Low-dimensional multi-spectral space for color reproduction based on nonnegative constrained principal component analysis

基于非负主成分分析的低维光谱色彩空间表示法(英文)

In order to overcome the shortcomings that the reconstructed spectral reflectance may be negative when using the classic principal component analysis （PCA）to reduce the dimensions of the multi-spectral data, a nonnegative constrained principal component analysis method is proposed to construct a low-dimensional multi-spectral space and accomplish the conversion between the new constructed space and the multispectral space. First, the reason behind the negative data is analyzed and a nonnegative constraint is imposed on the classic PCA. Then a set of nonnegative linear independence weight vectors of principal components is obtained, by which a lowdimensional space is constructed. Finally, a nonlinear optimization technique is used to determine the projection vectors of the high-dimensional multi-spectral data in the constructed space. Experimental results show that the proposed method can keep the reconstructed spectral data in [ 0, 1 ]. The precision of the space created by the proposed method is equivalent to or even higher than that by the PCA.

针对采用主成分分析法进行多光谱数据降维会使重构光谱反射比出现负值的问题,提出一种非负约束主成分分析法,并用该法构造低维空间,实现高维多光谱数据向低维空间的转换.首先分析主成分分析法产生非光谱数据的原因,据此对经典主成分分析模型增加非负约束;然后求出一组线性无关的非负主成分权向量,用该组向量构造低维空间;最后用非线性优化技术确定高维数据在该低维空间中的投影值,实现了高维空间与低维空间的相互转换.实验结果表明,新方法能使重构光谱数据在[0,1]内,保持了光谱反射比的物理意义,同时所构造低维空间的精度能与经典主成分分析法保持一致.