# Inverse document frequency

Up to this point, we've been concerned only with the total number of times a word occurs across the entire corpus. Karen Sparck Jones has observed that, from a discrimination point of view, what we'd really like to know is the number of documents containing a keyword. This thinking underlies the INVERSE DOCUMENT FREQUENCY (IDF) weighting:

The basis for IDF weighting is the observation that people tend to express their information needs using rather broadly defined, frequently occurring terms, whereas it is the more specific, i.e., low-frequency terms that are likely to be of particular importance in identifying relevant material. This is because the number of documents relevant to a query is generally small, and thus any frequently occurring terms must necessarily occur in many irrelevant documents; infrequently occurring terms have a greater probability of occurring in relevant documents --- and should thus be considered as being of greater potential when searching a database. [SparckJones97] \eq

Rather than looking at the raw occurrence frequencies, we will aggregate occurrences within any document and consider only the { number of documents} in which a keyword occurs. IDF proposes, again using a statistical interpretation of term specificity'' [SparckJones72] that the value of a keyword varies inversely with the $\log$ of the number of documents in which it occurs: w_{kd}=f_{kd} * \left(\log {\mathname{Norm} \over D_k} + 1\right) where $D_{k}$ is defined in Equation (FOAref) .

The formula in (FOAref) is still not fully specified, in that the count $$D_{k}$$ must be normalized with respect to a constant $$\mathname{Norm}$$. We could normalize with respect to the total number of documents in the corpus [SparckJones72] [ Croft79] ; another possibility is to normalize against the maximum document frequency (i.e., the most documents any keyword appears in) [SparckJones79a] [SparckJones79b] .

\mathname{Norm}=\left\{ \begin{array}{ll} \mathname{\mathname{NDoc}} &[SparckJones72] \\ % \stackunder{k}{\mathname{argmax}} D_k &[SparckJones79] \\ {\mathname{argmax}_{k}} D_k &[SparckJones79a] [SparckJones79b] \\ \right.

Today the most common form of IDF weighting is that used by Robertson and Sparck Jones [Robertson76] , which normalizes with respect to the number of documents not containing a keyword $(\mathname{NDoc}- D_k)$ and adds a constant of $\frac{1}{2}$ to both numerator and denominator to moderate extreme values: w_{kd}=f_{kd} * \left(\log {(\mathname{NDoc}- D_k)+0.5\over D_k + 0.5}\right)

FOA © R. K. Belew - 00-09-21