In order to emphasize that such classification can only be done in terms of the acquired application state of the client I suggest the term "hypermedia context" instead of "classification". REST interface descriptions could then for example state: "The hypermedia context of a resource is called Member if its URI is listed in a collection". There is probably also value in distinguishing the client-acquired knowledge about a resource from the context used in the specification by calling the former acquired hypermedia context or just hypermedia context and the latter named hypermedia context.
I can also see possibilities to formalize hypermedia contexts along the lines of predicates, for example as an AND combination of known links, appearance of links in received hypermedia and (XPath-)matches on the representations of resources.
But I'll address that in a follow up.