Principal Curvatures Estimation with Applications to Single Cell Data
This provides a novel curvature estimation method for single-cell data analysis, addressing a specific bottleneck in manifold learning for high-dimensional biological datasets.
The authors tackled the challenge of analyzing massive single-cell transcriptomic sequencing datasets by developing Adaptive Local PCA (AdaL-PCA), a data-driven method for accurately estimating intrinsic curvatures like principal curvatures on data manifolds, achieving state-of-the-art results on sampled surfaces and identifying key variations in cellular differentiation when applied to single-cell RNA sequencing data.
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.