Matrix Factorization

Matrix factorization is generally purposing to represent a matrix as a product of two or more matrices. It has multiple functions. For example, if two matrices used to represent the original matrix by multiplication are small enough (i.e., lower rank), it can be considered to be reduction of degrees of freedom. Even if the matrix cannot be exactly represented as a product of two lower rank matrices, if it is possible for the product of matrices with smaller rank to approximate the original one, it can be considered to be a good approximation. Matrix factorization also has some relationship with geometrical representation. Generated matrices can be considered to be projection onto lower dimensional space.