Scalable, fidelity-preserving topology for large and streaming data

Design algorithms and workflows that reduce the computational cost of computing persistent homology and related topological summaries on large-scale or streaming datasets while preserving the structural fidelity that makes these summaries scientifically meaningful for complex-systems monitoring and analysis.

Background

Topological analyses in complex systems often require repeated or streaming computations (e.g., sliding windows, online monitoring), making computational cost a practical bottleneck.

Although there have been major algorithmic advances, the authors stress that real-time deployment and repeated-window settings remain challenging, especially when interpretability requires identifying stable representatives.

They call for methods that are both operationally feasible and faithful to the structural signals of interest.