Add to ORKGAbstract. In this paper we focus on preprocessing for persistent homology computations. We adapt some techniques which were successfully used for standard homology computations. The main idea is to reduce the complex prior to generating its boundary ma-trix, which is costly to store and process. We discuss the following reduction methods: elementary collapses, coreductions (as defined by Mrozek and Batko) and acyclic subspace method (introduced by Mrozek, Pilarczyk and Żelazna). 1
We describe a parallel algorithm that computes persistent homology, an algebraic descriptor of a fil...
We present a parallel algorithm for computing the persistent homology of a filtered chain complex. O...
Persistent homology is a branch of computational topology which uses geometry and topology for shape...
This paper tackles an important problem in topological data analysis – improving computational effic...
The persistence diagram of a filtered simplicial com- plex is usually computed by reducing the bound...
The Čech complex is one of the most widely used tools in applied algebraic topology. Unfortunately, ...
In this paper, we present the first output-sensitive algorithm to compute the persistence diagram of...
By general case we mean methods able to process simplicial sets and chain complexes not of finite ty...
Simplicial complexes are used in topological data analysis (TDA) to extract topological features of ...
We describe a parallel algorithm that computes persistent homology, an algebraic descriptor of a fil...
The theory of homology generalizes the notion of connectivity in graphs to higher dimensions. It def...
The theory of homology generalizes the notion of connectivity in graphs to higher dimensions. It def...
Abstract:In this work, the reader is introduced to the theory of persistent ho- mology and its appli...
The alpha complex efficiently computes persistent homology of a point cloud X in Euclidean space whe...
The alpha complex efficiently computes persistent homology of a point cloud X in Euclidean space whe...
We describe a parallel algorithm that computes persistent homology, an algebraic descriptor of a fil...
We present a parallel algorithm for computing the persistent homology of a filtered chain complex. O...
Persistent homology is a branch of computational topology which uses geometry and topology for shape...
This paper tackles an important problem in topological data analysis – improving computational effic...
The persistence diagram of a filtered simplicial com- plex is usually computed by reducing the bound...
The Čech complex is one of the most widely used tools in applied algebraic topology. Unfortunately, ...
In this paper, we present the first output-sensitive algorithm to compute the persistence diagram of...
By general case we mean methods able to process simplicial sets and chain complexes not of finite ty...
Simplicial complexes are used in topological data analysis (TDA) to extract topological features of ...
We describe a parallel algorithm that computes persistent homology, an algebraic descriptor of a fil...
The theory of homology generalizes the notion of connectivity in graphs to higher dimensions. It def...
The theory of homology generalizes the notion of connectivity in graphs to higher dimensions. It def...
Abstract:In this work, the reader is introduced to the theory of persistent ho- mology and its appli...
The alpha complex efficiently computes persistent homology of a point cloud X in Euclidean space whe...
The alpha complex efficiently computes persistent homology of a point cloud X in Euclidean space whe...
We describe a parallel algorithm that computes persistent homology, an algebraic descriptor of a fil...
We present a parallel algorithm for computing the persistent homology of a filtered chain complex. O...
Persistent homology is a branch of computational topology which uses geometry and topology for shape...