How to evaluate HDBSCAN text clusters?
Its the same problem everywhere in unsupervised learning.
It is unsupervised, you are trying to discover something new and interesting. There is no way for the computer to decide whether something is actually interesting or new. It can decide and trivial cases when the prior knowledge is coded in machine processable form already, and you can compute some heuristics values as a proxy for interestingness. But such measures (including density-based measures such as DBCV are actually in no way better to judge this than the clustering algorithm itself is choosing the "best" solution).
But in the end, there is no way around manually looking at the data, and doing the next steps - try to put into use what you learned of the data. Supposedly you are not invory tower academic just doing this because of trying to make up yet another useless method... So use it, don't fake using it.
I'm currently trying to use HDBSCAN to cluster movie data. The goal is to cluster similar movies together (based on movie info like keywords, genres, actor names, etc) and then apply LDA to each cluster and get the representative topics. However, I'm having a hard time evaluating the results (apart from visual analysis, which is not great as the data grows). With LDA, although it's hard to evaluate it, i've been using the coherence measure. However, does anyone have any idea on how to evaluate the clusters made by HDBSCAN? I haven't been able to find much info on it, so if anyone has any idea, I'd very much appreciate!