Matrix Factorization for Recommender Systems
Table of Contents
 Introduction
 What is Matrix Factorization?
 Types of Matrix Decomposition
 Matrix Factorization Techniques
Introduction
As soon as we open Netflix, the platform is filled with relevant suggestions for movies or shows that we might like. Similarly, when we shop online, the ecommerce store automatically customizes the range of recommended products based on our requirements, budget, and preferences. There is no denying that such personalized experiences keep us engaged in these platforms, and we tend to go back to them.
Almost every website or application strives to enhance our online experience to retain users, improve engagement, get positive feedback, and stay ahead of the competition. Hence, they require an effective and robust recommendation system.
Whether it’s an ecommerce store or an OTT platform, every website uses a recommendation engine, which not only provides relevant options but also tells about user behavior and preferences.
There are two types of recommendation systems:
2 Collaborativebased filtering
However, in this blog, we will talk about matrix factorization techniques for recommender systems.
What is Matrix Factorization?
Matrix factorization is among the most soughtafter machine learning recommendation techniques used to generate latent features when two distinct entities are multiplied. It works like a catalyst to enable the system to understand the purpose of a customer’s purchase, browse various pages, select and rank the relevant content or items, and recommend multiple options. After the result matches the requirements, the lead converts into a purchase or transaction, and the deal clicks.
Collaborative filtering is a machine learning matrix factorization application and is used to identify relationships between the entities of products and users. Based on users' ratings on the purchased products, it predicts how they will rate other items to recommend relevant products to users.
Matrix factorization for recommender systems became popular after the Netflix competition, i.e., in 2006, when the OTT platform announced $1 million worth of prize money to the person who could improve its root mean square performance by 10%. Netflix even provides a training data set of 100,480,507 ratings of 480,189 users given to 17,770 movies.
Types of Matrix Decomposition
Matrix decomposition is of three types

LU decomposition
It refers to the decomposition of the matrix into L and U matrices. Here, L is the lower triangular matrix, and U is the upper triangular matrix commonly used to find the coefficient of linear regression. This decomposition will fail if the matrix can’t decompose easily.

QR matrix decomposition
It means the decomposition of the matrix into Q and R. Q refers to the square matrix, while R is the upper triangular matrix. It is used for system analysis.

Cholesky decomposition
Machine learning frequently uses this decomposition to calculate linear least squares for linear regression.
We can use matrix factorization collaborative filtering across different domains, such as recommendation and image recognition. Here, the matrix used in the problem is sparse as there is a possibility that a user can rate just a few products or movies. Its applications include
Dimensionality reduction, latent value decomposition, and more.
Matrix Factorization Techniques
There are four main techniques for the matrix factorization:

Singular value decomposition

Probabilistic matrix factorization

Nonnegative matrix factorization

Tensor matrix factorization
1. Singular value decomposition
SVD is based on dimensionality reduction and generates superiorquality recommendations for users. It is used for producing lowrank approximations in collaborative filtering systems before computing neighborhoods. It is also used to find latent associations between users and items to help compute the predicted probability of certain items by a user.
2. Probabilistic Matrix Factorization
PMF is a modelbased matrix factorization collaborative filtering technique that performs well on sparse, extensive, and imbalanced data and scales linearly with several datasets.
3. Nonnegative Matrix Factorization
It grew out of Principal Component Analysis. It can automatically extract important and sparse features from a set of nonnegative data vectors. Hence, it is commonly used for exploring highdimensional data.
One benefit of using the NMF technique in collaborative filtering is when a nonnegativity is imposed on nonnegative matrices; it reduces prediction errors as compared to techniques such as singular value decomposition (SVD).
This results in interpretable and sparse decomposition. Moreover, with lowrank nonnegative matrix factorization, users can work with compressed dimensional models that accelerate effective statistical classification, data organization, and clustering. This leads to equally faster searches for trends.
4. Tensor Matrix Factorization
To overcome the limitations of the traditional collaborative filtering system, an efficient recommendation system was introduced recently that considers the multidimensional nature of realworld situations to generate suggestions.
Hence, resulting in an enhanced design algorithm tensor factorization techniques. TF integrates contextbased information to extend the conventional twodimensional matrix factorization issue into an ndimensional style of the same issue.
The technique is not only used in matrix factorization for recommendation but also to uncover hidden structures within data in some scenarios, such as hyperspectral unfixing, face identification, etc. This powerful technique is used to produce a model from a tensor with extensive information and higher accuracy as more features are available.