近年来, p值统计量的使用规范引起了统计学界的极大关注和集中讨论, 广泛认为, p值统计量可表达观测数据与备择假设之间的不相容程度。为探究高光谱图像波段的相关分析p值与其样本独立性的联系, 进行了演绎推理和实例验证, 研究表明, 与相关系数r统计量相比, 相关分析p统计量可直接表达波段样本的独立性, 且p值矩阵具有高水平的自稀疏性, 便于建模和计算。进而, 对相关性p值矩阵进行直方图频数统计, 提出一种基于p值的高光谱自适应波段选择方法pSMBS。选取典型数据进行了监督分类实验, 结果表明, 在Kappa系数、总体精度(OA)和平均精度(AA)上, pSMBS均优于同类方法ABS、InfFS和LSFS。说明pSMBS在高光谱波段选择方面具有突出的有效性, 这也佐证了相关性p值对波段独立性的强表征能力。

The usage specifications of p-value statistic were stimulated by highly visible discussions in the field of Statistics over the last few years. It is generally considered that a p-value can indicate how incompatible sample data are with the alternative hypothesis model. To explore the connection between the p-value of correlation analysis and spectral independence, the deductive reasoning and example verification were carried out. Compared with correlation coefficient(r-value statistic), results show that the band independence can be directly expressed by p-value statistic of correlation analysis. And p-value matrix has a kind of high-level self-sparsity, which can be used to model easily. And then an unsupervised band selection method(p-value sparsity matrix band selection, pSMBS) through p-value statistic modeling independence was proposed, based on the histogram frequency statistics of p-value matrix. Using two typical hyperspectral images (HSI) data, the experiments of supervised classification were carried out. The results indicate that, on Kappa coefficient, overall accuracy(OA) and average accuracy(AA), pSMBS is superior to three kinds of methods, adaptive band selection(ABS), infinite feature selection (InfFS) and Laplacian score feature selection(LSFS). Therefore, the effectiveness and the practicability of pSMBS were verified on HSI band selection, and the characterization ability of p-value of correlation analysis on expressing band independence was evidenced.hyperspectral image