Use of negative correlation coefficient in pearson correlation algorithm for recommender systems

Question

I'm new in recommender systems and I try to find similar users of a base users for user-based collaborative filtering. When I calculated the similarity score now between two users (based on there ratings with pearson algorithm [or resnick's weighted pearson algorithm]) I get a similarity score from -1 to 1.

Is it a good idea to normalize this values to 0 to 1 (-1 would become 0 and 1 would be 1) to make it comparable to other algorithms?

In fact I try to build recommendations and with a negative similarity score of a user the calculated/predicted rating could be negative as well which make no sense.

Should I normalize/scale "-1 to 1" to "0 to 1" or cut off all users with similarity score below 0?

(maybe the question also could be: "Which users should be taken as mentor to recommend new items on a similarity score from -1 to 1? Or should I take the top n users with highest similarity score?")

Answer 1

One thing you can do is to separate the contributions of:

• a) who have a positive correlation with you
• b) who have a negative correlation with you

Then you can:

1. Predict the rating using only users in a) $\to$ those will have positive correlation, this positive weights. Call this $\hat{r}_a$
2. Predict the rating using only users in b) $\to$ in this case, consider the weights as positive (even in they are negative correlation). Call this $\hat{r}_b$
3. The final predicted rating is $\hat{r} = \frac{\hat{r}_a - \hat{r}_b}{2}$