Bottleneck distance

[pandey-tushar]

Is there a way to comment on the projections using bottleneck distance or heat kernel distance?

For example, suppose I have a huge dataset and I project it using some lens(say TSNE). Since there are multiple hyperparameters, I wish to get some kind of optimal values so that the projection is not too far from the original dataset.
Also, since I will be looking at the number of clusters, I should be looking for H_0 and the bottleneck in H_0, right?

I think the same applies to the heat kernel distance or Wasserstein distance?