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- Collaborative filtering(recommendation) relies on groups with similar properties or preferences to the current user.\\
- The data scope for collaborative filtering is comprised of users who have expressed preferences on Items, action referenced from this point as rating, using the following triple representation User,Item,Rating.\\
- Other types of data can be also represented, as it’s done by large ecommerce sites: hasPurchased, hasViewed.. These are called unary ratings.\\
- The whole set of ratings triples is represented as a tuple User Item.
- In order to infer the relevance for a user a sparse matrix with the tuples User,Item is created.
- There are different types of algorithms used to provide these recommendations:\\
- \textbf{Baseline predictors}\\
- These are methods used before any type of personalized /sophisticated algorithm are deployed. They do not depend on user’s ratings and can be of use while providing predictions for new users.\\
- For a user u and item I, the prediction is given by the formula:\\
- $B_{ui}=\mu$, where u is the average overall rating
- The general formula for a baseline predictor is given by
- $b_{ui}=\mu+b_u+b_i$\\\\
- This sort of algorithms can be further tuned by computing other baselines that can respond to various effects ( a new item which is added to the site with no ratings..). They mostly capture effects of user bias, item popularity and can be leveraged over a large timeframe.\\\\
- \textbf{User-User collaborative filtering}
- This is one of the first automated collaborative filtering methods. At its core is a direct implementation of the core premise of collaborative filtering: based on other users with similar preferences, use their rating to predict what the current user will like.\\
- The likeliness of a user liking an item is calculated using a weighted average of neighboring user’s ratings using the similarity as weight.\\
- Using u as the user and I as the item, $s(u,u')$ as the similarity between the users
- $r_{ui,i}$ as the rating for item i by user $u_i$
- $r_{ui}$ as the average rating (to compensate for users who give generally higher scores\\
- The similarity computation is analogous to the one in the next section.
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