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首页> 外文期刊>IEEE Geoscience and Remote Sensing Letters >Limitations of Principal Components Analysis for Hyperspectral Target Recognition
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Limitations of Principal Components Analysis for Hyperspectral Target Recognition

机译：主成分分析在高光谱目标识别中的局限性

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摘要

Dimensionality reduction is a necessity in most hyperspectral imaging applications. Tradeoffs exist between unsupervised statistical methods, which are typically based on principal components analysis (PCA), and supervised ones, which are often based on Fisher's linear discriminant analysis (LDA), and proponents for each approach exist in the remote sensing community. Recently, a combined approach known as subspace LDA has been proposed, where PCA is employed to recondition ill-posed LDA formulations. The key idea behind this approach is to use a PCA transformation as a preprocessor to discard the null space of rank-deficient scatter matrices, so that LDA can be applied on this reconditioned space. Thus, in theory, the subspace LDA technique benefits from the advantages of both methods. In this letter, we present a theoretical analysis of the effects (often ill effects) of PCA on the discrimination power of the projected subspace. The theoretical analysis is presented from a general pattern classification perspective for two possible scenarios: (1) when PCA is used as a simple dimensionality reduction tool and (2) when it is used to recondition an ill-posed LDA formulation. We also provide experimental evidence of the ineffectiveness of both scenarios for hyperspectral target recognition applications.
机译：在大多数高光谱成像应用中，降维是必不可少的。在通常基于主成分分析（PCA）的无监督统计方法与通常基于Fisher线性判别分析（LDA）的有监督统计方法之间存在折衷，并且遥感社区中存在每种方法的支持者。最近，已经提出了一种称为子空间LDA的组合方法，其中采用PCA来调节不适定的LDA公式。这种方法背后的关键思想是使用PCA变换作为预处理器来丢弃秩不足的散布矩阵的空空间，以便可以将LDA应用于此经过调整的空间。因此，从理论上讲，子空间LDA技术受益于这两种方法的优点。在这封信中，我们介绍了PCA对投影子空间的辨别力的影响（通常为不良影响）的理论分析。从一般模式分类的角度针对两种可能的情况提出了理论分析：（1）当PCA用作简单的降维工具时；（2）当其用于调节不适定的LDA公式时。我们还提供了两种情况对高光谱目标识别应用无效的实验证据。

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