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1. The Utility Matrix

In a recommendation-system application there are two classes of entities, which we shall refer to as users and items. Users have preferences for certain items, and these preferences must be teased out of the data. The data itself is represented as a utility matrix, giving for each user-item pair, a value that represents what is known about the degree of preference of that user for that item. 

We assume that the matrix is sparse, meaning that most entries are “unknown.” The goal of a recommendation system is to predict the blanks in the utility matrix.

2. How to get the Utility Matirx ? 

Without a utility matrix, it is almost impossible to recommend items. 

(1) We can ask users to rate items. <Explicit>

(2) We can make inferences from users’ behavior. <Implicit>

3. Extrapolate unknown ratings from the known ones. 

Mainly interested in high unknow ratings. We are not interested in knowing what you don't like but what you like.

There are three appraoches to recommender systems:

(1) Content-based

Content-Based systems focus on properties of items. Similarity of items is determined by measuring the similarity in their properties.

Item Profiles: for each item, creat an item profile. Profile is a set(vector) of features.

User Profiles: We not only need to create vectors describing items; we need to create vectors with the same components that describe the user’s preferences. 

Recommending Items to Users Based on Content: u(x,i) = cos(x,i) x:user profile;i:item profile

(2) Collaborative Filtering

Collaborative-Filtering systems focus on the relationship between users and items. Similarity of items is determined by the similarity of the ratings of those items by the users who have rated both items. 

<1>User-user collaboration filtering

identifying similar users:

recommending what similar users like

<2>Item-item

For item i ,found other similar items.

Estimate rating for item i based.(on rating for similar items)

(3) Latent Factor Models

An entirely different approach to estimating the blank entries in the utility matrix is to conjecture that the utility matrix is actually the product of two long, thin matrices. This view makes sense if there are a relatively small set of features of items and users that determine the reaction of most users to most items. In this section, we sketch one approach to discovering two such matrices; the approach is called “UV-decomposition,” and it is an instance of a more general theory called SVD (singular-value decomposition)

4. Evaluating extrapolation methods.

How to measure success/perfoemance of recommendation methods.

(1) Root-mean-square error (RMSE)

(2) Coverage: number of items/users for which system can make predictions.

(3) Precision: accuracy of predictions

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