Table 1. Synthetic benchmark datasets.

The synthetic benchmark datasets used for comparison are the first 15 manifolds from Campadelli et al. (2015). The datasets represent various types of manifolds with or without curvature, also with uniform or non-uniform sampling of n = 2, 500 points.

	Dataset	Description	d	embed-dim
1	M 1	10d sphere	10	11
2	M 2	3d affine space	3	5
3	M 3	4 figure	4	6
4	M 4	4d manifold in 8d	4	8
5	M 5	2d helix in 3d	2	3
6	M 6	6dim manifold in 36d	6	36
7	M 7	swiss roll	2	3
8	M 9	20d affine space	20	20
9	M 10a	10d hypercube	10	10
10	M 10b	17d hypercube	17	17
11	M 10c	24d hypercube	24	24
12	M 10d	70d hypercube	70	70
13	M 11	Moebius band 10x twisted	2	3
14	M 12	Multivariate Gaussian	20	20
15	M 13	1d curve in 13d	1	13