# Machine Learning Glossary: Recommendation Systems

## candidate generation

#recsystems

The initial set of recommendations chosen by a recommendation system. For example, consider a bookstore that offers 100,000 titles. The candidate generation phase creates a much smaller list of suitable books for a particular user, say 500. But even 500 books is way too many to recommend to a user. Subsequent, more expensive, phases of a recommendation system (such as scoring and re-ranking) reduce those 500 to a much smaller, more useful set of recommendations.

## collaborative filtering

#recsystems

Making predictions about the interests of one user based on the interests of many other users. Collaborative filtering is often used in recommendation systems.

## item matrix

#recsystems

In recommendation systems, a matrix of embedding vectors generated by matrix factorization that holds latent signals about each item. Each row of the item matrix holds the value of a single latent feature for all items. For example, consider a movie recommendation system. Each column in the item matrix represents a single movie. The latent signals might represent genres, or might be harder-to-interpret signals that involve complex interactions among genre, stars, movie age, or other factors.

The item matrix has the same number of columns as the target matrix that is being factorized. For example, given a movie recommendation system that evaluates 10,000 movie titles, the item matrix will have 10,000 columns.

## items

#recsystems

In a recommendation system, the entities that a system recommends. For example, videos are the items that a video store recommends, while books are the items that a bookstore recommends.

## matrix factorization

#recsystems

In math, a mechanism for finding the matrixes whose dot product approximates a target matrix.

In recommendation systems, the target matrix often holds users' ratings on items. For example, the target matrix for a movie recommendation system might look something like the following, where the positive integers are user ratings and 0 means that the user didn't rate the movie:

Casablanca The Philadelphia Story Black Panther Wonder Woman Pulp Fiction
User 1 5.0 3.0 0.0 2.0 0.0
User 2 4.0 0.0 0.0 1.0 5.0
User 3 3.0 1.0 4.0 5.0 0.0

The movie recommendation system aims to predict user ratings for unrated movies. For example, will User 1 like Black Panther?

One approach for recommendation systems is to use matrix factorization to generate the following two matrixes:

• A user matrix, shaped as the number of users X the number of embedding dimensions.
• An item matrix, shaped as the number of embedding dimensions X the number of items.

For example, using matrix factorization on our three users and five items could yield the following user matrix and item matrix:

User Matrix                 Item Matrix

1.1   2.3           0.9   0.2   1.4    2.0   1.2
0.6   2.0           1.7   1.2   1.2   -0.1   2.1
2.5   0.5


The dot product of the user matrix and item matrix yields a recommendation matrix that contains not only the original user ratings but also predictions for the movies that each user hasn't seen. For example, consider User 1's rating of Casablanca, which was 5.0. The dot product corresponding to that cell in the recommendation matrix should hopefully be around 5.0, and it is:

(1.1 * 0.9) + (2.3 * 1.7) = 4.9


More importantly, will User 1 like Black Panther? Taking the dot product corresponding to the first row and the third column yields a predicted rating of 4.3:

(1.1 * 1.4) + (2.3 * 1.2) = 4.3


Matrix factorization typically yields a user matrix and item matrix that, together, are significantly more compact than the target matrix.

## recommendation system

#recsystems

A system that selects for each user a relatively small set of desirable items from a large corpus. For example, a video recommendation system might recommend two videos from a corpus of 100,000 videos, selecting Casablanca and The Philadelphia Story for one user, and Wonder Woman and Black Panther for another. A video recommendation system might base its recommendations on factors such as:

• Movies that similar users have rated or watched.
• Genre, directors, actors, target demographic...

## re-ranking

#recsystems

The final stage of a recommendation system, during which scored items may be re-graded according to some other (typically, non-ML) algorithm. Re-ranking evaluates the list of items generated by the scoring phase, taking actions such as:

• Eliminating items that the user has already purchased.
• Boosting the score of fresher items.

## scoring

#recsystems

The part of a recommendation system that provides a value or ranking for each item produced by the candidate generation phase.

## user matrix

#recsystems

In recommendation systems, an embedding vector generated by matrix factorization that holds latent signals about user preferences. Each row of the user matrix holds information about the relative strength of various latent signals for a single user. For example, consider a movie recommendation system. In this system, the latent signals in the user matrix might represent each user's interest in particular genres, or might be harder-to-interpret signals that involve complex interactions across multiple factors.

The user matrix has a column for each latent feature and a row for each user. That is, the user matrix has the same number of rows as the target matrix that is being factorized. For example, given a movie recommendation system for 1,000,000 users, the user matrix will have 1,000,000 rows.

## Weighted Alternating Least Squares (WALS)

#recsystems

An algorithm for minimizing the objective function during matrix factorization in recommendation systems, which allows a downweighting of the missing examples. WALS minimizes the weighted squared error between the original matrix and the reconstruction by alternating between fixing the row factorization and column factorization. Each of these optimizations can be solved by least squares convex optimization. For details, see the Recommendation Systems course.

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