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Front. Inform. Technol. Electron. Eng.  2016, Vol. 17 Issue (5): 403-412    DOI: 10.1631/FITEE.1600028
    
高光谱图像主成分非负矩阵分解方法
Xiu-rui Geng, Lu-yan Ji, Kang Sun
Key Laboratory of Technology in Geo-spatial Information Processing and Application System, Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China; MOE Key Laboratory for Earth System Modeling, Center for Earth System Science, Tsinghua University, Beijing 100084, China; The 54th Research Institute of China Electronics Technology Group Corporation, Shijiazhuang 050000, China
Non-negative matrix factorization based unmixing for principal component transformed hyperspectral data
Xiu-rui Geng, Lu-yan Ji, Kang Sun
Key Laboratory of Technology in Geo-spatial Information Processing and Application System, Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China; MOE Key Laboratory for Earth System Modeling, Center for Earth System Science, Tsinghua University, Beijing 100084, China; The 54th Research Institute of China Electronics Technology Group Corporation, Shijiazhuang 050000, China
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摘要： 目的：在高光谱混合像元分析技术领域中，非负矩阵分解的应用十分广泛。然而，由于高光谱数据量较大，导致使用非负矩阵分解的计算复杂度很高。另一方面，非负矩阵分解对高光谱数据中的噪声十分敏感。虽然主成分分析技术可以很好地解决这两个问题，但是由于经过主成分分析变换后的数据存在负值，使得基于乘式迭代的非负矩阵分解技术不能直接应用于主成分变换后的数据。因此，本文着力于提出一种可以应用于主成分变换后数据的非负矩阵分解方法。
创新点：本文研究了主成分分析的两个步骤（平移和投影）对非负矩阵分解的影响。然后提出了利用强迫正交的手段将主成分变换后的数据重新旋转到第一象限，使之能够适用于非负矩阵分解的乘式迭代公式。
方法：研究了主成分分析对非负矩阵分解的影响，并提出了消除主成分变换数据负值的方法。
结论：本文提出了一种在主成分特征空间中使用非负矩阵分解的高光谱图像解混方法。该方法使用强迫正交有效解决了主成分变换后的负值问题。模拟和真实数据均表明，相比于原始的非负矩阵分解，本文所提方法速度更快，提取的端元误差更小。
关键词： 非负矩阵分解;  主成分分析;  端元;  高光谱    
Abstract: Non-negative matrix factorization (NMF) has been widely used in mixture analysis for hyperspectral remote sensing. When used for spectral unmixing analysis, however, it has two main shortcomings: (1) since the dimensionality of hyperspectral data is usually very large, NMF tends to suffer from large computational complexity for the popular multiplicative iteration rule; (2) NMF is sensitive to noise (outliers), and thus the corrupted data will make the results of NMF meaningless. Although principal component analysis (PCA) can be used to mitigate these two problems, the transformed data will contain negative numbers, hindering the direct use of the multiplicative iteration rule of NMF. In this paper, we analyze the impact of PCA on NMF, and find that multiplicative NMF can also be applicable to data after principal component transformation. Based on this conclusion, we present a method to perform NMF in the principal component space, named ‘principal component NMF’ (PCNMF). Experimental results show that PCNMF is both accurate and time-saving.
Key words: Non-negative matrix factorization (NMF)    Principal component analysis (PCA)    Endmember    Hyperspectral
收稿日期: 2016-01-19 出版日期: 2016-05-04
CLC:  TP751.1  
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引用本文:

Xiu-rui Geng, Lu-yan Ji, Kang Sun. Non-negative matrix factorization based unmixing for principal component transformed hyperspectral data. Front. Inform. Technol. Electron. Eng., 2016, 17(5): 403-412.

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http://www.zjujournals.com/xueshu/fitee/CN/10.1631/FITEE.1600028    或    http://www.zjujournals.com/xueshu/fitee/CN/Y2016/V17/I5/403

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