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工程科学与技术:2010,42(2):165-170
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一种用于低维光谱空间构造的非负主成分分析法
(1.西安电子科技大学 计算机外部设备研究所;2.西安电子科技大学计算机外部设备研究所;3.西安石油大学 计算机学院)
Nonnegative Constrained Principal Component Analysis for the Construction of Low-dimensional Spectral Space
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投稿时间:2009-04-03    修订日期:2009-10-26
中文摘要: 针对经典主成分分析法进行多光谱图像数据降维会使重构光谱反射比出现负值的问题,提出一种非负主成分分析法,并用该法构造低维光谱空间,实现高维多光谱数据与低维光谱空间的转换。首先分析主成分分析法产生非光谱反射比数据的原因,据此对主成分分析模型增加非负约束,建立迭代方程,求出一组线性无关的非负主成分权向量;然后用该组向量构造低维光谱空间;最后用非线性优化技术确定高维数据在低维空间中的投影值。实验表明,新方法与经典主成分分析法相比,能使重构光谱反射比数据限制在[0,1]范围内,保持了光谱反射比的物理意义,同时所构造低维光谱空间的精度能与经典主成分分析法保持一致。
Abstract:A nonnegative constrained principal component analysis method was proposed to construct a low-dimensional space by which the conversion between it and the multi-spectral space could be achieved.This method overcame the shortcoming that the reconstructed spectral reflectance may be negative when using the classic principal component analysis (PCA) to reduce the dimension of the multi-spectral image data. The reason behind the negative data produced by the PCA was analyzed firstly. According to this, a nonnegative constraint was imposed on the classic principal component analysis model and an iteration equation was constructed. Then through solving that equation, a set of nonnegative linear independence weight vectors of principal components was obtained, by which a low-dimensional spectral space was spanned. Finally a nonlinear optimization technique was used to determine the projection vectors of the multi-spectral image data in the constructed space. Experiments showed that comparing with the classic PCA, the new method can make the reconstructed spectral reflectance data in the interval of [0, 1], which maintains the physical significance of the spectral reflectance. The precision of the space founded by the new method is almost equivalent to that by classic PCA.
文章编号:200900329     中图分类号:    文献标志码:
基金项目:国家部委预研基金资助项目(9140A16050109DZ01);陕西省教育厅科研计划资助项目(09JK701)
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王莹,曾平,罗雪梅,谢琨.一种用于低维光谱空间构造的非负主成分分析法[J].工程科学与技术,2010,42(2):165-170.
Wang Ying,Zeng Ping,Luo Xuemei,Xie Kun.Nonnegative Constrained Principal Component Analysis for the Construction of Low-dimensional Spectral Space[J].Advanced Engineering Sciences,2010,42(2):165-170.