Topological data analysis of truncated contagion maps.

Area of Science:

• Network science
• Computational topology
• Data science

Background:

• Dynamical processes on networks, particularly contagion processes, are crucial for understanding network structure.
• Contagions can reveal information about node embedding in Euclidean space.
• Contagion maps, derived from threshold contagion activation times, offer a manifold-learning approach.

Purpose of the Study:

• To address the high computational cost associated with constructing contagion maps.
• To enhance the viability of contagion maps for empirical network data analysis.
• To demonstrate the application of contagion maps in revealing biological structures within single-cell RNA-sequencing data.

Main Methods:

• Investigated threshold contagion dynamics on networks.
• Developed a truncation method for threshold contagions to optimize computation.
• Applied contagion maps to construct low-dimensional embeddings for cell-similarity networks derived from single-cell RNA-sequencing data.

Main Results:

• A truncation of threshold contagions significantly speeds up the construction of contagion maps.
• Contagion maps successfully generated insightful low-dimensional embeddings for single-cell RNA-sequencing data.
• Biological manifolds were revealed within the cell-similarity networks.

Conclusions:

• Truncating threshold contagions offers a computationally efficient way to generate contagion maps.
• Contagion maps provide a viable manifold-learning approach for empirical network data.
• This method facilitates the analysis of complex biological data, such as single-cell RNA-sequencing data, by revealing underlying structures.