-cluster structures in high-dimensional manifold embedding, we proposes an Adaptive Multi-Scale Manifold Embedding (AMSME) algorithm. By introducing ordinal distance to replace traditional Euclidean distances, we theoretically demonstrate that ordinal distance overcomes the constraints of the curse of dimensionality in high-dimensional spaces, effectively distinguishing heterogeneous samples. We design an adaptive neighborhood adjustment method to construct similarity graphs that simultaneously balance intra-cluster compactness and inter-cluster separability. Furthermore, we develop a two-stage embedding framework: the first stage achieves preliminary cluster separation while preserving connectivity between structurally similar clusters via the similarity graph, and the second stage enhances inter-cluster separation through a label-driven distance reweighting. Experimental results demonstrate that AMSME significantly preserves intra-cluster topological structures and improves inter-cluster separation on real-world datasets. Additionally, leveraging its multi-resolution analysis capability, AMSME discovers novel neuronal subtypes in the mouse lumbar dorsal root ganglion scRNA-seq dataset, with marker gene analysis revealing their distinct biological roles.

高维可视化流形学习单细胞分析多尺度嵌入

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