Lydia Mezrag

PhD - Université de Montréal

Supervisor

Guy Wolf

Research Topics

Deep Learning

Graph Neural Networks

Publications

Principal Curvatures Estimation with Applications to Single Cell Data

Yanlei Zhang

Lydia Mezrag

Xingzhi Sun

Charles Xu

Kincaid MacDonald

Dhananjay Bhaskar

Smita Krishnaswamy

Guy Wolf

Bastian Rieck

The rapidly growing field of single-cell transcriptomic sequencing (scRNAseq) presents challenges for data analysis due to its massive datas… (see more)ets. 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.

2025-02-06

ArXiv (preprint)

arxiv.org