Hyperspectral Data Processing: Algorithm Design and Analysis

17.3 Component Analysis-Based ULSMA

As noted in the introduction, hyperspectral signatures can be categorized into background signatures characterized by second-order statistics of IBSI(S) and target signatures characterized by HOS of IBSI(S). Recall that the commonly used PCA is a second-order statistics-based transform that uses a set of PCs to represent the data where eigenvectors are projection vectors to specify PCs with eigenvalues being data variances. In this case, PCA can be then used to extract background signatures characterized by second-order statistics of IBSI(S) in PCs. On the other hand, ICA is an HOS-based transform that uses mutual information to generate a set of ICs to represent data. Therefore, ICA can be used to find desired target signatures characterized by HOS of IBSI(S) in ICs. In both cases, VD is again used to determine how many PCs and ICs are required to extract signatures. Since PCs and ICs are obtained by mapping all data samples onto the projection vectors, the projection values of data samples are real values. So, an issue arises: how many data sample vectors should be selected from each PC and each IC? Two sample values in each IC are of major interest: one with maximal projection value and the other with minimal projection value. These two samples represent maximal projections in two opposite directions of a projection vector that specifies an IC. They both indicate their importance in data analysis. This idea was previously explored in pixel ...