Spatiotemporal persistent homology for dynamic metric spaces
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Publication:2230910
DOI10.1007/s00454-019-00168-wzbMath1480.55007arXiv1812.00949OpenAlexW2991962490MaRDI QIDQ2230910
Publication date: 29 September 2021
Published in: Discrete \& Computational Geometry (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1812.00949
Gromov-Hausdorff distancecomputational topologypersistent Betti numbersrank invariantmultiparameter persistent homologydynamic metric spaces
Persistent homology and applications, topological data analysis (55N31) Simplicial sets and complexes in algebraic topology (55U10)
Related Items (12)
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Cites Work
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- Categorified Reeb graphs
- Limit theorems for Betti numbers of random simplicial complexes
- Persistence stability for geometric complexes
- Stability of persistence diagrams
- The persistent homology of a self-map
- Reporting flock patterns
- Time-varying Reeb graphs for continuous space-time data
- The theory of multidimensional persistence
- Generalized persistence diagrams
- Algebraic stability of zigzag persistence modules
- Multidimensional persistence and noise
- The rank invariant stability via interleavings
- Homology and robustness of level and interlevel sets
- Zigzag persistence
- Computing the interleaving distance is NP-hard
- Categorification of persistent homology
- Erosion distance for generalized persistence modules
- The theory of the interleaving distance on multidimensional persistence modules
- Computational aspects of the Gromov-Hausdorff distance and its application in non-rigid shape matching
- Betti numbers in multidimensional persistent homology are stable functions
- Clique topology reveals intrinsic geometric structure in neural correlations
- Trajectory grouping structure
- Grouping time-varying data for interactive exploration
- A New Approximation Algorithm for the Matching Distance in Multidimensional Persistence
- Computing the Gromov-Hausdorff Distance for Metric Trees
- Topology and data
- Search in an Ordered Array Having Variable Probe Cost
- Geometry Helps to Compare Persistence Diagrams
- A Refined Definition for Groups of Moving Entities and its Computation
- Computational Complexity of the Interleaving Distance
- Trajectory Grouping Structure under Geodesic Distance
- Proximity of persistence modules and their diagrams
- Zigzag persistent homology and real-valued functions
- Persistent Homology of Morse Decompositions in Combinatorial Dynamics
- Barcodes: The persistent topology of data
- Exact computation of the matching distance on 2-parameter persistence modules
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