Limitations of Principal Component Analysis for Dimensionality-Reduction for Classification of Hyperspectral Data

It is a popular practice in the remote-sensing community to apply principal component analysis (PCA) on a higher-dimensional feature space to achieve dimensionality-reduction. Several factors that have led to the popularity of PCA include its simplicity, ease of use, availability as part of popular remote-sensing packages, and optimal nature in terms of mean square error. These advantages have prompted the remote-sensing research community to overlook many limitations of PCA when used as a dimensionality-reduction tool for classification and target-detection applications. This thesis addresses the limitations of PCA when used as a dimensionality-reduction technique for extracting discriminating features from hyperspectral data. Theoretical and experimental analyses are presented to demonstrate that PCA is not necessarily an appropriate feature-extraction method for high-dimensional data when the objective is classification or target-recognition. The influence of certain data-distribution characteristics, such as within-class covariance, between-class covariance, and correlation on PCA transformation, is analyzed in this thesis. The classification accuracies obtained using PCA features are compared to accuracies obtained using other feature-extraction methods like variants of Karhunen-Loève transform and greedy search algorithms on spectral and wavelet domains. Experimental analyses are conducted for both two-class and multi-class cases. The classification accuracies obtained from higher-order PCA components are compared to the classification accuracies of features extracted from different regions of the spectrum. The comparative study done on the classification accuracies that are obtained using above feature-extraction methods, ascertain that PCA may not be an appropriate tool for dimensionality-reduction of certain hyperspectral data-distributions, when the objective is classification or target-recognition