We explore classifier training for data sets with very few labels. We investigate this task using a neural network for nonnegative data. The network is derived from a hierarchical normalized Poisson mixture model with one observed and two hidden layers. With the single objective of likelihood optimization, both labeled and unlabeled data are naturally incorporated into learning. The neural activation and learning equations resulting from our derivation are concise and local. As a consequence, the network can be scaled using standard deep learning tools for parallelized GPU implementation. Using standard benchmarks for nonnegative data, such as text document representations, MNIST, and NIST SD19, we study the classification performance when very few labels are used for training. In different settings, the network's performance is compared to standard and recently suggested semisupervised classifiers. While other recent approaches are more competitive for many labels or fully labeled data sets, we find that the network studied here can be applied to numbers of few labels where no other system has been reported to operate so far.