Weighted Sum

As the name implies, this method computes the prediction on an item i for a user u by computing the sum of the ratings given by the user on the items similar to i. Each ratings is weighted by the corresponding similarity s_i,j between items i and j. Formally, using the notion shown in Figure 3 we can denote the prediction P_u,i as

$$P_{u,i} = \frac {\sum_{\mbox{\tiny {all similar items, N}}}(s... ...sum_{\mbox{\tiny {all similar items, N}}}(\vert s_{i,N}\vert)}$$

Basically, this approach tries to capture how the active user rates the similar items. The weighted sum is scaled by the sum of the similarity terms to make sure the prediction is within the predefined range.

  

Figure 3: Item-based collaborative filtering algorithm. The prediction generation process is illustrated for 5 neighbors