Geometric Sketching

Summary

Geometric Sketching is an algorithm designed to select a representative subset (or "sketch") of cells from a large single-cell RNA-sequencing (scRNA-seq) dataset. Unlike random downsampling, which preserves the density distribution of cell states, geometric sketching partitions transcriptomic space using hypercubes and samples cells uniformly across these partitions. This allows it to capture rare cell types and transitional states without relying on prior cell-type metadata.

Method Details

The geometric sketching algorithm operates as follows: 1. Normalisation and Dimensionality Reduction: Single-cell expression counts are normalised (e.g., to 10,000 counts per cell), logarithmised, and restricted to highly variable genes (HVGs). 2. Plaid Covering: A grid of equal-sized hypercubes is constructed in transcriptomic space to cover the data points. 3. Uniform Sampling: An equal number of cells are randomly selected from each occupied hypercube.

Because each hypercube is sampled equally regardless of how many cells fall into it, dense cell populations (e.g., common immune cells) are downweighted, while sparse cell populations (e.g., rare progenitors or transitional states) are relatively overrepresented.

Evaluation in Foundation Models

In a systematic evaluation by DenAdel et al. (2026), geometric sketching was compared to random downsampling and cell-type re-weighting as a pretraining dataset selection strategy for Single-Cell Foundation Models. The study found that while geometric sketching successfully increased the Vendi Score (transcriptional diversity) of the pretraining data, it did not lead to improved performance on downstream cell-type classification, batch integration, or perturbation prediction compared to simple random downsampling.

Citations

[1] Hie, B., Cho, H., DeMeo, B., Bryson, B. & Berger, B. Geometric sketching compactly summarizes the single-cell transcriptomic landscape. Cell Syst. 8, 483–493 (2019). [2] DenAdel, A. et al. (2026). Evaluating the role of pretraining dataset size and diversity on single-cell foundation model performance. Nature Methods, 23, 1447–1457. DOI: 10.1038/s41592-026-03120-y. Source paper: s41592-026-03120-y.pdf