From Persistence to Survival: Hypothesis Testing, Effect Sizes and Vectorisation for Topological Features
arXiv:2606.11911v1 Announce Type: cross Abstract: Persistence diagrams are common representations in topological data analysis, but they do not naturally live in a vector space, and the statistical tools developed for comparing them have largely evolved separately from those used for downstream prediction. We introduce STRAND (Survival Topological Representation ANalysis of Diagrams), which treats (collections of) PDs as survival data: each topological feature with persistence value $p = d - b$ is a fully observed time-to-event, and the persistence survival function $S(t) = \mathbb{P}(p > t)$
The rapid advancement in AI necessitates more robust and statistically sound methods for data analysis, particularly for complex topological features.
Improved methods for topological data analysis can enhance the reliability and interpretability of AI models, crucial for applications in scientific discovery and complex systems.
This research introduces a novel statistical framework for analyzing topological features, potentially bridging the gap between topological data representations and conventional statistical tools.
- · AI/ML researchers
- · Data scientists
- · Developers of robust AI models
- · Organizations relying on less rigorous topological data analysis
The development of STRAND offers a new, statistically robust way to compare and utilize topological data.
This could lead to more accurate and reliable AI applications in fields like materials science, drug discovery, or sensor networks by better interpreting complex data shapes.
Broader adoption of these methods could accelerate scientific discovery by unlocking insights from previously intractable topological data, potentially feeding into new AI capabilities.
This signal links to a primary source. Continuum Brief monitors and indexes it as part of the live intelligence stream — we do not republish source content.
Read at arXiv cs.LG