High Dimensional Spheres Dataset — taspheres • snedata

Creates a dataframe consisting of samples from the d-spheres of radius r enclosed within a larger d-sphere of radius 5 * r.

Usage

taspheres(n_samples = 500, d = 100, n_spheres = 11, r = 5)

Arguments

n_samples: Number of points to sample from each of the n_spheres d-spheres. The larger d-sphere has 10 * n_samples points.
d: The dimensionality of each sphere. The returned dataframe will have the d + 1 dimensions of the Euclidean space in which the sphere is embedded.
n_spheres: Number of spheres to return. There will be n_spheres - 1 small spheres and 1 larger sphere.
r: The radius of each of the smaller spheres. The larger sphere has radius 5 * r.

Value

Data frame with d + 1 numerical columns containing the coordinates of the d-spheres and a labels factor column giving the identity of each d-sphere: levels 0 .. n_spheres - 2 are the smaller d-spheres. Level n_spheres - 1 is the label for the big d-sphere.

Details

This dataset was used by Moor and co-workers in their "Topological Autoencoders" paper and this function is based on the Python code in the GitHub repo for the paper.

References

Moor, M., Horn, M., Rieck, B., & Borgwardt, K. (2020). Topological Autoencoders. In Proceedings of the 37th International Conference on Machine Learning (ICML) (pp. 7045–7054). PMLR.

https://michaelmoor.ml/blog/topoae/main/

https://github.com/BorgwardtLab/topological-autoencoders