8.6 High-Order Statistics-Based SQ-EEAS

In Section 7.3, a second-order statistics SM-EEA, SPCA-EEA, is derived to find a set of endmembers that yield the least statistical correlation. However, there are no HOS SM-EEAs that are similar to SPCA-EEA developed in Chapter 7. The reason for this is that no analytic form can be derived for HOS-EEAs in the same way as SPCA-EEA that solves a characteristic polynomial equation to find all eigenvalues simultaneously. In this case, instead of solving a known equation such as the characteristic polynomial equation, HOS-based EEAs must appeal for an algorithm that allows one to find projection vectors similar to eigenvectors found by SPCA-EEA through eigenvalues and each of such projection vectors can only be found one at a time. Then, each projection vector produces an HOS component from which an endmember can be extracted. An EEA design, based on this approach, is called an HOS-based SQ-EEA.

More specifically, we assume that the ith HOS component, denoted by img, can be described by a random variable ζi with values taken by the gray level value of the nth pixel in the component img, denoted by img. Therefore, criteria used to generate various HOS components ...

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