You are presented with multiple paper abstracts, alongside the associated literature review and chapter titles. Given the provided information, you are going to do a literature review. Please generate a coherent literature review that synthesizes the content, draws connections between different works, highlights major findings, and identifies any gaps in the existing research.

Literature Review Title: Survey on Probabilistic Models of Low-Rank Matrix Factorizations 
Chapter Title:  Matrix Factorizations 
1. Abstract of Cited Paper (BIB001):  A method of principal component analysis (PCA) based on a new L1-norm optimization technique is proposed. Unlike conventional PCA which is based on L2-norm, the proposed method is robust to outliers because it utilizes L1-norm which is less sensitive to outliers. It is invariant to rotations as well. The proposed L1-norm optimization technique is intuitive, simple, and easy to implement. It is also proven to find a locally maximal solution. The proposed method is applied to several datasets and the performances are compared with those of other conventional methods.

Literature Review:
For given data matrix X, its low-rank factorization model is written as where W ∈ R d×r , Z ∈ R r×N , E is the noise matrix and r < d. We assume that E ij ∼ N (0, σ 2 ) are independent and identically distributed. We can get the optimal W and Z according to the maximum likelihood estimation. More specifically, we need to solve the following minimization problem: The closed-form solution to problem (60) can be obtained by the Singular Value Decomposition (SVD). To enhance the robustness to outliers or large sparse noise, we now assume that E ij ∼ Lap(0, σ). For the moment, we solve the following optimization problem: where · 1 is the L1-norm of a matrix (i.e., the sum of the absolute value of all elements). This problem is also called L1-norm PCA and the corresponding optimization methods were proposed in  BIB002 . Srebro and Jaakkola considered the weighted low-rank approximations problems and provided an EM algorithm BIB001 .