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What are the advantages of using level set trees, compared to say, DBSCAN? I googled but didn't find a lot except this paper: http://jmlr.csail.mit.edu/proceedings/papers/v19/steinwart11...

(and the explanations there are a little over my head)

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The most immediate advantage is that dbscan requires you to choose a specific density level, while level set trees don't. This means that with LSTs you can see the clusters at any density level without rerunning the algorithm, and in fact obtain clusters at different density levels. The dendrogram representation of the LST is also a useful visualization for densities in more than two dimensions.

I'm reading through the paper on DeBaCl right now which might be a little more accessible than the paper you found. I think the gist of it is that Level set trees offer better theoretical guarantees due to other methods being less rigorous with their theory. http://arxiv.org/pdf/1307.8136v1.pdf

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