Cosine similarity for recommendation systems

Question

Recently picked up recommendation systems and was going through User Based Collaborative Filtering(UB-CF).

Somewhere in the text, it specified that cosine similarity is one of the measures to find similar users and then give a recommendation.

for example a movie recommendation model:

To begin we make a matrix of users and movies filled with the ratings they have provided. now consider

       movie1 movie2 movie3
User1   5       5      5
User2   1       1      1   

In this case, the cosine similarity will be 1 while both the users have given a very different opinion of the movie and are not similar. How such issues are handled by cosine similarity? Is it not misleading?

PS: I understand that the case is way too hypothetical from a recommendation system point of view where I considered only 3 movies and both the users have watched it while in reality the matrix would be way sparse.

Answer 1

When using cosine similarity, you makes the assumption that User2 is a very difficult person who tend to give very low rating whereas User1 likes every movie. So 1 may be a very good rating for User2. Of course in this extreme case you can consider it is an issue that cosine similarity does not handle.

If you consider this example instead:

       movie1 movie2 movie3 movie4
User3   4       4      4      5
User4   2       2      2      3
User5   2       2      3      2

User3 and User4 are considered similar by cosine similarity because they prefer movie4 to all other movies regardless the mean of their ratings. User5 is considered different since it prefers movie3.