Spectral imaging is a powerful tool for providing in situ material classification across a spatial scene. Typically, spectral imaging analyses are interested in classification, though often the classification is performed only after reconstruction of the spectral datacube. We present a computational spectral imaging system, the Adaptive Feature-Specific Spectral Imaging Classifier (AFSSI-C), which yields direct classification across the spatial scene without reconstruction of the source datacube. With a dual disperser architecture and a programmable spatial light modulator, the AFSSI-C measures specific projections of the spectral datacube which are generated by an adaptive Bayesian classification and feature design framework. We experimentally demonstrate multiple order-of-magnitude improvement of classification accuracy in low signal-to-noise (SNR) environments when compared to legacy spectral imaging systems.