In the last few years I have been involved in a major effort to enhance our understanding of the mutational processes in human cancer. A particularly popular method is an unsupervised learning method called non-negative matrix factorization (NMF). Parameter estimation in the NMF model is a difficult high-dimensional optimization problem. I will describe and compare a number of NMF optimization algorithms, including a majorize-minimize algorithm, an expectation-maximization algorithm, and a procedure based on cone projection in convex analysis. A major finding is that a mix-and-match strategy often performs better than running each algorithm in isolation.
This is joint work with Astrid Kousholt, Qianyun Guo and Jens Ledet Jensen.