Pearson Correlation Coefficient 77B Recommender Systems.

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Presentation transcript:

Pearson Correlation Coefficient 77B Recommender Systems

Collaborative Filtering Find the nearest neighbors of a particular user u by some measure of similarity. Average the ratings of these nearest neighbors for some item to predict its rating for user u.

Pearson Correlation Coefficient If there are many data-cases for which x i is approximately equal to y i then the value is large. If x i is approximately equal to –y i then it is large and negative. If the values are unrelated then it is close to 0. We subtract the mean so that if someone is rating consistently higher it would have no influence. We divide by the scale (standard deviation) so that a wider range of values has no influence.

Correlated Data

Prediction We assume we have all ratings (relax later) Pcc is the similarity between two users. We first remove user “v” her mean rating behavior Then we add her rating to the pool weighted by similarity to the user u. Divide by total weight so that sum of weights = 1 Add user u’s mean back.