Persistent Laplacians: Properties, Algorithms and Implications
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Publication:5089724
DOI10.1137/21M1435471zbMath1496.55007arXiv2012.02808MaRDI QIDQ5089724
Zhengchao Wan, Facundo Mémoli, Yusu Wang
Publication date: 15 July 2022
Published in: SIAM Journal on Mathematics of Data Science (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2012.02808
Persistent homology and applications, topological data analysis (55N31) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Hodge theory in global analysis (58A14) Applications of graph theory to circuits and networks (94C15)
Related Items
Harmonic representatives in homology over arbitrary fields, Persistent hyperdigraph homology and persistent hyperdigraph Laplacians, Persistent path Laplacian, Neighborhood hypergraph model for topological data analysis
Cites Work
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- General Cheeger inequalities for \(p\)-Laplacians on graphs
- A Cheeger-type inequality on simplicial complexes
- Persistent cohomology and circular coordinates
- Simplicial networks and effective resistance
- Multiscale projective coordinates via persistent cohomology of sparse filtrations
- Computing persistent homology
- A generalized Schur complement for nonnegative operators on linear spaces
- Topological persistence and simplification
- Induced graphs of uniform spanning forests
- Evolutionary de Rham-Hodge method
- HERMES: persistent spectral graph software
- Spatiotemporal persistent homology for dynamic metric spaces
- Erosion distance for generalized persistence modules
- Toward a spectral theory of cellular sheaves
- Spectra of combinatorial Laplace operators on simplicial complexes
- Harmonic functions and boundary value problems on a chain complex
- Probability on Trees and Networks
- Annotating Simplices with a Homology Basis and Its Applications
- Higher dimensional discrete Cheeger inequalities
- Shifted simplicial complexes are Laplacian integral
- Lean Algebraic Multigrid (LAMG): Fast Graph Laplacian Linear Solver
- Expander graphs and their applications
- Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear systems
- Homological connectivity of random k -dimensional complexes
- A note on the isoperimetric constant
- Higher Dimensional Cheeger Inequalities
- On Extension of Effective Resistance with Application to Graph Laplacian Definiteness and Power Network Stability
- Kron Reduction of Graphs With Applications to Electrical Networks
- Hodge Laplacians on Graphs
- Lx = b
- Multi-way spectral partitioning and higher-order cheeger inequalities
- A Generalization of the Schur Complement by Means of the Moore–Penrose Inverse
- Graph Sparsification by Effective Resistances
