The spheres are an example that we generated to showcase the benefits. It is arguably a little bit contrived, but we think that preserving this sort of relation

The spheres are an example that we generated to showcase the benefits. It is arguably a little bit contrived, but we think that preserving this sort of relationship can be useful. The experiments in this paper indicate that this is also a suitable perspective to assume for more complex data sets, such as image manifolds. There's also the option to go for a more local perspective, but in general I would say that preserving connectivity information is important because it aids reconstruction.