We present a novel machine learning architecture for classification suggested by experiments on olfactory systems. The network separates input stimuli, represented as spatially distinct currents, via winnerless competition---a process based on the intrinsic sequential dynamics of the neural system---then uses a support vector machine (SVM) to provide precision to the space-time separation of the output. The combined network uses biophysical models of neurons and shows high discrimination among inputs and robustness to noise. While using the SVM alone does not permit determination of the components of mixtures of classified inputs, the combined network is able to tell the precise concentrations of the constituent parts.