
Computing Minimal Presentations and Bigraded Betti Numbers of 2Parameter Persistent Homology
Motivated by applications to topological data analysis, we give an effic...
read it

Generalized Persistence Algorithm for Decomposing Multiparameter Persistence Modules
The classical persistence algorithm virtually computes the unique decomp...
read it

Computing Minimal Presentations and Betti Numbers of 2Parameter Persistent Homology
Motivated by applications to topological data analysis, we give an effic...
read it

Computing Bottleneck Distance for 2D Interval Decomposable Modules
Computation of the interleaving distance between persistence modules is ...
read it

LUMÁWIG: An Efficient Algorithm for Dimension Zero Bottleneck Distance Computation in Topological Data Analysis
Stability of persistence diagrams under slight perturbations is a key ch...
read it

Dory: Overcoming Barriers to Computing Persistent Homology
Persistent homology (PH) is an approach to topological data analysis (TD...
read it

Persistence Lenses: Segmentation, Simplification, Vectorization, Scale Space and Fractal Analysis of Images
A persistence lens is a hierarchy of disjoint upper and lower level sets...
read it
Fast Minimal Presentations of Bigraded Persistence Modules
Multiparameter persistent homology is a recent branch of topological data analysis. In this area, data sets are investigated through the lens of homology with respect to two or more scale parameters. The high computational cost of many algorithms calls for a preprocessing step to reduce the input size. In general, a minimal presentation is the smallest possible representation of a persistence module. Lesnick and Wright proposed recently an algorithm (the LWalgorithm) for computing minimal presentations based on matrix reduction. In this work, we propose, implement and benchmark several improvements over the LWalgorithm. Most notably, we propose the use of priority queues to avoid extensive scanning of the matrix columns, which constitutes the computational bottleneck in the LWalgorithm, and we combine their algorithm with ideas from the multiparameter chunk algorithm by Fugacci and Kerber. Our extensive experiments show that our algorithm outperforms the LWalgorithm and computes the minimal presentation for data sets with millions of simplices within a few seconds. Our software is publicly available.
READ FULL TEXT
Comments
There are no comments yet.