DOI10.1007/s11263-007-0056-xzbMath1477.68463OpenAlexW2104339857WikidataQ59442813 ScholiaQ59442813MaRDI QIDQ942833
Gunnar Carlsson, Afra Zomorodian, Tigran Ishkhanov, Vin De Silva
Publication date: 5 September 2008
Published in: International Journal of Computer Vision (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11263-007-0056-x
Approximate and discrete Euclidean vector bundles,
Rank-based persistence,
A higher-dimensional homologically persistent skeleton,
Algebraic stability of zigzag persistence modules,
Object-oriented persistent homology,
Generalization of the weighted nonlocal Laplacian in low dimensional manifold model,
Vector diffusion maps and the connection Laplacian,
Persistent homology and string vacua,
The Persistent Homology of Cyclic Graphs,
Topological data analysis of financial time series: landscapes of crashes,
Aspects of topological approaches for data science,
A topological approach for protein classification,
On Vietoris-Rips complexes of hypercube graphs,
Unnamed Item,
Linear-size approximations to the Vietoris-Rips filtration,
Metric Reconstruction Via Optimal Transport,
Wasserstein-Based Projections with Applications to Inverse Problems,
Leave-One-Out Kernel Density Estimates for Outlier Detection,
The cubical cohomology ring: an algorithmic approach,
\(A_\infty\) persistent homology estimates detailed topology from pointcloud datasets,
Zigzag zoology: Rips zigzags for homology inference,
The persistent homology of a self-map,
Field choice problem in persistent homology,
Universality of the homotopy interleaving distance,
Robust statistics, hypothesis testing, and confidence intervals for persistent homology on metric measure spaces,
Topological data analysis for the string landscape,
Stable volumes for persistent homology,
Optimising the topological information of the \(A_\infty \)-persistence groups,
Multidimensional persistence and noise,
Only distances are required to reconstruct submanifolds,
Stabilizing the unstable output of persistent homology computations,
Splitting multidimensional necklaces,
On Vietoris–Rips Complexes (with Scale 3) of Hypercube Graphs,
Computing the multicover bifiltration,
A Klein-bottle-based dictionary for texture representation,
Homological Shape Analysis Through Discrete Morse Theory,
Hodge theory on metric spaces. Appendix by Anthony W. Baker,
Topological Approaches to Deep Learning,
Sparse Circular Coordinates via Principal $$\mathbb {Z}$$-Bundles,
Continuous quivers of type \(A (I)\) foundations,
Multiscale persistent functions for biomolecular structure characterization,
Computing multiparameter persistent homology through a discrete Morse-based approach,
Manifold reconstruction using tangential Delaunay complexes,
Neural network coding of natural images with applications to pure mathematics,
Zigzag persistence,
Shapley Homology: Topological Analysis of Sample Influence for Neural Networks,
Topological data analysis and cosheaves,
Persistent Homology of Geospatial Data: A Case Study with Voting,
Localized homology,
Another look at recovering local homology from samples of stratified sets,
Local Linear Regression on Manifolds and Its Geometric Interpretation,
Persistent topology of syntax,
Kernel method for persistence diagrams via kernel embedding and weight factor,
Boundary measures for geometric inference,
Extremal Betti numbers of Vietoris-Rips complexes,
Orientability and diffusion maps,
Vietoris-Rips complexes of planar point sets,
Topological pattern recognition for point cloud data,
Weighted persistent homology,
Low Dimensional Manifold Model for Image Processing,
Evolutionary de Rham-Hodge method,
A game-based approximate verification of deep neural networks with provable guarantees,
The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes,
A persistence landscapes toolbox for topological statistics,
Computational tools in weighted persistent homology,
Computing Persistent Homology of Flag Complexes via Strong Collapses,
The theory of multidimensional persistence,
Learning slosh dynamics by means of data,
Divisive cover,
Sparse Dowker nerves,
Computing persistent homology with various coefficient fields in a single pass,
Unnamed Item,
BPS spectra, barcodes and walls,
The Why, How, and When of Representations for Complex Systems,
New formulas for cup-\(i\) products and fast computation of Steenrod squares,
A Tale of Two Bases: Local-Nonlocal Regularization on Image Patches with Convolution Framelets,
Approximating persistent homology in Euclidean space through collapses,
A Bayesian Framework for Persistent Homology,
The theory of the interleaving distance on multidimensional persistence modules,
Sliding windows and persistence: an application of topological methods to signal analysis,
Topological data analysis for the energy and stability of endohedral metallofullerenes