information retrieval - Why is log used when calculating term frequency weight and IDF, inverse document frequency?

Question

The formula for IDF is log( N / df t ) instead of just N / df t.

Where N = total documents in collection, and df t = document frequency of term t.

Log is said to be used because it “dampens” the effect of IDF. What does this mean?

Also, why do we use log frequency weighing for term frequency as seen here:

question from:https://stackoverflow.com/questions/27067992/why-is-log-used-when-calculating-term-frequency-weight-and-idf-inverse-document

Answer 1

Debasis's answer is correct. I am not sure why he got downvoted.

Here is the intuition: If term frequency for the word 'computer' in doc1 is 10 and in doc2 it's 20, we can say that doc2 is more relevant than doc1 for the word 'computer.

However, if the term frequency of the same word, 'computer', for doc1 is 1 million and doc2 is 2 millions, at this point, there is no much difference in terms of relevancy anymore because they both contain a very high count for term 'computer'.

Just like Debasis's answer, adding log is to dampen the importance of term that has a high frequency, e.g. Using log base 2, the count of 1 million will be reduced to 19.9!

We also add 1 to the log(tf) because when tf is equal to 1, the log(1) is zero. By adding one, we distinguish between tf=0 and tf=1.

Hope this helps!