Fast implementation of kernel simplex volume analysis based on modified Cholesky factorization for endmember extraction

  • Jing Li
  • Xiao-run Li
  • Li-jiao Wang
  • Liao-ying Zhao


Endmember extraction is a key step in the hyperspectral image analysis process. The kernel new simplex growing algorithm (KNSGA), recently developed as a nonlinear alternative to the simplex growing algorithm (SGA), has proven a promising endmember extraction technique. However, KNSGA still suffers from two issues limiting its application. First, its random initialization leads to inconsistency in final results; second, excessive computation is caused by the iterations of a simplex volume calculation. To solve the first issue, the spatial pixel purity index (SPPI) method is used in this study to extract the first endmember, eliminating the initialization dependence. A novel approach tackles the second issue by initially using a modified Cholesky factorization to decompose the volume matrix into triangular matrices, in order to avoid directly computing the determinant tautologically in the simplex volume formula. Theoretical analysis and experiments on both simulated and real spectral data demonstrate that the proposed algorithm significantly reduces computational complexity, and runs faster than the original algorithm.

Key words

Endmember extraction Modified Cholesky factorization Spatial pixel purity index (SPPI) New simplex growing algorithm (NSGA) Kernel new simplex growing algorithm (KNSGA) 

CLC number



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Copyright information

© Journal of Zhejiang University Science Editorial Office and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Jing Li
    • 1
  • Xiao-run Li
    • 1
  • Li-jiao Wang
    • 1
  • Liao-ying Zhao
    • 2
  1. 1.College of Electrical EngineeringZhejiang UniversityHangzhouChina
  2. 2.Institute of Computer Application TechnologyHangzhou Dianzi UniversityHangzhouChina

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