A recommender system's task is to inform a user about an object that could be the most interesting to them at a given time. Most often, such an object is a product or service, but it may be information—for example, in the form of a recommended news article.

Despite the many existing algorithms, we can divide recommender systems into several basic approaches. The most common are as follows:

• Summary-based: Non-personal models based on the average product rating
• Content-based: Models based on the intersection of product descriptions and user interests
• Collaborative filtering: Models based on interests of similar user groups
• Matrix factorization: Methods based on the preferences matrix decomposition

The basis of any recommender system is the preferences matrix. The preferences matrix has all users of the service laid on one of the axes, and recommendation objects on the other. The recommendation objects are usually called items. At the intersection of rows and columns (user, item), this matrix is filled with ratings—this is a known indicator of user interest in this product, expressed on a given scale (for example, from 1 to 5), as illustrated in the following table:

Users usually evaluate only a small number of the items in the catalog, and the task of the recommender system is to summarize this information and predict the attitude the user might have toward other items. In other words, you need to fill in all the blank cells in the preceding table.

People's consumption patterns are different, and new products do not have to be recommended all the time. You can show repeated items—for example, when a user has bought something they'll definitely need again. According to this principle, there are the following two groups of items:

• Repeatable: For example, shampoos or razors that are always needed
• Unrepeatable: For example, books or films that are rarely purchased repeatedly

If the product cannot be attributed to one of these groups, it makes sense to determine the group type of repetitive purchases individually (someone usually buys only a specific brand, but someone else might try everything in the catalog).

Determining what is an interesting product to a user is also subjective. Some users need things only from their favorite category (conservative recommendations), while someone else, on the other hand, responds more to non-standard goods (risky recommendations). For example, a video-hosting service may recommend only new series from their favorite TV series (conservative), but may periodically recommend new shows or new genres. Ideally, you should choose a strategy for displaying recommendations for each client separately, using generalized information about the client's preferences.

The essential part of datasets used to build recommendation models is user reactions to different objects or items. These reactions are typically named as user ratings of objects. We can obtain user ratings in the following two ways:

• Explicit ratings: The user gives their own rating for the product, leaves a review, or likes the page.
• Implicit ratings: The user clearly does not express their attitude, but an indirect conclusion can be made from their actions. For example, if they bought a product, it means they like it; if they read the description for a long time, it means there is serious interest.

Of course, explicit preferences are better. However, in practice, not all services provide an opportunity for users to express their interests clearly, and not all users have the desire to do so. Both types of assessments are most often used in tandem, and complement each other well.

It is also essential to distinguish between the terms prediction (prediction of the degree of interest) and the recommendation itself (showing the recommendation). How to show something is a separate task from the task of what to show. How to show is a task that uses the estimates obtained in the prediction step, and can be implemented in different ways.

In this section, we discussed the basics of recommender systems. In the following sections, we will look at essential building blocks of recommender systems. Let's begin by looking at the main principles of content-based filtering, user- and item-based collaborative filtering, and collaborative filtering based on matrix factorization.