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07/14/2023
Computing Zigzag Vineyard Efficiently Including Expansions and Contractions
Vines and vineyard connecting a stack of persistence diagrams have been ...
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04/11/2023
GRIL: A 2-parameter Persistence Based Vectorization for Machine Learning
1-parameter persistent homology, a cornerstone in Topological Data Analy...
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03/14/2023
Meta-Diagrams for 2-Parameter Persistence
We first introduce the notion of meta-rank for a 2-parameter persistence...
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03/05/2023
Computing Connection Matrices via Persistence-like Reductions
Connection matrices are a generalization of Morse boundary operators fro...
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02/24/2023
Revisiting Graph Persistence for Updates and Efficiency
It is well known that ordinary persistence on graphs can be computed mor...
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12/03/2022
Cup Product Persistence and Its Efficient Computation
It is well-known that cohomology has a richer structure than homology. H...
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04/23/2022
Fast Computation of Zigzag Persistence
Zigzag persistence is a powerful extension of the standard persistence w...
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03/11/2022
Tracking Dynamical Features via Continuation and Persistence
Multivector fields and combinatorial dynamical systems have recently bec...
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12/04/2021
Updating Zigzag Persistence and Maintaining Representatives over Changing Filtrations
Computing persistence over changing filtrations give rise to a stack of ...
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11/30/2021
Computing Generalized Rank Invariant for 2-Parameter Persistence Modules via Zigzag Persistence and its Applications
The notion of generalized rank invariant in the context of multiparamete...
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10/27/2021
Approximating 1-Wasserstein Distance between Persistence Diagrams by Graph Sparsification
Persistence diagrams (PD)s play a central role in topological data analy...
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10/12/2021
On Association between Absolute and Relative Zigzag Persistence
Duality results connecting persistence modules for absolute and relative...
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08/17/2021
Rectangular Approximation and Stability of 2-parameter Persistence Modules
One of the main reasons for topological persistence being useful in data...
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07/05/2021
Persistence of Conley-Morse Graphs in Combinatorial Dynamical Systems
Multivector fields provide an avenue for studying continuous dynamical s...
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05/02/2021
Computing Optimal Persistent Cycles for Levelset Zigzag on Manifold-like Complexes
In standard persistent homology, a persistent cycle born and dying with ...
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04/27/2021
Topological Filtering for 3D Microstructure Segmentation
Tomography is a widely used tool for analyzing microstructures in three ...
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03/17/2021
2D Points Curve Reconstruction Survey and Benchmark
Curve reconstruction from unstructured points in a plane is a fundamenta...
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03/12/2021
Computing Zigzag Persistence on Graphs in Near-Linear Time
Graphs model real-world circumstances in many applications where they ma...
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03/12/2020
Persistence of the Conley Index in Combinatorial Dynamical Systems
A combinatorial framework for dynamical systems provides an avenue for c...
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01/27/2020
An efficient algorithm for 1-dimensional (persistent) path homology
This paper focuses on developing an efficient algorithm for analyzing a ...
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09/15/2019
Road Network Reconstruction from Satellite Images with Machine Learning Supported by Topological Methods
Automatic Extraction of road network from satellite images is a goal tha...
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07/10/2019
Computing Minimal Persistent Cycles: Polynomial and Hard Cases
Persistent cycles, especially the minimal ones, are useful geometric fea...
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04/07/2019
Generalized Persistence Algorithm for Decomposing Multi-parameter Persistence Modules
The classical persistence algorithm virtually computes the unique decomp...
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10/11/2018
Persistent 1-Cycles: Definition, Computation, and Its Application
Persistence diagrams, which summarize the birth and death of homological...
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10/10/2018
Filtration Simplification for Persistent Homology via Edge Contraction
Persistent homology is a popular data analysis technique that is used to...
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07/10/2018
Computing Height Persistence and Homology Generators in R^3 Efficiently
Recently it has been shown that computing the dimension of the first hom...
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03/14/2018
Graph Reconstruction by Discrete Morse Theory
Recovering hidden graph-like structures from potentially noisy data is a...
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03/07/2018
Computing Bottleneck Distance for 2-D Interval Decomposable Modules
Computation of the interleaving distance between persistence modules is ...
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01/21/2018
Efficient algorithms for computing a minimal homology basis
Efficient computation of shortest cycles which form a homology basis und...
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01/19/2018
Persistent Homology of Morse Decompositions in Combinatorial Dynamics
We investigate combinatorial dynamical systems on simplicial complexes c...
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07/31/2017
