  Principal skewness analysis (PSA) has been introduced for feature extraction
in hyperspectral imagery. As a third-order generalization of principal
component analysis (PCA), its solution of searching for the locally maximum
skewness direction is transformed into the problem of calculating the
eigenpairs (the eigenvalues and the corresponding eigenvectors) of a coskewness
tensor. By combining a fixed-point method with an orthogonal constraint, it can
prevent the new eigenpairs from converging to the same maxima that has been
determined before. However, the eigenvectors of the supersymmetric tensor are
not inherently orthogonal in general, which implies that the results obtained
by the search strategy used in PSA may unavoidably deviate from the actual
eigenpairs. In this paper, we propose a new nonorthogonal search strategy to
solve this problem and the new algorithm is named nonorthogonal principal
skewness analysis (NPSA). The contribution of NPSA lies in the finding that the
search space of the eigenvector to be determined can be enlarged by using the
orthogonal complement of the Kronecker product of the previous one, instead of
its orthogonal complement space. We give a detailed theoretical proof to
illustrate why the new strategy can result in the more accurate eigenpairs. In
addition, after some algebraic derivations, the complexity of the presented
algorithm is also greatly reduced. Experiments with both simulated data and
real multi/hyperspectral imagery demonstrate its validity in feature
extraction.
