Topological data analysis of truncated contagion maps

TL;DR

This paper introduces a truncated contagion map method that reduces computational costs and effectively uncovers low-dimensional biological manifolds in single-cell RNA-sequencing data, enhancing manifold learning on networks.

Contribution

It proposes a truncation technique for contagion maps that speeds up manifold learning and demonstrates its application to biological data analysis.

Findings

Truncated contagion maps are computationally faster.

Contagion maps reveal biological manifolds in RNA-seq data.

Method improves efficiency of manifold learning on networks.

Abstract

The investigation of dynamical processes on networks has been one focus for the study of contagion processes. It has been demonstrated that contagions can be used to obtain information about the embedding of nodes in a Euclidean space. Specifically, one can use the activation times of threshold contagions to construct contagion maps as a manifold-learning approach. One drawback of contagion maps is their high computational cost. Here, we demonstrate that a truncation of the threshold contagions may considerably speed up the construction of contagion maps. Finally, we show that contagion maps may be used to find an insightful low-dimensional embedding for single-cell RNA-sequencing data in the form of cell-similarity networks and so reveal biological manifolds. Overall, our work makes the use of contagion maps as manifold-learning approaches on empirical network data more viable.