This paper proposes a nonlinear classification algorithm S3C (supervised spectral space classifier), short for supervised spectral space classifier. S3C integrates the discriminative information into the construction of the low-dimensional supervised spectral space. The input training data is mapped into the supervised spectral space, followed by the optimization of the partitioning hyperplane with maximum margin. The test data is also transformed into the same feature space via an intermediate “bridge” between the original feature space and the target feature space. The classification result of S3C is obtained by applying the optimal partitioning hyperplane to the transformed test data, directly. S3C enables researchers to examine the transformed data in the supervised spectral space, which is beneficial to both algorithm evaluation and parameter selection. Moreover, the study presents a supervised spectral space transformation algorithm (S³T) on the basis of S3C. S³T (supervised spectral space transformation) estimates the class indicating matrix by projecting the data from the supervised spectral space to the class indicating space. S³T can directly deal with multi-class classification problems, and it is more robust on the data sets containing noise. Experimental results on both synthetic and real-world data sets demonstrate the superiority of S3C and S³T algorithms compared with other state-of-the-art classification algorithms.