Despite the popularity of mathematical morphology with remote sensing image analysis, its application to hyperspectral data remains problematic. The issue stems from the need to impose a complete lattice structure on the multi-dimensional pixel value space, that requires a vector ordering. In this article , we introduce such a supervised ordering relation, which conversely to its alternatives, has been designed to be image-specific and exploits the spectral purity of pixels. The practical interest of the resulting multivariate morphological operators is validated through classification experiments where it achieves state-of-the-art performance.