提出自适应局部PCA方法，精准估算单细胞数据流形的主曲率。
Principal Curvatures Estimation with Applications to Single Cell Data
- 基于局部PCA自适应估计流形切空间与主曲率。
- 在采样曲面上实现当前最优的曲率估计性能。
- 结合PHATE可揭示细胞分化中的关键变化路径，适合生物数据分析者。
单细胞转录组测序（scRNAseq）数据量庞大，分析挑战显著。流形学习常假设数据分布于低维流形上，从而通过提取曲率等几何特征研究点云结构。本文提出自适应局部PCA（AdaL-PCA），一种数据驱动的方法，可准确估计数据流形上的多种内在曲率，特别是曲面的主曲率。该方法基于局部PCA估计切空间。在采样曲面上的评估表明，其性能达到当前最先进水平。结合PHATE嵌入，应用于单细胞RNA测序数据后，能够识别细胞分化过程中的关键变异，揭示潜在发育轨迹。
原文摘要 · Abstract (English)
The rapidly growing field of single-cell transcriptomic sequencing (scRNAseq) presents challenges for data analysis due to its massive datasets. A common method in manifold learning consists in hypothesizing that datasets lie on a lower dimensional manifold. This allows to study the geometry of point clouds by extracting meaningful descriptors like curvature. In this work, we will present Adaptive Local PCA (AdaL-PCA), a data-driven method for accurately estimating various notions of intrinsic curvature on data manifolds, in particular principal curvatures for surfaces. The model relies on local PCA to estimate the tangent spaces. The evaluation of AdaL-PCA on sampled surfaces shows state-of-the-art results. Combined with a PHATE embedding, the model applied to single-cell RNA sequencing data allows us to identify key variations in the cellular differentiation.
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