hausdorff_distance: Hausdorff Distance
In peekxc/Mapper: Topological Data Analysis using Mapper

Description Usage Arguments Details Value References

Computes a smooth approximation to the Hausdorff distance between the vertices of a mapper. Implements the equation in Section 5 of the original Mapper paper.

DH(Xi, Xj) = max{ ∑ min(d(x, y)) / nj, ∑ min(d(x, y)) / ni}

where x, y are elements of the clusters Ci, Cj respectively, and Xi, Xj are the clusters corresponding vertices in the mapper. See the reference below for more details.

WARNING: This function may be very computationally expensive.

1	hausdorff_distance(m)

`m`	A `MapperRef` object.

Currently, this requires the RANN to be installed, and only considers euclidean distance.

A dist object with Size equal to the number of vertices.

Singh, Gurjeet, Facundo Memoli, and Gunnar E. Carlsson. "Topological methods for the analysis of high dimensional data sets and 3d object recognition." SPBG. 2007.

peekxc/Mapper documentation built on June 12, 2020, 2:14 a.m.