Hyperspectral Data Processing: Algorithm Design and Analysis

8.4 Vertex Component Analysis (VCA)

The VCA developed by Nascimento and Dias (2005) is also designed to reduce costly computational complexity suffered in MVT and CCA by replacing simple volume calculation with OP and growing convex hulls vertex by vertex until it reaches a p-vertex convex hull instead of replacing p-vertex convex hulls all together as MVT and CCA do. Its idea is similar to SGA in the sense that VCA also grows convex hulls one vertex at a time sequentially in succession, but has a major difference from that of SGA in how to find a vertex to grow a convex hull. More specifically, VCA grows convex hulls with maximal orthogonal projections instead of simplexes with maximal volume used by SGA. In other words, VCA appeals for the maximum orthogonal projection as a criterion as PPI does to grow its convex hulls compared to SGA that uses the maximal volume of a simplex as a criterion to grow simplexes as N-FINDR does. In light of this interpretation, VCA can be considered a sequential version of PPI, and SGA can be viewed as a sequential version of N-FINDR. A comparative analysis between VCA and SGA was conducted by Chang et al. (2006) with more details to be discussed in Chapters 9 and 11. The algorithmic implementation of VCA can be described as follows.

Vertex Component Analysis (VCA)

1. Let the number of endmembers to be generated be p. Set a counter to .

2. Perform ...