Mathematical models such as matrix factorization and SVD have proved to be very accurate when it comes to building recommendation engines over the similarity calculation measures. Another advantage is their ability to scale down easily also allowed to design the systems easily. In this chapter, we will learn about the mathematical models as explained next.

A matrix can be decomposed into two low rank matrices, which when multiplied back will result in a single matrix approximately equal to the original matrix.

Let's say that *R*, a rating matrix of size *U X M* can be decomposed into two low rank matrices, *P* and *Q*, of size *U X K* and *M X K* respectively, where *K* is called the rank of the matrix.

In the following ...

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