Multiscale methods for signal selection in single-cell data

TL;DR

This paper introduces three topologically motivated multiscale methods for unsupervised feature selection in single-cell transcriptomics, capturing both discrete and continuous gene expression patterns across multiple scales.

Contribution

The paper presents novel mathematical techniques—eigenscores, MLS, and PRQ—for identifying biologically relevant genes considering complex data geometry and scale, improving upon traditional clustering-based methods.

Findings

Validated methods on published datasets, detecting known and new biologically meaningful genes.

Provided multidimensional gene rankings and visualizations of gene relationships.

Demonstrated the ability to separate genes involved in bifurcation processes like pseudo-time.

Abstract

Analysis of single-cell transcriptomics often relies on clustering cells and then performing differential gene expression (DGE) to identify genes that vary between these clusters. These discrete analyses successfully determine cell types and markers; however, continuous variation within and between cell types may not be detected. We propose three topologically motivated mathematical methods for unsupervised feature selection that consider discrete and continuous transcriptional patterns on an equal footing across multiple scales simultaneously. Eigenscores ($\text{eig}_i$) rank signals or genes based on their correspondence to low-frequency intrinsic patterning in the data using the spectral decomposition of the Laplacian graph. The multiscale Laplacian score (MLS) is an unsupervised method for locating relevant scales in data and selecting the genes that are coherently expressed at these respective scales. The persistent Rayleigh quotient (PRQ) takes data equipped with a filtration, allowing the separation of genes with different roles in a bifurcation process (e.g., pseudo-time). We demonstrate the utility of these techniques by applying them to published single-cell transcriptomics data sets. The methods validate previously identified genes and detect additional biologically meaningful genes with coherent expression patterns. By studying the interaction between gene signals and the geometry of the underlying space, the three methods give multidimensional rankings of the genes and visualisation of relationships between them.