I have always though of it as "Capacity", as in you are constraining the capacity of the classifier. However I think the true origin may be more mundane, in that a letter was simply needed for the upper bound of the box constraints in the optimisation problem (the lower bound being 0).
I agree that the meaning of 'C' is not important to understand what C-Value stands for, so it could be somehow arbitrary.
However, if I had to assign a meaning to it (and who knows if it is not the real one), from the context it would help me to consider that C might stand for "Candidate". The reason is that you assign Candidate terms a value: 'C-Value' related to the statistical frequency of that term in text corpus. And then, in a later refinement step you also consider context information, that comes from words that are not candidate terms, which leads me to think that the letters 'NC' in 'NC-value' that computes this new metric might come from the character of "Non-Candidates" of the items being used as information sources at this stage. So we would eventually have:
C(andidate)-Value
N(on)C(andidate)-Value
See http://personalpages.manchester.ac.uk/staff/sophia.ananiadou/ijodl2000.pdf for the use of the expression "Candidate term"
Anyway, if you don't like any of the proposals so far and what to call it something, there is still another option.
If a value is so widely used and manages to keep its own name in mistery for so long, it seems to me it might deserve the following name:
"Cool-Value"
Sometimes its nicer when some things remain in mistery.
Hi Mona, please clarify your update: did you know that C stood for collocation or have you taken Fernando's advice and decided to define it, in your context, as collocation?
My understanding was that C was not defined; perhaps simply stood for constant!