The importance of this rather vague relationship is that the two factors are related to the distribution of index terms in the collection.
The relationships postulated are consistent with the observed trade-off between precision and recall just mentioned.
Changes in the number of index terms per document lead to corresponding changes in the number of documents per term and vice versa.
I am arguing that in using distributional information about index terms to provide, say, index term weighting we are really attacking the old problem of controlling exhaustivity and specificity.
If we go back to Luhn's original ideas, we remember that he postulated a varying discrimination power for index terms as a function of the rank order of their frequency of occurrence, the highest discrimination power being associated with the middle frequencies.
His model was proposed for the selection of significant terms from a document.
However, the same frequency counts can be used to provide a weighting scheme for the individual terms in a document.
In fact, there is a common weighting scheme in use which gives each index term a weight directly proportional to its frequency of occurrence in the document.
At first this scheme would appear to be inconsistent with Luhn's hypothesis that the discrimination power drops off at higher frequencies.
However, referring back to Figure 2.1, the scheme would be consistent if the upper cut-off is moved to the point where the peak occurs.
It is likely that this is in fact what has happened in experiments using this particular form of weighting.
Attempts have been made to apply weighting based on the way the index terms are distributed in the entire collection.
The index term vocabulary of a document collection often has a Zipfian distribution, that is, if we count the number of documents in which each index term occurs and plot them according to rank order then we obtain the usual hyperbolic shape.
Sparck Jones showed experimentally that if there are N documents and an index term occurs in n of them then a weight of log(N/n) + 1 leads to more effective retrieval than if the term were used unweighted.
If indexing specificity is assumed to be inversely proportional to the number of documents in which an index term occurs then the weighting can be seen to be attaching more importance to the more specific terms.
The difference between the last mode of weighting and the previous one may be summarised by saying that document frequency weighting places emphasis on content description whereas weighting by specificity attempts to emphasise the ability of terms to discriminate one document from another.
Salton and Yang have recently attempted to combine both methods of weighting by looking at both inter document frequencies