# Topological data analysis of truncated contagion maps

arXiv: https://arxiv.org/abs/2203.01720 · HTML: https://mlsanity.com/paper/2203.01720/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 57 references that are in the map.
- First posted on arXiv 3 Mar 2022.

## Builds on (most cited first, 16 of 16)

- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [What are higher-order networks?](https://mlsanity.com/paper/2104.11329/) (2021)
- [Two's company, three (or more) is a simplex: Algebraic-topological tools for understanding higher-order structure in neural data](https://mlsanity.com/paper/1601.01704/) (2016)
- [Dynamical Systems on Networks: A Tutorial](https://mlsanity.com/paper/1403.7663/) (2014)
- [Topological data analysis of contagion maps for examining spreading processes on networks](https://mlsanity.com/paper/1408.1168/) (2014)
- [Complex Contagions: A Decade in Review](https://mlsanity.com/paper/1710.07606/) (2017)
- [Persistent Homology of Geospatial Data: A Case Study with Voting](https://mlsanity.com/paper/1902.05911/) (2019)
- [The Topological "Shape" of Brexit](https://mlsanity.com/paper/1610.00752/) (2016)
- [Contagion Dynamics for Manifold Learning](https://mlsanity.com/paper/2012.00091/) (2020)
- [The small-world effect is a modern phenomenon](https://mlsanity.com/paper/1310.2636/) (2013)
- [Complex Contagions with Timers](https://mlsanity.com/paper/1706.04252/) (2017)
- [Co-occurrence simplicial complexes in mathematics: identifying the holes of knowledge](https://mlsanity.com/paper/1803.04410/) (2018)
- [Analysis of contagion maps on a class of networks that are spatially embedded in a torus](https://mlsanity.com/paper/1812.09806/) (2018)
- [A network-based microfoundation of Granovetter's threshold model for social tipping](https://mlsanity.com/paper/1911.04126/) (2019)
- [Spatial Applications of Topological Data Analysis: Cities, Snowflakes, Random Structures, and Spiders Spinning Under the Influence](https://mlsanity.com/paper/2001.01872/) (2020)
- [Simplicial cascades are orchestrated by the multidimensional geometry of neuronal complexes](https://mlsanity.com/paper/2201.02071/) (2022)

## Abstract (arXiv)

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.