Personal recommendations use the maximum information available about the user—primarily, information on their previous purchases. Content-based filtering was one of the first approaches to this. In this approach, the product's description (content) is compared with the interests of the user, obtained from their previous assessments. The more the product meets these interests, the higher the potential interest of the user. The obvious requirement here is that all products in the catalog should have a description.
Historically, the subject of content-based recommendations was products with unstructured descriptions: films, books, or articles. Their features may be—for example—text descriptions, reviews, or casts. However, nothing prevents the use of usual numerical or categorical features.
Unstructured features are described in a text-typical way—vectors in the space of words (vector-space model). Each element of a vector is a feature that potentially characterizes the interest of the user. Similarly, an item (product) is a vector in the same space.
As users interact with the system (say, they buy films), the vector descriptions of the goods they've purchased merge (sum up and normalize) into a single vector and, thus, form the vector of a user's interests. Using this vector of interests, we can find the product, the description of which is closest to it—that is, solve the problem of finding the nearest neighbors.
When forming the vector space of a product presentation, instead of individual words, you can use shingles or n-grams (successive pairs of words, triples of words, or other numbers of words). This approach makes the model more detailed, but more data is required for training.
In different places of the description of the product, the weight of keywords may differ (for example, the description of the film may consist of a title, a brief description, and a detailed description). Product descriptions from different users can be weighed differently. For example, we can give more weight to active users who have many ratings. Similarly, you can weigh them by item. The higher the average rating of an object, the greater its weight (similar to PageRank). If the product description allows links to external sources, then you can also analyze all third-party information related to the product.
The cosine distance is often used to compare product representation vectors. This distance measures the value of proximity between two vectors.
When adding a new assessment, the vector of interests is updated incrementally (only for those elements that have changed). During the update, it makes sense to give a bit more weight to new estimates since the user's preferences may change. You'll notice that content-based filtering almost wholly repeats the query-document matching mechanism used in search engines such as Google. The only difference lies in the form of a search query—content filtering systems use a vector that describes the interests of the user, and search engines use keywords of the requested document. When search engines began to add personalization, this distinction was erased even more.