Have you heard about the Nonnegative Matrix Factorization (NMF)? It has some similarities with the Principal Component Analysis (PCA) and belongs to the rank or dimension reduction techniques. The NMF incorporates a sign constraint, and is not based on the Singular Value Decomposition (SVD). It can be used with a Bregman entropic pseudo-distance. I have heard about NMF during a talk on speach recognition in INRIA Bordeaux I. It seems that NMF has some success in various domains of applications. It is quite natural to think about some adaptive sparse NMF, an analogue of the sparse PCA.