# Bi-Objective Nonnegative Matrix Factorization: Linear Versus Kernel-Based Models

arXiv: https://arxiv.org/abs/1501.05684 · HTML: https://mlsanity.com/paper/1501.05684/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jan 2015.

## Built on by (most cited first, 2 of 2)

- [Hyperspectral Unmixing Based on Nonnegative Matrix Factorization: A Comprehensive Review](https://mlsanity.com/paper/2205.09933/) (2022)
- [DTU-Net: A Multi-Scale Dilated Transformer Network for Nonlinear Hyperspectral Unmixing](https://mlsanity.com/paper/2503.03465/) (2025)

## Abstract (arXiv)

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.