Correlation-based Similarity
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### Correlation-based Similarity

In this case, similarity between two items i and j is measured by computing the Pearson-r correlation corri,j. To make the correlation computation accurate we must first isolate the co-rated cases (i.e., cases where the users rated both i and j) as shown in Figure 2. Let the set of users who both rated i and j are denoted by U then the correlation similarity is given by

Here Ru,i denotes the rating of user u on item i, is the average rating of the i-th item.