I slightly prefer the terms accept/reject over negative/positive.
PROPORTION DEFINITION:
I think that a 2x2 matrix is most straightforward presentation:
{accept,reject} x {ham,spam}
accept reject total
ham TA FR NHAM = TA+FR
spam FA TR NSPAM = FA+TR
total TA+FA FR+TR NTOTAL
and the most helpful intuitive proportions (I think) would be
FRp = FR/NHAM and FAp = FA/NSPAM.
Numbers will ALWAYS be dependent on a particular corpus.
However, I think that the definitions above will be stable
(measuring classifier quality, not corpus composition) over
a wide range of ham-spam ratios. Using FR/NTOTAL or FA/NTOTAL
will be dominated by ham-spam ratio of the test set, obscuring
the performance of the classifier, making results unnecessarily
corpus-specific.
This is exactly correct, IMHO.