Partially Geometric-Constrained Progressive Endmember Finding: Growing Convex Cone Volume Analysis

Abstract

Chapter 7 presents a Convex Cone Volume Analysis (CCVA) approach developed by Chang et al. (2016) to finding endmembers which maximizes convex cone volumes for a given fixed number of convex cone vertices in the same way that N-FINDR maximizes simplex volumes in Chap. 6 for a given fixed number of simplex vertices. Its main idea is to project a convex cone onto a hyperplane so that the projected convex cone becomes a simplex. With this advantage, what can be derived from N-FINDR in Chap. 6 can also be applied to CCVA in Chap. 7. To reduce computational complexity and relieve the computing time required by N-FINDR, a Simplex Growing Analysis (SGA) approach developed by Chang et al. (2006) is further discussed in Chap. 10. More specifically, instead of working on fixed-size simplexes as does N-FINDR, SGA grows simplexes to find maximal volumes of growing simplexes by adding new vertices one at a time. Because CCVA can be derived from N-FINDR, it is expected that a similar approach can also be applied to SGA. This chapter develops a Growing Convex Cone Volume Analysis (GCCVA) approach, which is a parallel theory to SGA and can be considered to be a progressive version of CCVA in the same way as SGA is developed in Chap. 10 as a progressive version of N-FINDR. Accordingly, what SGA is to N-FINDR is exactly what GCCVA is to CCVA.