Multiobjective Sparse Non-Negative Matrix Factorization

Non-negative matrix factorization (NMF) is becoming increasingly popular in many research fields due to its particular properties of semantic interpretability and part-based representation. Sparseness constraints are usually imposed on the NMF problems in order to achieve potential features and sparse representation. These constrained NMF problems are usually reformulated as regularization models to solve conveniently. However, the regularization parameters in the regularization model are difficult to tune and the frequently used sparse-inducing terms in the regularization model generally have bias effects on the induced matrix and need an extra restricted isometry property (RIP). This paper proposes a multiobjective sparse NMF paradigm which refrains from the regularization parameter issues, bias effects, and the RIP condition. A novel multiobjective memetic algorithm is also proposed to generate a set of solutions with diverse sparsity and high factorization accuracy. A masked projected gradient local search scheme is specially designed to accelerate the convergence rate. In addition, a priori knowledge is also integrated in the algorithm to reduce the computational time in discovering our interested region in the objective space. The experimental results show that the proposed paradigm has better performance than some regularization algorithms in producing solutions with different degrees of sparsity as well as high factorization accuracy, which are favorable for making the final decisions.