Thursday, 11 January 2018

Introduction of Recommender Systems

We would try to clearly explain the concept of a recommender system.

What is a Recommender System
A recommender system is a system that is used to make prediction about what the user preference may be on the items before the user does it.

We are going to briefly discuss the following three topics:
  1. Matrix Factorization
  2. Singular value decomposition(SVD)
  3. Probabilistic Matrix Factorization (PMF)
1. Matrix Factorization
Matrix factorization is aspect of linear algebra which is the factorization of a matrix into two or more matrices such that when multiplied together would give the original matrix

2. Singular Value Decomposition(SVD)
SVD is a method of matrix factorization. It is a generalization of the eigen-decomposition  of a positive semi-definite orthonomal matrix to an m x n matrix through an extension of the polar decomposition.
The singular value decomposition of a matrix M of m x n dimension is a factorization given by
 {\displaystyle \mathbf {U\Sigma V^{*}} }
where :
\mathbf {U} is an m x n matrix
\mathbf{\Sigma} is an m x n rectangular diagonal matrix with non-negative real numbers on the diagonal
\mathbf {V} is an n x n real or complex unitary matrix

3. Probabilistic Matrix Factorization(PMF) 
PMF does the factorization of a matrix by learning models using maximum a posterior approximation