Pareto front of bi-objective kernel-based nonnegative matrix factorization

Fei Zhu (1) , Paul Honeine (1)

1 LM2S - Laboratoire Modélisation et Sûreté des Systèmes

The nonnegative matrix factorization (NMF) is a powerful data analysis and dimensionality reduction technique. So far, the NMF has been limited to a single-objective problem in either its linear or nonlinear kernel-based formulation. This paper presents a novel bi-objective NMF model based on kernel machines, where the decomposition is performed simultaneously in both input and feature spaces. The problem is solved employing the sum-weighted approach. Without loss of generality, we study the case of the Gaussian kernel, where the multiplicative update rules are derived and the Pareto front is approximated. The performance of the proposed method is demonstrated for unmixing hyperspectral images

Mots clés: machine learning; hyperspectral; nonnegative matrix factorization; dimensionality reduction; multi-objective optimization; bi-objective optimization problem; kernel methods; nonlinear mode; sum-weighted approach; Pareto front approximation; Pareto optimal; NMF; biobjective nonnegative matrix factorization; Pareto optimisation; Pareto optimization

Domaines: Apprentissage [cs.LG]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]; Vision par ordinateur et reconnaissance de formes [cs.CV]

Fei Zhu, Paul Honeine. Pareto front of bi-objective kernel-based nonnegative matrix factorization. Proc. 23rd European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN), 2015, Bruges, Belgium. pp.585 - 590. ⟨hal-01965982⟩