Bi-Objective Nonnegative Matrix Factorization: Linear Versus Kernel-Based Models
This work addresses the problem of feature extraction in signal and image processing by extending NMF to a multi-objective framework, offering incremental improvements for applications like hyperspectral unmixing.
The paper tackles the limitation of single-objective nonnegative matrix factorization (NMF) by proposing a bi-objective NMF that considers both input and feature spaces, using multi-objective optimization to find Pareto optimal solutions, with experimental results on real hyperspectral images showing improved efficiency over state-of-the-art methods.
Nonnegative matrix factorization (NMF) is a powerful class of feature extraction techniques that has been successfully applied in many fields, namely in signal and image processing. Current NMF techniques have been limited to a single-objective problem in either its linear or nonlinear kernel-based formulation. In this paper, we propose to revisit the NMF as a multi-objective problem, in particular a bi-objective one, where the objective functions defined in both input and feature spaces are taken into account. By taking the advantage of the sum-weighted method from the literature of multi-objective optimization, the proposed bi-objective NMF determines a set of nondominated, Pareto optimal, solutions instead of a single optimal decomposition. Moreover, the corresponding Pareto front is studied and approximated. Experimental results on unmixing real hyperspectral images confirm the efficiency of the proposed bi-objective NMF compared with the state-of-the-art methods.