vietoris_rips_filtration#
- vietoris_rips_filtration(domain, population=None, include_boundaries=None, exclude_boundaries=None, boundary_exclude_distance=0, max_dimension=1, max_distance=inf, distance_metric='euclidean', visualise_output=False, visualise_peristence_diagram_kwargs={})#
Compute the Vietoris-Rips filtration for a given domain. Given a set of points in a metric space and a distance threshold ϵ, the Vietoris-Rips complex is a simplicial complex. It is built by including a k-simplex (e.g., a triangle or higher-dimensional counterpart) whenever the distance between any two points in the k-simplex is less than or equal to ϵ. As ϵ increases from 0, new simplices are added, creating a nested sequence of simplicial complexes called a filtration. This helps track the appearance and disappearance of topological features (such as connected components, loops, or voids) at different scales.
- Parameters:
- domainobject
A muspan domain object.
- populationquery-like, optional
A query, list/tuple of indices, or a single int specifying the objects to consider. Defaults to None.
- include_boundariesarray-like, query-like, or None, optional
Boundaries to include in the analysis. Defaults to None.
- exclude_boundariesarray-like, query-like, or None, optional
Boundaries to exclude from the analysis. Defaults to None.
- boundary_exclude_distancefloat, optional
Buffer to exclude objects located within boundary_exclude_distance from the boundaries. Defaults to 0.
- max_dimensionint, optional
The maximum dimension of the simplices to be considered in the filtration. Default is 1.
- max_distancefloat, optional
The maximum distance up to which simplices are considered. Default is np.inf.
- distance_metricstr, optional
The metric used to compute distances between objects. Default is ‘euclidean’.
- visualise_outputbool, optional
If True, visualise the persistence diagram. Default is False.
- visualise_peristence_diagram_kwargsdict, optional
Additional keyword arguments to pass to the persistence_diagram function when visualising the persistence diagram.
- Returns:
- dict
A dictionary containing the persistent features computed by the ripser library.
- Raises:
- ValueError
If the query provided is not of the correct type.
Notes
This function uses the Ripser library to compute the persistent homology of the Vietoris-Rips filtration. The distance matrix is computed using the specified distance metric, and then passed to Ripser.