Scientifically matched null models for TDA in complex-systems data

Develop domain-appropriate null models for topological data analysis that are scientifically matched to weighted, temporal, correlation-derived, higher-order, and spatially constrained datasets arising in complex-systems applications, so that statistical significance of persistence-based summaries can be assessed against meaningful alternatives rather than generic random baselines.

Background

The paper emphasizes that statistical significance for persistence-based summaries cannot rely solely on generic random-point-cloud baselines because many complex-systems datasets are weighted, temporal, correlation-derived, higher-order, or spatially constrained.

While recent advances provide universal null distributions in limited settings, the authors argue that complex-systems applications require null models that preserve key structural constraints (e.g., marginal distributions, degree/strength sequences, spatial embedding, autocorrelation) to avoid misleading inferences.

They identify the lack of such scientifically tailored null models as a central barrier to rigorous inference with TDA in real-world systems.