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Zusammenfassung:
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.
It is known that the analysis of spreading processes on networks may reveal their hidden geometric structures. These techniques, called contagion maps, are computationally expensive, which raises the question of whether they can be methodologically improved. Here, we demonstrate that a truncation (i.e., early stoppage) of the spreading processes leads to a substantial speedup in the computation of contagion maps. For synthetic networks, we find that a carefully chosen truncation may also improve the recovery of hidden geometric structures. We quantify this improvement by comparing the topological properties of the original network with the constructed contagion maps by computing their persistent homology. Finally, we explore the embedding of single-cell transcriptomics data and show that contagion maps can help us to distinguish different cell types.
