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

  • Chein-I Chang
Chapter

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.

Keywords

Convex Cone Little Square Error Endmember Extraction Vertex Component Analysis Simplex Grow Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2016

Authors and Affiliations

  1. 1.BaltimoreUSA

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