Nonparametric Orthogonal NMF and its Application in Cancer Clustering

Abstract

Orthogonal nonnegative matrix factorization (NMF) is an NMF objective function that enforces orthogonality constraint on its factor. There are two challenges in optimizing this objective function: the first is how to design an algorithm that has convergence guarantee, and the second is how to automatically choose the regularization parameter. In our previous work, we have been able to develop a convergent algorithm for this objective function. However, the second challenge remains unsolved. In this paper, we provide an attempt to answer the second challenge. The proposed method is based on the L-curve approach and has a simple form which is preferable since it introduces only a small additional computational cost. This method transforms the algorithm into nonparametric, and is also extendable to other NMF objective functions as long as the functions are differentiable with respect to the corresponding regularization parameters. Numerical results are then provided to evaluate the feasibility of the method in choosing the appropriate regularization parameter values by utilizing it in cancer clustering tasks.