This mechanism uses user rating data to compute similarity between users or items. This is used for making recommendations. This was the earlier mechanism and is used in many commercial systems. It is easy to implement and is effective. Typical examples of this mechanism are neighbourhood based CF and item-based/user-based top-N recommendations.[3] For example, in user based approaches, the value of ratings user 'u' gives to item 'i' is calculated as an aggregation of some similar users rating to the item:
where 'U' denotes the set of top 'N' users that are most similar to user 'u' who rated item 'i'. Some examples of the aggregation function includes:
where k is a normalizing factor defined as k =1/sum_{u^prime in U}|operatorname{simil}(u,u^prime)| . and ar{r_u} is the average rating of user u for all the items rated by that user.
The neighborhood-based algorithm calculates the similarity between two users or items, produces a prediction for the user taking the weighted average of all the ratings. Similarity computation between items or users is an important part of this approach. Multiple mechanisms such as Pearson correlation and vector cosine based similarity are used for this.
The Pearson correlation similarity of two users x, y is defined as