A Fast Gradient Method for Nonnegative Sparse Regression with Self Dictionary

Understand

A nonnegative matrix factorization (NMF) can be computed efficiently under the separability assumption, which asserts that all the columns of the given input data matrix belong to the cone generated by a (small) subset of them.

• The provably most robust methods to identify these conic basis columns are based on nonnegative sparse regression and self dictionaries, and require the solution of large-scale convex optimization problems.
• In this paper we study a particular nonnegative sparse regression model with self dictionary.
• As opposed to previously proposed models, this model yields a smooth optimization problem where the sparsity is enforced through linear constraints.