Sentence examples for persistent homology from inspiring English sources

For a given data space, persistent homology yields a description of its homological structure in terms of the properties of the homology generators along a series of successive approximations of the real dataset.

PH: persistent homology   5.

Mathematical details of the persistent homology.

Persistent homology is able to do that.

Figure 7 Classification method based on persistent homology.

We give an example of persistent homology in Figure 5. Figure 5 Example of persistent homology for a finite filtered simplicial complex.

One way to address all three points is a method in TDA called persistent homology (PH).

(pdf) 13688_2017_109_MOESM2_ESM.pdf Tutorial for 'A roadmap for the computation of persistent homology'.

Persistent homology is a good solution for topological data analysis, but it involves high computational complexity.

RIVET, a package for visualizing 2-parameter persistent homology, is slated to be released soon [158].

In particular, it is important to develop approaches for statistical analysis of persistent homology.