Spectral similarity measures can be regarded as potential metrics for kernel functions, and can be used to generate spectral-similarity-based kernels. However, spectral-similarity-based kernels have not received significant attention from researchers. In this paper, we propose two novel spectral-similarity-based kernels based on spectral angle mapper (SAM) and spectral information divergence (SID) combined with the radial basis function (RBF) kernel: Power spectral angle mapper RBF (Power-SAM-RBF) and normalized spectral information divergence-based RBF (Normalized-SID-RBF) kernels. First, we prove these spectral-similarity-based kernels to be Mercer’s kernels. Second, we analyze their efficiency in terms of local and global kernels. Finally, we consider three hyperspectral datasets to analyze the effectiveness of the proposed spectral-similarity-based kernels. Experimental results demonstrate that the Power-SAM-RBF and SAM-RBF kernels can obtain an impressive performance, particularly the Power-SAM-RBF kernel. For example, when the ratio of the training set is $20\%$ , the kappa coefficient of Power-SAM-RBF kernel (0.8561) is $1.61\%$ , $1.32\%$ , and $1.23\%$ higher than that of the RBF kernel on the Indian Pines, University of Pavia, and Salinas Valley datasets, respectively. We present three conclusions. First, the superiority of the Power-SAM-RBF kernel compared to other kernels is evident. Second, the Power-SAM-RBF kernel can provide an outstanding performance when the similarity between spectral signatures in the same hyperspectral dataset is either extremely high or extremely low. Third, the Power-SAM-RBF kernel provides even greater benefits compared to other commonly used kernels when the sizes of the training sets increase. In future work, multiple kernels combining with the spectral-similarity-based kernel are expected to be provide better hyperspectral classification.

中文翻译：

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基于光谱相似度的SVM核用于高光谱图像分类

频谱相似性度量可被视为内核功能的潜在度量，并可用于生成基于频谱相似性的内核。但是，基于光谱相似性的内核尚未受到研究人员的广泛关注。在本文中，我们提出了两个基于光谱角度映射器（SAM）和光谱信息散度（SID）并结合径向基函数（RBF）内核的基于光谱相似性的内核：功率光谱角度映射器RBF（Power-SAM- RBF）和基于归一化频谱信息发散的RBF（归一化SID-RBF）内核。首先，我们证明这些基于光谱相似性的内核是Mercer的内核。其次，我们根据本地和全局内核分析它们的效率。最后，我们考虑了三个高光谱数据集，以分析所提出的基于光谱相似性的核的有效性。实验结果表明，Power-SAM-RBF和SAM-RBF内核可以获得令人印象深刻的性能，尤其是Power-SAM-RBF内核。例如，当训练集的比例为 $20％$ ，则Power-SAM-RBF内核的kappa系数（0.8561）为 $1.61％$ ， $1.32％$ 和 $1.23％$ 分别高于印度松，帕维亚大学和萨利纳斯山谷数据集上的RBF内核。我们提出三个结论。首先，与其他内核相比，Power-SAM-RBF内核具有明显优势。其次，当同一高光谱数据集中的光谱特征之间的相似度极高或极低时，Power-SAM-RBF内核可以提供出色的性能。第三，当训练集的大小增加时，与其他常用内核相比，Power-SAM-RBF内核具有更大的优势。在未来的工作中，与基于光谱相似性的内核相结合的多个内核有望提供更好的高光谱分类。