AI RESEARCH
The Density of Cross-Persistence Diagrams and Its Applications
arXiv CS.AI
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ArXi:2603.11623v1 Announce Type: new Topological Data Analysis (TDA) provides powerful tools to explore the shape and structure of data through topological features such as clusters, loops, and voids. Persistence diagrams are a cornerstone of TDA, capturing the evolution of these features across scales. While effective for analyzing individual manifolds, persistence diagrams do not account for interactions between pairs of them. Cross-persistence diagrams (cross-barcodes