This paper culminates a bit of work I’ve started on since seeing a talk by Phil Chodrow on a paper that eventually became his quite interesting NAS paper paper on segregation and entropy surfaces. I was intrigued by the prospect of using spectral clustering for constrained clustering problems. Specifically, I’d known that affinity matrix clustering could be adapted to constrained contexts ever since reading about hierarchical ward clustering, but I hadn’t seen a really convincing method that showed me how I could work this out for a general affinity-matrix clustering method.