Implementation and evaluation distributed mixed pixels analysis algorithm for hyperspectral image based on constraint non-negative matrix factorization

Abstract

As an effective blind source separation method, non-negative matrix factorization has been widely adopted to analyze mixed data in hyperspectral images. To avoid trapping in local optimum, appropriate constraints are added to the objective function of NMF, whose reflections of image essential attribute determine the performance finally. In this paper, a new NMF-based mixed data analysis algorithm is presented, with maximum overall coverage constraint introduced in traditional NMF. The new constraint was proposed using data geometrical properties in the feature space to maximizes the number of pixels contained in the simplex constructed by endmembers compulsorily and introduced in objective function of NMF, named maximum overall coverage constraint NMF (MOCC-NMF), to analyze mixed data in highly mixed hyperspectral data without pure pixels. For implementing easily, multiplicative update rules are applied to avoid step size selection problem occurred in traditional gradient-based optimization algorithm frequently. Furthermore, in order to handle huge computation involved, parallelism implementation of the proposed algorithm using MapReduce is described and the new partitioning strategy to obtain matrix multiplication and determinant value is discussed in detail. In the numerical experiments conducted on real hyperspectral and synthetic datasets of different sizes, the efficiency and scalability of the proposed algorithm are confirmed.

GRAPHICAL ABSTRACT

KEYWORDS:

• Hyperspectral image
• MapReduce
• non-negative matrix factorization
• convex geometry
• simplex
• endmember

Acknowledgements

We thank School of Software, Henan University and College of Environment and Planning, Henan University for providing experiment environment.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Ying Wang http://orcid.org/0000-0001-9628-7904

Yunfeng Kong http://orcid.org/0000-0002-0777-3116

Additional information

Funding

This work is supported by National Natural Science Foundation of China (No. 61703141), the Natural Science Foundation of Henan Province (No. 182300410164).