Sublinear tf scaling

It seems unlikely that twenty occurrences of a term in a document truly carry twenty times the significance of a single occurrence. Accordingly, there has been considerable research into variants of term frequency that go beyond counting the number of occurrences of a term. A common modification is to use instead the logarithm of the term frequency, which assigns a weight given by

$$\mbox{wf}_{t,d}=\left\{ \begin{array}{ll} 1+\log \mbox{tf}... ...x{tf}_{t,d}>0 \\ 0 & \mbox{otherwise} \end{array}. \right.$$ (28)

In this form, we may replace $\mbox{tf}$ by some other function $\mbox{wf}$ as in (28), to obtain:

$$\mbox{wf-idf}_{t,d} = \mbox{wf}_{t,d} \times \mbox{idf}_t.$$ (29)

Equation (23) can then be modified by replacing tf-idf by wf-idf as defined in (29).