Matrix decompositions have been used for almost a century for data analysis and a large set of different decompositions are known. The most important ones are:

• Singular Value Decomposition (SVD), and its close relation, Principal Component Analysis (PCA);

• SemiDiscrete Decomposition (SDD); • Independent Component Analysis (ICA); • Non-Negative Matrix Factorization (NNMF);

Some of these are really families of related decompositions; there are also a number of variants and extensions, and we will briefly discuss some of them as well.