# Non-negative matrix factorization based on generalized dual divergence

## TL;DR

This paper introduces a comprehensive theoretical framework for non-negative matrix factorization using generalized dual divergence, encompassing various models and noise structures, with proven convergence and adaptable extensions.

## Contribution

It develops a unified framework for NMF based on generalized dual divergence, including convergence proofs and potential for extensions like penalties and tensors.

## Key findings

- Framework generalizes existing NMF methods
- Convergence of algorithms is proven
- Provides a goodness-of-fit measure

## Abstract

A theoretical framework for non-negative matrix factorization based on generalized dual Kullback-Leibler divergence, which includes members of the exponential family of models, is proposed. A family of algorithms is developed using this framework and its convergence proven using the Expectation-Maximization algorithm. The proposed approach generalizes some existing methods for different noise structures and contrasts with the recently proposed quasi-likelihood approach, thus providing a useful alternative for non-negative matrix factorizations. A measure to evaluate the goodness-of-fit of the resulting factorization is described. This framework can be adapted to include penalty, kernel and discriminant functions as well as tensors.