Is there utility in replacing the Euclidean hard clustering heuristic (e.g., $k$-means) step in spectral clustering with a fuzzy clustering step to detect overlapping clusters? I am assuming this does not work very well, since I have never heard of it before (closest would be something like this: https://arxiv.org/abs/1412.3432). But thought it was worth asking about.
EDIT: actually, I did find this: https://www.cs.montana.edu/sheppard/pubs/flairs-2015.pdf , which uses Laplacian eigenmaps followed by fuzzy $c$-means as a substep of a larger algorithm. So maybe there is precedent...
