Topological data analysis of truncated contagion maps
This work makes contagion maps more viable for empirical network data analysis, particularly in biological applications like single-cell RNA-sequencing, but it is incremental as it builds on existing methods.
The authors tackled the high computational cost of constructing contagion maps for manifold learning by proposing a truncation method that speeds up the process, and they applied this to single-cell RNA-sequencing data to reveal biological manifolds.
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.