We propose a new method to construct representative spectra from a large database of spectral reflectances. The key is the optimisation of a Support Vector type functional. The representatives are constructed such that they sit at positions of high density in the set of spectra. At the same time they are constructed to be as orthogonal as possible. The representatives are expressible as a linear combination of data samples with positive coefficients. Therefore, they are positive and physically realisable. We show the differences of these representatives to representatives found with well-known methods like principal component analysis and k–means clustering.