This article proposes a neural network model of supervised learning that employs biologically motivated constraints of using local, on-line, constructive learning. The model possesses two novel learning mechanisms. The first is a network for learning topographic mixtures. The network's internal category nodes are the mixture components, which learn to encode smooth distributions in the input space by taking advantage of topography in the input feature maps. The second mechanism is an attentional biasing feedback circuit. When the network makes an incorrect output prediction, this feedback circuit modulates the learning rates of the category nodes, by amounts based on the sharpness of their tuning, in order to improve the network's prediction accuracy. The network is evaluated on several standard classification benchmarks and shown to perform well in comparison to other classifiers.