An Iterative Algorithm for Regularized Non-negative Matrix Factorizations

TL;DR

This paper extends non-negative matrix factorization algorithms to include weighted norms and regularization, presenting an additive update method and demonstrating its application in reducing cocktail database complexity.

Contribution

It introduces a generalized iterative algorithm for regularized NMF with weighted norms and additive updates, improving upon previous multiplicative methods.

Findings

The algorithm supports ridge and Lasso regularization.

The additive update avoids getting stuck at zero values.

Applied successfully to cocktail database reduction.

Abstract

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.