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# Recommendation systems

This is a blog post about recommender systems. This month, I’ve been working on several projects involving sophisticated recommendation algorithms. So It might be good to summarize some of my knowledge and thoughts on the subject.

As machine learning is getting more and more popular in the industry, recommender systems are particularly doing well. Netflix, the popular streaming service, is the host of a contest (i.e. The Netflix Prize) where scientists and engineers participate to improve the accuracy of predictions about how much an individual will enjoy a movie. In 2009, the best team came to be awarded a prize of 1 million dollars for a 10% improvement against their previous systems. Recommender systems take gradually an important part in the business model of various companies.

The recommendation problem can intuitively be represented as a matrix containing ratings where the columns define the users and the rows, the items.

Let $C$ be the set of all users and let $S$ be the set of all possible items that can be recommended. The central problem of recommender systems lies in that the utility function $u$ which maps a user and an item to a rating, i.e. $C \times S \rightarrow R$ where $R$ is often a nonnegative integer with a certain range, is often not defined on the whole $C \times S$ space. The goal of recommenders might then be to extrapolate the missing ratings.

In the literature, recommender systems are usually divided in three categories:

• Content-based recommendations: The users are recommended items similar to the ones they preferred in the past.
• Collaborative recommendations: The users are recommended items based on people with similar tastes.
• Hybrid approaches: These techniques combine collaborative and content-based methods.

They all show pros and cons but the hybrid versions often show more attractiveness in several problems as they try to solve issues such as the new user problem, the new item problem, nonintrusiveness and more… We’ll talk more about it later on.

# Content-Based Recommendations

As previously stated, content-based methods predict user’s missing ratings based on his past actions. In order to do so, the items need features such as keywords, dates or authors to evaluate level of similarities between items. In the case of movies this could simply be the genre. (i.e. horror, action, comedy…)

Information retrieval and information filtering has a long history with problems of such nature.

We can easily see that content-based recommendations mainly favor text based applications. So, how do we weight similarities between items and predict ratings? Various machine learning techniques have been used in the past to answer this question. Methods such as Bayesian classifiers, clustering, decision trees and artificial neural networks can score very well in those tasks. We might for example, use a Naive Bayes classifier to classify items as “relevant” or “irrelevant” by the user given a set of keywords:

$P(C\_i|k\_{1j},...,k\_{nj})$

We can then make the assumption that keywords are independent and, therefore, the above probability is proportional to

$P(C\_i)\prod\limits\_{x}P(k\_{xj}|C\_i)$

Both factors $P(C_i)$ and $\prod_{x}P(k_{xj}|C_i)$ can be estimated from the underlying training data. Therefore, for each page $p_j$, the probability $P(C_i|k_{1j},…,k_{nj})$ is computed for each class $C_i$ and page $p_j$ is assigned to class $C_i$ having the highest probability.

Content-based recommendations present some limitation such as:

• Limited content analysis: The techniques are limited by the features that are explicitly associated with the objects that the systems recommend. The features might, for example, need to be extracted from text documents.
• Overspecialization: The recommendations are limited in being similar to those already rated by the users. Introducing some randomness could be necessary.
• New user problem: The user often has to rate a sufficient number of items before content based recommender systems can understand the user’s preferences.

# Collaborative Recommendations

Collaborative recommendation systems make the assumption that the missing ratings of an individual can be predicted through the users’ ratings who share similar tastes.

One commonly used technique is known as the nearest neighbor.

TODO(rzagabe): More is yet to come

Collaborative recommendations present some limitation such as:

• New user problem:
• New item problem:

# Hybrid Approaches

Most popular recommendation systems are hybrid approaches where content based and collaborative recommendation techniques are combined in order to overcome their individual limitations.

TODO(rzagabe): More is yet to come