Endmember-Finding Algorithms: Comparative Studies and Analyses

Abstract

Design and development of Endmember Extraction Algorithms (EEAs) was treated in great detail in Chaps. 7–11 of Chang (2013) where EEAs are grouped into four different categories—SiMultaneous EEAs (SM EEAs) in Chap. 7, SeQuential EEAs (SQ EEAs) in Chap. 8, Initialization Driven EEAs (ID-EEAs) in Chap. 9, and Random EEAs (REEAs) in Chap. 10—according to how endmembers are extracted. The premise of EEA is to assume the existence of endmembers in the data. As described in Chap. 3, Sects. 5.2.3.2 and 5.3.2, if the data to be processed does not contain data sample vectors with pure signatures as endmembers, extracting something which does not exist is meaningless. Unfortunately, in reality this is generally true, that is, there is no guarantee for the presence of endmembers in the data. Therefore, using the term endmember extraction seems inappropriate. To address this issue, this book particularly uses the term of “Endmember Finding” to reflect real situations to deal with this dilemma where endmembers do not necessarily exist in the data. Under such circumstances, this book looks into a more practical manner to categorize algorithms in terms of how an algorithm is implemented and further partitions algorithms into two categories—Sequential EFAs in Chaps. 6– 9 and Progressive EFAs in Chaps. 10– 12—where the former produces all endmembers simultaneously in a sequential manner, while the latter produces endmembers one after another and one at a time in a progressive manner. For each category, four design rationales are considered as optimal criteria for finding endmembers, which are fully geometric-constrained-based approaches such as Simplex Volume Analysis (SVA) in Chap. 6 and Growing Simplex Volume Analysis (GSVA) in Chap. 10, partially geometric-constrained Convex Cone Volume (CCV)-based approaches, Convex Cone Volume Analysis (CCVA) in Chap. 7 and Growing Convex Cone Volume Analysis (GCCVA) in Chap. 11, geometric-unconstrained orthogonal projection-based approaches such as Causal Iterative Pixel Purity Index (C-IPPI) in Chap. 8 and Progressive Iterative Pixel Purity Index (P-IPPI) in Chap. 12 plus Fully Abundance Constrained Least Squares Error (LSE)-based Linear Spectral Mixture Analysis (LSMA) approaches in Chap. 9. Because each of these chapters is devoted to and focused on a specific subject, their chapter–chapter interconnections and interrelationships are not explored. This chapter is specifically included for this purpose to conduct comparative studies and analyses among various EFAs developed in previous chapters.