arXiv Machine Learning
The sublevel Flood bifiltration: towards scalable 2-parameter persistent homology
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A differentiability framework for zigzag persistent homology via linear interpolation
The paper introduces a differentiability framework for zigzag persistent homology, enabling the use of zigzag persistence in learning pipelines. By linearly interpolating filtering values on a fixed complex and assigning real-valued times to persistence diagram endpoints, the authors transfer continuity from filtering values to diagram points, yielding smooth local lifts and almost everywhere differentials under mild regularity conditions. They prove local Lipschitz continuity outside an explicit measure‑zero exclusion set and demonstrate the framework’s practical effectiveness through experiments on sensor network coverage optimization and dynamic graph classification.
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Persistent Homology of Time Series through Complex Networks
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