6

Data Dimensionality Reduction

Dimensionality reduction (DR) has been used in hyperspectral data exploitation for various purposes. In particular, it has been used as a preprocessing technique to reduce a very high-dimensional data space to a manageable low-dimensional space in which data analysis can be performed more effectively. Two common approaches are widely used for DR, here referred to as DR by transform (DRT) and DR by band selection (DRBS). While the former utilizes a transform to compact data in some optimal sense, the latter finds an appropriate band subset to represent data via a certain optima criterion. Two types of transforms, components analysis (CA), and feature extraction (FE), are developed for DRT. A CA transform is generally considered as a transformation that uses statistics as a criterion to de-correlate and convert data into a set of uncorrelated data components for analysis. The transforms of this type include two commonly used second-order statistics component transforms, data variance-based principal components analysis (PCA) and signal-to-noise ratio (SNR)-based maximum noise fraction (MNF) transform as well as high-order statistics-based CA transforms with criteria such as a third-order statistics-based skewness, a fourth-order statistics-based kurtosis, plus statistical independence-based independent component analysis (ICA) that requires infinite order of statistics. An FE transform uses a feature extraction-based criterion to produce a set of feature vectors so that data can be represented by these feature vectors. The transforms of this type include Fisher's ratio-based linear discriminant analysis (FLDA) and linear mixture model-based orthogonal subspace projection (OSP). All these transformation techniques can be very useful in processing of hyperspectral imagery and will be used in later chapters in this book. A second approach to DR is DRBS. Unlike DRT that produces transformed data DRBS seeks a band subset to represent the original data so that the data information of interest can be preserved in the selected band subset. Interestingly, as will be seen, most of the criteria designed for DRT are also applicable to DRBS.