Inverse Document Frequency

Similar to the normalized Term Frequency we want to find out how much a given word tt is found in a collection of documents DD.

idf⁡(t,D):=log⁡10(N∣{d∈D∣t∈d}∣)\operatorname{idf}(t, D):=\log _{10}\left(\frac{N}{|\{d \in D \mid t \in d\}|}\right)

Intuition
This formula is near 00 when a word is present in nearly all documents. For example, the word "the" will most likely have a value of zero. This will ensure that "meaningless" words will not be used for Information Retrieval.