Recently, I have implemented U-V decomposition technique for Recommendation Systems using Particle Swarm Optimization.

U-V decomposition is an optimization problem for a matrix. Here, our matrix elements represent some users review about movies.

We have 5 users and 5 movies. Each row represents a user’s review for each movie. There are some missing values from the matrix which means that the user hasn’t put his/her review on that movie.

You can check the code here https://github.com/AhmedHani/CS624-ML/tree/master/Implementations/U-V%20Decomposition . Later, I will write another post to explain my code.

**Input**: Matrix 5×5 with unknown reviews

**Intermediate output**: Matrix U and V which multiplication gives a new matrix without unknown reviews

**Output**: Matrix 5×5 without unknown values.

**References **

– The matrix example is taken from the book http://infolab.stanford.edu/~ullman/mmds/book.pdf at chapter 9