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.
$$
d_h(X_i, X_j) = \max{( \frac{\sum_y \min_x(d(x, y)) }{n_j}, \frac{\sum_x \min_y(d(x, y)) }{n_i})}
$$
where \(x, y\) are elements of the clusters \(C_i, C_j\) respectively, and \(X_i, X_j\) are the clusters corresponding
vertices in the mapper. See the reference below for more details.
WARNING: This function may be very computationally expensive.
hausdorff_distance(m)
| m | A |
|---|
A dist object with Size equal to the number of vertices.
Currently, this requires the RANN to be installed, and only considers euclidean distance.
Singh, Gurjeet, Facundo Memoli, and Gunnar E. Carlsson. "Topological methods for the analysis of high dimensional data sets and 3d object recognition." SPBG. 2007.