The Density of Cross-Persistence Diagrams and Its Applications
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), introduced recently, address this limitation by characterizing relationships between topological features of two point clouds. In this work, we present the first systematic study of the density of cross-persistence diagrams. We prove its existence, establi...
| Authors | Alexander Mironenko, Evgeny. Burnaev, Serguei Barannikov |
|---|---|
| Primary category | cs.AI |
| Published | 12 March 2026 |
| Last updated at source | 12 March 2026 |
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