What's the difference between Pearson correlation similarity and adjust cosine similarity?

Question

While they are very similar, I am sure there is some difference between Pearson correlation similarity and adjust cosine similarity, because all the papers and web pages divide them into two different kinds.

However none of them provide a clear definition. Here is one of the pages.

Can anyone tell the difference?

Thanks

Answer 1

The two definations look very similar, but be aware that:

• In pearson correlation, the mean which subtracted is about the particular item itself (ratings from all users), mean(Ri)
• In adjusted cosine correlation, the mean is about the particular user (ratings to all items), mean(Ru)

This tiny difference may lead to totally disparate results.