The recommendation system model uses the utility matrix and the concept of “long-tail” which explains the advantage of online vendors over conventional, brick-and-mortar vendors.

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. Values come from an ordered set, e.g., integers 1–5 representing the number of stars that the user gave as a rating for that item. We assume that the matrix is sparse, meaning that most entries are “unknown.” An unknown rating implies that we have no explicit information about the user’s preference for the item.

Example: In Fig. A we see an example utility matrix, representing users’ ratings of movies on a 1–5 scale, with 5 the highest rating. Blanks represent the situation where the user has not rated the movie. The movie names are HP1, HP2, and HP3 for Harry Potter I, II, and III, TW for Twilight, and SW1, SW2, and SW3 for Star Wars episodes 1, 2, and 3. The users are represented by capital letters A through D.

Notice that most user-movie pairs have blanks, meaning the user has not rated the movie. In practice, the matrix would be even sparser, with the typical user rating only a tiny fraction of all available movies.

The goal of a recommendation system is to predict the blanks in the utility matrix. For example, would user A like SW2? There is little evidence from the tiny matrix in Fig. A. We might design our recommendation system to take into account properties of movies, such as their producer, director, stars, or even the similarity of their names. If so, we might then note the similarity between SW1 and SW2, and then conclude that since A did not like SW1, they were unlikely to enjoy SW2 either. Alternatively, with much more data, we might observe that the people who rated both SW1 and SW2 tended to give them similar ratings. Thus, we could conclude that A would also give SW2 a low rating, similar to A’s rating of SW1.

It is not necessary to predict every blank entry in a utility matrix. Rather, it is only necessary to discover some entries in each row that are likely to be high.

The Long Tail:

Physical delivery systems are characterized by a scarcity of resources. Brick-and-mortar stores have limited shelf space, and can show the customer only a small fraction of all the choices that exist. On the other hand, on-line stores can make anything that exists available to the customer. Thus, a physical bookstore may have several thousand books on its shelves, but Amazon offers millions of books. A physical newspaper can print several dozen articles per day, while on-line news services offer thousands per day.

Recommendation in the physical world is fairly simple. First, it is not possible to tailor the store to each individual customer. Thus, the choice of what is made available is governed only by the aggregate numbers. Typically, a bookstore will display only the books that are most popular, and a newspaper will print only the articles it believes the most people will be interested in. In the first case, sales figures govern the choices, in the second case, editorial judgment serves.

The distinction between the physical and on-line worlds has been called the long tail phenomenon, and it is suggested in Fig. B. The vertical axis represents popularity (the number of times an item is chosen). The items are ordered on the horizontal axis according to their popularity. Physical institutions provide only the most popular items to the left of the vertical line, while the corresponding on-line institutions provide the entire range of items: the tail as well as the popular items.

The long-tail phenomenon forces on-line institutions to recommend items to individual users. It is not possible to present all available items to the user, the way physical institutions can. Neither can we expect users to have heard of each of the items they might like.

Applications of Recommendation Systems:

1. Product Recommendations: Perhaps the most important use of recommendation systems is at on-line retailers. We have noted how Amazon or similar on-line vendors strive to present each returning user with some suggestions of products that they might like to buy. These suggestions are not random, but are based on the purchasing decisions made by similar customers or on other techniques.

2. Movie Recommendations: Netflix offers its customers recommendations of movies they might like. These recommendations are based on ratings provided by users.

3. News Articles: News services have attempted to identify articles of interest to readers, based on the articles that they have read in the past. The similarity might be based on the similarity of important words in the documents, or on the articles that are read by people with similar reading tastes. The same principles apply to recommending blogs from among the millions of blogs available, videos on YouTube, or other sites where content is provided regularly.

4. Mobile Recommender Systems: One example of a mobile recommender system is one that offers potentially profitable driving routes for taxi drivers in a city. This system takes as input data in the form of GPS traces of the routes that taxi drivers took while working, which include location (latitude and longitude), time stamps, and operational status (with or without passengers). It then recommends a list of pickup points along a route that will lead to optimal occupancy times and profits. This type of system is obviously location-dependent, and as it must operate on a handheld or embedded device, the computation and energy requirements must remain low.