Principal Curvatures Estimation with Applications to Single Cell Data

TL;DR

This paper introduces AdaL-PCA, a data-driven method for estimating intrinsic curvature on data manifolds, which enhances analysis of single-cell RNA sequencing data by revealing key cellular differentiation variations.

Contribution

The paper presents AdaL-PCA, a novel local PCA-based approach for accurate curvature estimation on data manifolds, improving analysis of high-dimensional biological data.

Findings

AdaL-PCA achieves state-of-the-art curvature estimation results.

Application with PHATE reveals key cellular differentiation variations.

Method enhances understanding of data geometry in single-cell analysis.

Abstract

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.