Multiscale methods for signal selection in single-cell data

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.

arXiv comment32 pages, 15 figures, 1 table. Revised and published in Entropy, special issue Applications of Topological Data Analysis in the Life Sciences

References in corpus (11)

• Fast unfolding of communities in large networks
• Random walks and diffusion on networks
• Random Walks, Markov Processes and the Multiscale Modular Organization of Complex Networks
• Laplacian Dynamics and Multiscale Modular Structure in Networks
• Topological Signal Processing over Simplicial Complexes
• Markov dynamics as a zooming lens for multiscale community detection: non clique-like communities and the field-of-view limit
• Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond
• Flow-based network analysis of the Caenorhabditis elegans connectome
• The stability of a graph partition: A dynamics-based framework for community detection
• Graph-based data clustering via multiscale community detection
• Finding role communities in directed networks using Role-Based Similarity, Markov Stability and the Relaxed Minimum Spanning Tree