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Whereas no clear correlation was found to exist between the S/N ratings and the document or collection frequencies of the corresponding terms, a direct relation appears to exist for the discrimination value rankings. As the discrimination values decrease from good to average to poor, the document and collection frequencies of the terms go from average, to low, and finally to quite high. This correspondence is used as a basis for a theory of indexing in the last section of this study. In summary, a study of the frequency distributions of the terms ranked according to a number of different measures of term significance reveals the following characteristics: (a) When the terms are ranked in decreasing order of collection frequency F k , or document frequency Bk, the best terms are those with universal occurrence A THEORY OF INDEXING 23 characteristics; such terms may help in producing high recall output, but the retrieval results will certainly not be sufficiently precise for most purposes.

24 G. SALTON The signal-noise calculations are more expensive to perform than the EK values. Consider first the noise Nk (formula (6)); the requirements are K' additions for Fk, 2K' divisions, K' logarithms, K' multiplications, and K' additions to compute the final sum. In addition, the computation of the signal Sk (formula (7)) adds K' logarithms and 1 subtraction. The total requirements are then equal to 2K' + 1 additions or subtractions, 3X' multiplications or divisions, and 2K' logarithms. For t terms, this produces (2K' + l)t additions, 3K't multiplications, and 2K't logarithms.

D) The discrimination value (DV) ranking appears to reflect those term characteristics normally thought to be important in retrieval—the best terms being those with skewed frequency distributions that occur neither too frequently nor too rarely; the least attractive terms from the discrimination point of view are terms occurring everywhere that are not capable of distinguishing the items from each other. (e) The information value (IV) process must be based on a large number of user-system interactions; reliable frequency distribution characteristics remain to be generated in this case.

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