Welcome to The Matrix Factorization Jungle [ A living documention on the state of the art algorithms dedicated to matrix factorization ]
From the webpage:
Matrix Decompositions has a long history and generally centers around a set of known factorizations such as LU, QR, SVD and eigendecompositions. With the advent of new methods based on random projections and convex optimization that started in part in the compressive sensing literature, we are seeing a surge of very diverse algorithms dedicated to many different kinds of matrix factorizations with constraints based on rank, positivity, sparsity,… As a result of this large increase in interest, I have decided to keep a list of them here following the success of the big picture in compressive sensing.
If you are unfamiliar with the use of matrices in data mining, consider Non-negative matrix factorization and the examples cited under Text mining.