An Iterative Algorithm for Regularized Non-negative Matrix Factorizations

We generalize the non-negative matrix factorization algorithm of Lee and Seung to accept a weighted norm, and to support ridge and Lasso regularization. We recast the Lee and Seung multiplicative update as an additive update which does not get stuck on zero values. We apply the companion R package rnnmf to the problem of finding a reduced rank representation of a database of cocktails.