I am interested in reduced rank / matrix factorisation techniques and their uses across finance and portfolio optimisation. For example, PCA might be used to reduce the number of components you are dealing with or to suggestion correlation between by doing clustering, what might e.g. LU decomposition be useful for, how about non-negative matrix decomposition, ICA and other decompositions?
Thanks for any ideas or suggestions. Some suggestions: https://en.wikipedia.org/wiki/Low-rank_approximation