Superpixelwise Collaborative-Representation Graph Embedding for Unsupervised Dimension Reduction in Hyperspectral Imagery

Recently, graph-embedding framework has been developed for dimensionality reduction (DR) and classification of hyperspectral images (HSI). However, it suffers from intraclass difference and interclass similarity in complex scenarios. In this article, an unsupervised DR method called superpixelwise collaborative-representation graph embedding (SPCRGE) is proposed for the HSI classification. In SPCRGE, homogeneous regions called superpixels are generated by grouping spectral-similar and spatially adjacent pixels. Pixels in one homogeneous region come from one class with high probability. Then, Laplacian regularized superpixelwise collaborative representation (SPCR) of a query pixel, i.e., using all pixels in its superpixel to represent the pixel, is obtained by solving a generalized Sylvester equation to extract commonality and maintain individuality of the pixel to some extent. Finally, a global projection matrix to a low-dimensional space is calculated by reducing the discrepancy between SPCRs and the original spectral features, and reducing the differences between pixels from one superpixel and increasing the differences between pixels from different superpixels simultaneously. Superior classification performances on several HSI datasets demonstrate the effectiveness of the proposed SPCRGE.