Related Work on Matrix Factorization

Abstract

In this chapter, we provide the related work of basic matrix decomposition methods. The first method that we discuss is known as eigenvalue decomposition, which decomposes the initial matrix into a canonical form. The second method is nonnegative matrix factorization (NMF), which factorizes the initial matrix into two smaller matrices with the constraint that each element of the factorized matrices should be nonnegative. The third method is latent semantic indexing (LSI), which applies singular value decomposition (SVD) that uses singular values of the initial matrix to factorize it. The last method is CUR decomposition, which confronts the problem of high density in factorized matrices (a problem that is faced when using the SVD method). This chapter concludes with a description of other state-of-the-art matrix decomposition techniques.