Relevance-based Feature Extraction from Hyperspectral Images in the Complex Wavelet Domain

Generalized relevance learning vector quantization (GRLVQ) (B. Hammer and T. Villmann, 2002) is a "double action" supervised neural learning machine that simultaneously adapts classification boundaries and a weighting of the input dimensions to reflect the relevance of each dimension for the given classification. It is thus a joint classification and feature extraction technique. In (M. J. Mendenhall and E. Merenyi, Mar. 2006) we developed an improved version (GRLVQI) to handle intricate high-dimensional data. GRLVQI makes significant headway of feature reduction for hyperspectral images without compromising classification accuracy. However, the number of features to which the data can be reduced in the original (reflectance data) domain is naturally limited by higher order correlations. Here we investigate GRLVQI processing on wavelet coefficients because of the approximately decorrelated nature and the sparsity of those coefficients. We investigate the dual-tree complex wavelet transform (DTCWT) (I. W. Selesnick, et al., Nov. 2005) for its reduced oscillatory effects because spectral data often have discontinuities due to data fallout. We demonstrate that GRLVQI on the DTCWT coefficients achieves better classification with fewer features than using the critically sampled discrete wavelet transform (CSDWT), which was already shown to yield better results with far fewer features than GRLVQI applied in the original data space