Hyperspectral Data Processing: Algorithm Design and Analysis

5.2 Reinterpretation of VD

Since VD was introduced in Chang (2003a), it has shown promise in various applications, just to name a few, dimensionality reduction (Wang and Chang, 2006), band selection (Chang and Wang, 2006), and endmember extraction (Nascimento and Dias, 2005; Chang and Plaza, 2006; Chang et al. 2006). However, it also gives rise to some controversial issues caused by users' misinterpretation of VD. The first misinterpretation of VD is to tie VD to the technique that was originally developed by Harsanyi et al. (1994a), referred to as Harsanyi–Farrand–Chang (HFC) method for VD estimation. When the HFC method does not perform effectively, users blame VD for its inapplicability. A second misinterpretation is caused by the fact that VD does not address the second issue mentioned in the introduction, that is, how to find the p basic elements as a whole. More specifically, VD must be tuned to various applications that define basic elements. In other words, a different application may need a different set of basic elements in which case a different value of p is also required. A third misinterpretation results from a misconception that the techniques developed for finding ID should also be applicable to finding VD. Unfortunately, this is not true. Since ID does not specify any data properties, a default assumption about the data properties for ID is data variances in which case PCA becomes a classical approach to determine ID. Unlike ID, VD is specifically designed to preserve ...