9.1. A MODEL FOR RECOMMENDATION SYSTEMS
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We should also be aware of a slightly diﬀerent goal that makes sense in many
applications. 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. In most applications, the recommendation system does not oﬀer
users a ranking of all items, but rather suggests a few that the user should value
highly. It may not even be necessary to ﬁnd all items with the highest expected
ratings, but only to ﬁnd a large subset of those with the highest ratings.
9.1.2
The Long Tail
Before discussing the principal applications of recommendation systems, let us
ponder the long tail phenomenon that makes recommendation systems neces-
sary. 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
judgement serves.
The distinction between the physical and on-line worlds has been called
the long tail phenomenon, and it is suggested in Fig. 9.2. 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 institu-
tions 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.
9.1.3
Applications of Recommendation Systems
We have mentioned several important applications of recommendation systems,
but here we shall consolidate the list in a single place.
1. Product Recommendations: Perhaps the most important use of recom-
mendation systems is at on-line retailers. We have noted how Amazon
or similar on-line vendors strive to present each returning user with some
