Principal Curvatures Estimation with Applications to Single Cell Data
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arXiv
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| Main Authors: | , , , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910816710688768 |
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| author | Zhang, Yanlei Mezrag, Lydia Sun, Xingzhi Xu, Charles Macdonald, Kincaid Bhaskar, Dhananjay Krishnaswamy, Smita Wolf, Guy Rieck, Bastian |
| author_facet | Zhang, Yanlei Mezrag, Lydia Sun, Xingzhi Xu, Charles Macdonald, Kincaid Bhaskar, Dhananjay Krishnaswamy, Smita Wolf, Guy Rieck, Bastian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03750 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Principal Curvatures Estimation with Applications to Single Cell Data Zhang, Yanlei Mezrag, Lydia Sun, Xingzhi Xu, Charles Macdonald, Kincaid Bhaskar, Dhananjay Krishnaswamy, Smita Wolf, Guy Rieck, Bastian Machine Learning Artificial Intelligence 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. |
| title | Principal Curvatures Estimation with Applications to Single Cell Data |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2502.03750 |