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18 May 2013 Second order statistics target-specified virtual dimensionality
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Virtual dimensionality (VD) has received considerable interest in its use of specifying the number of spectrally distinct signatures. So far all techniques are decomposition approaches which use eigenvalues, eigenvectors or singular vectors to estimate the virtual dimensionality. However, when eigenvalues are used to estimate VD such as Harsanyi-Farrand- Chang’s method or hyperspectral signal subspace identification by minimum error (HySime), there will be no way to find what the spectrally distinct signatures are. On the other hand, if eigenvectors/singular vectors are used to estimate VD such as maximal orthogonal complement algorithm (MOCA), eigenvectors/singular vectors do not represent real signal sources. In this paper we introduce a new concept, referred to as target-specified VD (TSVD), which operates on the signal sources themselves to both determine the number of distinct sources and identify their signature. The underlying idea of TSVD was derived from that used to develop high-order statistics (HOS) VD where its applicability to second order statistics (2OS) was not explored. In this paper we investigate a 2OS-based target finding algorithm, called automatic target generation process (ATGP) to determine VD. Experiments are conducted in comparison with well-known and widely used eigen-based approaches.
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Drew Paylor and Chein-I Chang "Second order statistics target-specified virtual dimensionality", Proc. SPIE 8743, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XIX, 87430X (18 May 2013);

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