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Band selection for hyperspectral imagery based on weighted probabilistic archetypal analysis

  • role： First author第一作者
  • Affiliation：

    Department of Geography and Spatial Information Techniques, Ningbo University, Ningbo 315211, China

    Institute of Urban Studies, Shanghai Normal University, Shanghai 200234, China

  • Email：sunweiwei@nbu.edu.cn
  • Introduction：孙伟伟(1985—　)，男，副教授，研究方向为地理信息系统和遥感理论和方法及“3S”技术在海岸带资源管理与环境变化监测中的应用。E-mail：sunweiwei@nbu.edu.cn
Weiwei SUN12,  
  • Affiliation：

    Department of Geography and Spatial Information Techniques, Ningbo University, Ningbo 315211, China

Dianfa ZHANG1,  
  • Affiliation：

    Department of Geography and Spatial Information Techniques, Ningbo University, Ningbo 315211, China

Gang YANG1,  
  • Affiliation：

    Institute of Urban Studies, Shanghai Normal University, Shanghai 200234, China

    Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou 730000, China

Weiyue LI23

реферат

Hyperspectral imaging collects both spectral signals and images of ground objects on the Earth’s surface using hundreds of narrow bands. It has become a powerful technique for air-to-land observation. Unfortunately, numerous bands and strong intra-band correlations bring about information redundancy and heavy computational burdens for hyperspectral imagery (HSI) classification. Moreover, the “Hughes” problem traps the HSI data into a conflict between a high classification accuracy and an improbably large number of training samples. Therefore, proper bands should be selected from original hyperspectral data to reduce the high computations while achieving superior classification accuracies. In this study, a Weighted Probabilistic Archetypal Analysis (WPAA) method is proposed to extract proper bands from HSI data. WPAA considers the differences between pairwise bands and adopts a composite dissimilarity measure to construct a weighted matrix. This method improves the regular archetypal analysis by using the constructed weighted matrix in hyperspectral bands. Thereafter, the method considers the Dirichlet distribution of sparse coefficients and the quantum nature of hyperspectral imaging. It also introduces the Bayesian framework to construct its mathematical model for band selection. WPAA implements an iterative optimization scheme, transforms unconvex problems into two convex subproblems, and utilizes the Alternating Direction Method of Multipliers (ADMM) to estimate two sparse coefficient matrices. ADMM introduces proper auxiliary variables to augment the constraints in the objection function of WPAA, iteratively minimizes the Lagrangian function with respect to the primal variables, and maximizes it with respect to the Lagrange multipliers. The iteration procedure of two sparse coefficient matrices is repeated until the convergence conditions are satisfied or the number of iterations exceeds the predefined maximal number of iterations. The proper band subset is finally estimated using the sparse reconstruction equation. Two groups of classification experiments on the popular HSI datasets of PaviaU and Urban were designed to carefully test the performance of WPAA in band selection. Four state-of-the-art methods were compared against the proposed WPAA method, i.e., the sparse-based band selection, sparse nonnegative matrix factorization, improved sparse subspace clustering, and sparse self-representation. Experimental results show that WPAA achieves better overall classification accuracy than the other four state-of-the-art methods. WPAA could also obtain the best classification map regardless of the different sizes of the band subset and different training samples. The proposed composite dissimilarity weighted matrix makes great contributions to the improvement of the classification accuracy of the PAA model. WPAA could help select the proper bands for hyperspectral images, and it can serve as a good alternative for dimensionality reduction in hyperspectral image classification.

ключеви́че слова́

hyperspectral imagery;archetypal analysis;weighted probabilistic archetypal analysis;band selection;sparse representation

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