Coordinate Descent for mixed-norm NMF

Nonnegative matrix factorization (NMF) is widely used in a variety of machine learning tasks involving speech, documents and images. Being able to specify the structure of the matrix factors is crucial in incorporating prior information. The factors correspond to the feature matrix and the learnt representation. In particular, we allow an user-friendly specification of sparsity on the groups of features using the L1/L2 measure. Also, we propose a pairwise coordinate descent algorithm to minimize the objective. Experimental evidence of the efficacy of this approach is provided on the ORL faces dataset.