arXiv subjects

Fei Zhu

Publications and source records attributed to Fei Zhu.

75 records · Page 5Linked to original sources

arXiv2016

Kernel Nonnegative Matrix Factorization Without the Curse of the Pre-image - Application to Unmixing Hyperspectral Images

The nonnegative matrix factorization (NMF) is widely used in signal and image processing, including bio-informatics, blind source separation and hyperspectral image analysis in remote sensing. A great challenge arises when dealing with a nonlinear formulation of the NMF. Within the framework of kernel machines, the models suggested in the literature do not allow the representation of the factorization matrices, which is a fallout of the curse of the pre-image. In this paper, we propose a novel kernel-based model for the NMF that does not suffer from the pre-image problem, by investigating the estimation of the factorization matrices directly in the input space. For different kernel functions, we describe two schemes for iterative algorithms: an additive update rule based on a gradient descent scheme and a multiplicative update rule in the same spirit as in the Lee and Seung algorithm. Within the proposed framework, we develop several extensions to incorporate constraints, including sparseness, smoothness, and spatial regularization with a total-variation-like penalty. The effectiveness of the proposed method is demonstrated with the problem of unmixing hyperspectral images, using well-known real images and results with state-of-the-art techniques.

cs.CV↗

arXiv2016

Correntropy Maximization via ADMM - Application to Robust Hyperspectral Unmixing

In hyperspectral images, some spectral bands suffer from low signal-to-noise ratio due to noisy acquisition and atmospheric effects, thus requiring robust techniques for the unmixing problem. This paper presents a robust supervised spectral unmixing approach for hyperspectral images. The robustness is achieved by writing the unmixing problem as the maximization of the correntropy criterion subject to the most commonly used constraints. Two unmixing problems are derived: the first problem considers the fully-constrained unmixing, with both the non-negativity and sum-to-one constraints, while the second one deals with the non-negativity and the sparsity-promoting of the abundances. The corresponding optimization problems are solved efficiently using an alternating direction method of multipliers (ADMM) approach. Experiments on synthetic and real hyperspectral images validate the performance of the proposed algorithms for different scenarios, demonstrating that the correntropy-based unmixing is robust to outlier bands.

stat.ML↗

arXiv2015

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

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.

stat.ML↗