Hyperspectral Data Processing: Algorithm Design and Analysis

20.2 Dimensionality Prioritization

DRT takes advantage of transformed components produced by a custom-designed transformation to represent the original data in a new transformed data space with a different data representation in which each data dimension is specified by a particular transformed component. The DR is then performed by retaining a prescribed number of transformed components, q. Accordingly, the effectiveness of DRT is determined by three key factors: the DR transformation being used to produce transformed components, significance of transformed components measured by a selected information criterion, and the value of q.

Using the commonly used PCA as an example, we can illustrate these three issues as follows. First of all, PCA transforms the original 2D spatial/1D spectral data coordinate system into a new data representation system formed by a set of PCs, each of which is characterized by a specific eigenvector that corresponds to a particular eigenvalue, that is, a sample data variance. Then, the significance of each PC is further measured by the magnitude of the eigenvalue corresponding to the eigenvector that specifies this particular PC. In other words, each dimension in a PCA- transformed data space is no longer a wavelength-specified spectral dimension in the original data space. That is, the original data represented by the wavelength-based spectral dimensionality can be reduced via PCA to a small number of PCs specified by eigenvectors corresponding to large ...