[PDF][PDF] A roadmap for the computation of persistent homology
Persistent homology (PH) is a method used in topological data analysis (TDA) to study
qualitative features of data that persist across multiple scales. It is robust to perturbations of …
qualitative features of data that persist across multiple scales. It is robust to perturbations of …
[HTML][HTML] Phat–persistent homology algorithms toolbox
Phat is an open-source C++ library for the computation of persistent homology by matrix
reduction, targeted towards developers of software for topological data analysis. We aim for …
reduction, targeted towards developers of software for topological data analysis. We aim for …
[PDF][PDF] Ripser. py: A lean persistent homology library for python
Topological data analysis (TDA)(Edelsbrunner & Harer, 2010),(Carlsson, 2009) is a field
focused on understanding the shape and structure of data by computing topological …
focused on understanding the shape and structure of data by computing topological …
Persistence images: A stable vector representation of persistent homology
Many data sets can be viewed as a noisy sampling of an underlying space, and tools from
topological data analysis can characterize this structure for the purpose of knowledge …
topological data analysis can characterize this structure for the purpose of knowledge …
Clear and compress: Computing persistent homology in chunks
We present a parallel algorithm for computing the persistent homology of a filtered chain
complex. Our approach differs from the commonly used reduction algorithm by first …
complex. Our approach differs from the commonly used reduction algorithm by first …
Persistent homology analysis for materials research and persistent homology software: HomCloud
This paper introduces persistent homology, which is a powerful tool to characterize the
shape of data using the mathematical concept of topology. We explain the fundamental idea …
shape of data using the mathematical concept of topology. We explain the fundamental idea …
Convergence rates for persistence diagram estimation in topological data analysis
F Chazal, M Glisse, C Labruère… - … on Machine Learning, 2014 - proceedings.mlr.press
Computational topology has recently seen an important development toward data analysis,
giving birth to Topological Data Analysis. Persistent homology appears as a fundamental …
giving birth to Topological Data Analysis. Persistent homology appears as a fundamental …
Efficient computation of persistent homology for cubical data
In this paper we present an efficient framework for computation of persistent homology of
cubical data in arbitrary dimensions. An existing algorithm using simplicial complexes is …
cubical data in arbitrary dimensions. An existing algorithm using simplicial complexes is …
Stable vectorization of multiparameter persistent homology using signed barcodes as measures
Persistent homology (PH) provides topological descriptors for geometric data, such as
weighted graphs, which are interpretable, stable to perturbations, and invariant under, eg …
weighted graphs, which are interpretable, stable to perturbations, and invariant under, eg …
Using persistent homology and dynamical distances to analyze protein binding
V Kovacev-Nikolic, P Bubenik, D Nikolić… - Statistical applications in …, 2016 - degruyter.com
Persistent homology captures the evolution of topological features of a model as a
parameter changes. The most commonly used summary statistics of persistent homology are …
parameter changes. The most commonly used summary statistics of persistent homology are …