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It is a popular practice in the remote sensing community to apply principal component analysis (PCA) on a high dimensional feature space to achieve dimensionality reduction. Typically, there are two primary goals for dimensionality reduction: (i) data compression and (ii) feature extraction for classification purposes. While PCA has been proven to be an optimal method for data compression, it is not necessarily an optimal method for feature extraction, particularly when the features are used in a supervised classifier. This paper addresses the issue of using PCA on hyperspectral data, specifically why PCA is not optimal for dimensionality reduction in target detection and classification applications. The authors provide theoretical and experimental analysis of PCA to demonstrate why and when PCA is not appropriate. There are variations of the Karhunen-Loeve transform that outperform PCA in a supervised classification scheme, and some of these alternative approaches are discussed in this paper.