🍿 STEFLIX: A Movie-based Recommender System

Steflix is a Recommender System that uses Weighted Matrix Factorisation to learn embeddings from movies ratings, and uses Content-based filtering and Collaborative filtering to suggest new (ranked) movies to the user.

Usage

First of all, clone the repository to your local machine:

mkdir project/folder
cd project/folder
git clone git@github.com:enstit/Steflix.git

and then install the required Python packages in order to correctly run the code:

pip install -r requirements.txt

The utils folder contains source code used for the project:

• the matfac.py script contains the declaration of the WeightedMatrixFactorization class, used by the Recommender System to calculate users and items embeddings starting from the (sparse) reviews matrix of users and items;
• the recsys.py script contains the declaration of the RecommenderSystem class. It uses the above embeddings to perform Content-based filtering and Collaborative filtering of any user of the system.

In the RecommenderSystem.ipynb Jupyter notebook, a RecommenderSystem is built starting from the reviews of 943 users to 1682 movies (data is taken from the MovieLens 100k dataset¹). From the reviews matrix, the tastes of a specific user have been analyzed as an example, and suggestions have been made that seem to reflect what is expected from a recommendation engine.

Theoretical stuff

How exactly does the Recommender System work, from a theoretical point of view?

First of all, we start from a matrix $C$ that we are going to call the reviews matrix (or feedbacks matrix) of dimensions $M\times N$. Each row of the matrix correspond to a different user of the system, and each column to a particolar item (or movie, in our study case). It follows that a cell represents the rating that a particular user has given to an item (can be in a $1$/$0$ form, a rating from $1$ to $5$, $\dots$). Of course, no value means no rating left by a user to an item.

$$ C_{M\times N} = \begin{bmatrix} & 3 & & 1 & 2 & & 5 \\ 4 & & & 2 & & 2 & \\ & 3 & 1 & & & 3 & 4 \\ 2 & & 4 & & 3 & & 5 \\ 5 & 2 & 2 & & 3 & & \\ \end{bmatrix} $$

Empty cells (i.e., unknown users' ratings) is exactly what we want to infer from the model. Knowing that, we would be able to suggest a user items that they would probably like, and keep them away from items that would probably dislike.

But what exactly are the features that a particular user considers when rating an item? If we knew them, and if we also knew how a particular item can be expressed as a combination of this features, we would also be able to retrieve expeced ratings for un-rated items.

It turns out that we don't need to know what this features are at all. Indeed, we call them latent features.

We can find two matrices $U$ and $V$ (respectively, the users embedding and the items embedding) with $k$ columns (with $k$ the number of latent factors) such that

$$ C \approx U_{M\times k} \cdot V_{N\times k}^{T}. $$

The algorithm used for this decomposition is the Weighted Alternating Least Squares algorithm², in which:

1. we start with $U$ and $V$ randomly generated;
2. we fix $U$ and fin, by solving a linear system, the best $V$;
3. we fix $V$ and fin, by solving a linear system, the best $U$;
4. we repeat 2. and 3. for a fixed number of iterations.

Basically, with this algorithm we optimise the difference between the original matrix $C$, and its approximation $C'$ by also weighting the observed and unobserved values using different values $w_{i,j}$ and $w_{0}$ to reflect the uncertainty in the projection.

Once we obtain this new matrices, we can use them to compute similarities (in our case, cosine similarity) of the rated items with respect to

• the unrated items, finding the ones nearest to a user tastes (Content-based filtering);
• the other users, finding clusters of people with similar interests (Collaborative filtering),from which we can extract new items to recommend to the user;
• a mix of these two methods, using an hybrid approach.

License

This project is licensed under the MIT License - see the LICENSE file for details.

Footnotes

1. F. Maxwell Harper and Joseph A. Konstan. 2015. The MovieLens Datasets: History and Context. ACM Transactions on Interactive Intelligent Systems (TiiS) 5, 4: 19:1–19:19. https://doi.org/10.1145/2827872 ↩

2. https://stanford.edu/~rezab/classes/cme323/S15/notes/lec14.pdf ↩