Geometry Helps to Compare Persistence Diagrams
From MaRDI portal
Publication:4577947
DOI10.1145/3064175zbMath1414.68129arXiv1606.03357OpenAlexW2294510945MaRDI QIDQ4577947
Dmitriy Morozov, Arnur Nigmetov, Michael Kerber
Publication date: 6 August 2018
Published in: ACM Journal of Experimental Algorithmics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1606.03357
Graph theory (including graph drawing) in computer science (68R10) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Other homology theories in algebraic topology (55N35)
Related Items
A feasibility study for a persistent homology-based \(k\)-nearest neighbor search algorithm in melanoma detection ⋮ Signal classification with a point process distance on the space of persistence diagrams ⋮ Topological Data Analysis on Simple English Wikipedia Articles ⋮ Persistence Flamelets: Topological Invariants for Scale Spaces ⋮ Cancer Fingerprints by Topological Data Analysis ⋮ Bayesian topological learning for classifying the structure of biological networks ⋮ Unnamed Item ⋮ Functional summaries of persistence diagrams ⋮ Topological learning for brain networks ⋮ On the Stability of Multigraded Betti Numbers and Hilbert Functions ⋮ Bottleneck profiles and discrete Prokhorov metrics for persistence diagrams ⋮ Filtration simplification for persistent homology via edge contraction ⋮ Same But Different: Distance Correlations Between Topological Summaries ⋮ Computing the interleaving distance is NP-hard ⋮ Spatiotemporal persistent homology for dynamic metric spaces ⋮ Optimal transport: discretization and algorithms ⋮ Barcode embeddings for metric graphs ⋮ Understanding the topology and the geometry of the space of persistence diagrams via optimal partial transport ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Computational Complexity of the Interleaving Distance ⋮ Unnamed Item ⋮ Generalized persistence diagrams for persistence modules over posets ⋮ Tropical Sufficient Statistics for Persistent Homology ⋮ Persistent topology of protein space ⋮ Compression for \(2\)-parameter persistent homology ⋮ Metric Spaces with Expensive Distances ⋮ An Overview of the Topology ToolKit ⋮ Supervised learning with indefinite topological Kernels
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Stability of persistence diagrams
- The auction algorithm for the transportation problem
- Lipschitz functions have \(L_{p}\)-stable persistence
- Exploring uses of persistent homology for statistical analysis of landmark-based shape data
- Parallel synchronous and asynchronous implementations of the auction algorithm
- The auction algorithm: A distributed relaxation method for the assignment problem
- Topological persistence and simplification
- Geometry Helps in Matching
- Algorithms for the Assignment and Transportation Problems
- Assignment Problems
- Space-time tradeoffs for approximate nearest neighbor searching
- Multidimensional binary search trees used for associative searching
- Improvements on geometric pattern matching problems
- Geometry Helps to Compare Persistence Diagrams
- Approximation algorithms for bipartite matching with metric and geometric costs
- Paths, Trees, and Flowers
- An $n^{5/2} $ Algorithm for Maximum Matchings in Bipartite Graphs
- Geometry helps in bottleneck matching and related problems