Generalized Persistence Diagrams

Abstract

We generalize the persistence diagram of Cohen-Steiner, Edelsbrunner, and Harer to the setting of constructible persistence modules valued in a symmetric monoidal category. We call this the type A persistence diagram of a persistence module. If the category is also abelian, then we define a second type B persistence diagram. In addition, we show that both diagrams are stable to all sufficiently small perturbations of the module.

References in corpus (2)

• Categorified Reeb Graphs
• Higher interpolation and extension for persistence modules

Cited by in corpus (27)

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• Persistent Homology of Fractional Gaussian Noise
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• Persistent Local Systems
• Capturing Dynamics of Time-Varying Data via Topology
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• Zig-Zag Modules: Cosheaves and K-Theory
• Invertibility in Category Representations
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• Poincaré Duality for Generalized Persistence Diagrams of (co)Filtrations
• Stability and Extension of Steady and Ranging Persistence