UMAP representation with more than three components

[alopgar]

Hello!
I have an experiment including two different datasets (one with 800 variables and another with 1500 variables) for the same samples. I am trying to determine which of both datasets is able to cluster my samples better (i.e., with clusters more compact and more separated between them).
I ended up using UMAP for dimensionality reduction plus HDBSCAN of the UMAP coordinates. The pipeline consists in:

• Perform UMAP with different hyperparameter combinations and iterate 100 times per combination.
• Perform HDBSCAN for each iteration and combination.
• Calculate the Davies-Bouldin index for each performed HDBSCAN.
• Keep the UMAP parameter combination giving the lowest average DB index.

My problem is the number of components. After the computation, the best clustering comes from a UMAP of 50 components in one dataset and 30 components in the other. For the HDBSCAN this is not a problem, because it seems obvious that more components might give more information to the clustering algorithm.

However, I am not sure about the UMAP plotting with this amount of components. I have been using the two first components for the representation, which is in fact separating the samples according to my HDBSCAN results, but is this correct? Am I properly reflecting the separation between samples using components 1 and 2, or are the rest of components equally important and leading to different representations?

Thanks in advance!