Principal component analysis (PCA) and its variations are still the primary tool for feature extraction (FE) in the remote sensing community. This is unfortunate, as there has been a strong argument against using PCA for this purpose due to its inherent linear properties and uninformative principal components. Therefore, several critical issues still should be considered in the hyperspectral image classification when using PCA, among which: the large number of spectral channels and a small number of training samples; the nonlinearities of hyperspectral data; the small-sample issue. In order to alleviate these problems, this article employs a new information-theoretic FE method, the so-called kernel entropic component analysis (KECA), which can not only extract more nonlinear information but also can adapt to the limited-sample environment. A theorem of the pivoted Cholesky decomposition is also introduced to improve the efficiency of the KECA. The optimized version can more rapidly implement spectral-spatial features extraction, particularly for large-scale HSIs, while effectively maintaining the clustering performances of KECA. Experiments implemented on several real HSIs verify the effectiveness of the new method armed with a support vector machine classifier, in comparison with other PCA-based and state-of-the-art HSI classification algorithms. The code will also be made publicly available.

中文翻译：

---

高光谱图像分类的核低阶熵分量分析

主成分分析 (PCA) 及其变体仍然是遥感界特征提取 (FE) 的主要工具。这是不幸的，因为由于其固有的线性特性和无信息的主成分，有强烈的论据反对将 PCA 用于此目的。因此，在使用PCA进行高光谱图像分类时，仍然需要考虑几个关键问题，其中：光谱通道数量多，训练样本数量少；高光谱数据的非线性；小样本问题。为了缓解这些问题，本文采用了一种新的信息论有限元方法，即所谓的核熵分量分析（KECA），它不仅可以提取更多的非线性信息，而且可以适应有限样本环境。还引入了枢轴 Cholesky 分解定理以提高 KECA 的效率。优化后的版本可以更快速地实现谱空间特征提取，特别是对于大规模的 HSI，同时有效地保持了 KECA 的聚类性能。与其他基于 PCA 和最先进的 HSI 分类算法相比，在几个真实 HSI 上实施的实验验证了配备支持向量机分类器的新方法的有效性。该代码也将公开提供。与其他基于 PCA 和最先进的 HSI 分类算法相比，在几个真实 HSI 上实施的实验验证了配备支持向量机分类器的新方法的有效性。该代码也将公开提供。与其他基于 PCA 和最先进的 HSI 分类算法相比，在几个真实 HSI 上实施的实验验证了配备支持向量机分类器的新方法的有效性。该代码也将公开提供。