Let's say i have search engine that uses Cosine similarity for retrieving pages. But, without the idf part, only the tf. If i add Page Rank for the formula of the Cosine. it's possible that the formula will change from one corpus to another ?
Example -
Corpus A - Doc A, Doc B ---> There is a line between A and B.
Corpus A - Doc B ---> There is a line between A and B.
The score of Page B will be different for the corpuses?
Thanks.
Your question is not completely clear. But let me try to address your concern.
When you said, you are only using tf, not tf-idf in cosine similarity calculation, I guess you are presenting web pages through the constituent terms' frequencies. Then you said if you add the PageRank values of each webpage to the similarity score calculated based on cosine similarity, whether the formula is going to change? I think here you have little ambiguity. The formula will never change but yes the combined scores may vary from corpus to corpus. Also, the example you provided is not clear.
So, here is the thing probably you want to know:
If you compute cosine similarity or PageRank for the different corpus, the scores may vary based on the corpus distribution. PageRank is computed over a collection of web pages which are considered as the entire web, so if you consider two different corpus, then the PageRank score of web pages can vary!
