Description Usage Arguments Details Value Author(s) References Examples

View source: R/wasserstein_distance.R

Compute the q-Wasserstein distance between persistence diagrams using an arbitrary L_p norm as ground metric.

1 | ```
wasserstein.distance(d1, d2, dimension, q, p = 2)
``` |

`d1` |
A persistence diagram (matrix with 3 col where the first one is the dimension, the second is the birth-time and the third is the death-time). |

`d2` |
A persistence diagram (matrix with 3 col where the first one is the dimension, the second is the birth-time and the third is the death-time). |

`dimension` |
Dimension of the topological features of interest (0 for connected components, 1 for cycles etc). |

`q` |
Order of the q-Wasserstein distance. |

`p` |
Order of the L_p norm to be used as a ground metric in the computation of the Wasserstein distance. |

This function provides an R interface for the efficient C++ library 'HERA' by Michael Kerber, Dmitriy Morozov, and Arnur Nigmetov (https://bitbucket.org/grey_narn/hera/src/master/).

The value for the L_p q-Wassesterstein between `d1`

and `d2`

.

Tullia Padellini, Francesco Palini. The included C++ library is authored by Michael Kerber, Dmitriy Morozov, and Arnur Nigmetov

kerber2017geometrykernelTDA

1 2 3 |

```
[1] 2.767767
```

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