The ability to learn re-occurring patterns in real-time sensory inputs in an unsupervised way is a key feature of neural networks that can enable them to carry out complex tasks directly, or to simplify the learning process of subsequent layers in powerful deep network configurations. Dedicated neuromorphic computing electronic systems can implement low-power real-time neural network inference engines. However, unsupervised online learning in these systems remains an open challenge. In this paper, we demonstrate spike-based unsupervised learning in a neuromorphic hardware device that has ultra low-power spiking neuron circuits and on-chip plasticity synapse circuits implemented with analog electronics. We configure populations of silicon neurons in a soft winner-take-all (WTA) network configuration, which enables them to learn the classification of different spike-rate input patterns in an unsupervised manner. We demonstrate the ability of this neuromorphic hardware to perform unsupervised learning of the pattern classification in real-time, and characterize its robustness as a function of network parameters and network configuration.