Non-negative matrix factorization based on generalized dual divergence
This work offers a generalized framework for non-negative matrix factorization, which is incremental as it builds on and contrasts with existing methods, potentially useful for researchers in machine learning and data analysis dealing with noise structures and model fitting.
The authors tackled the problem of non-negative matrix factorization by proposing a theoretical framework based on generalized dual Kullback-Leibler divergence, which generalizes existing methods for different noise structures and provides an alternative to quasi-likelihood approaches, with convergence proven using the Expectation-Maximization algorithm.
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.