Given a few words of input, I want to have a utility that will return a diverse set of relevant terms, phrases, or concepts. A caveat is that it would need to have a large graph of terms to begin with, or else the feature would not be very useful.
For example, submitting "baseball" would return
["shortstop", "Babe Ruth", "foul ball", "steroids", ... ]
Google Sets is the best example I can find of this kind of feature, but I can't use it since they have no public API (and I wont go against their TOS). Also, single-word input doesn't garner a very diverse set of results. I'm looking for a solution that goes off on tangents.
The closest I've experimented with is using WikiPedia's API to search Categories and Backlinks, but there's no way to directly sort those results by "relevance" or "popularity". Without that, the suggestion list is massive and all over the place, which is not immediately useful and very hard to whittle down.
Using A Thesaurus could also work minimally, but that would leave out any proper nouns or tangentially relevant terms (like any of the results listed above).
I would happily reuse an open service, if one exists, but I haven't found anything sufficient.
I'm looking for either a way to implement this either in-house with a decently-populated starting set, or reuse a free service that offers this.
Have a solution? Thanks ahead of time!
UPDATE: Thank you for the incredibly dense & informative answers. I'll choose a winning answer in 6 to 12 months, when I'll hopefully understand what you've all suggested =)