This letter presents a spike-based model that employs neurons with functionally distinct dendritic compartments for classifying high-dimensional binary patterns. The synaptic inputs arriving on each dendritic subunit are nonlinearly processed before being linearly integrated at the soma, giving the neuron the capacity to perform a large number of input-output mappings. The model uses sparse synaptic connectivity, where each synapse takes a binary value. The optimal connection pattern of a neuron is learned by using a simple hardware-friendly, margin-enhancing learning algorithm inspired by the mechanism of structural plasticity in biological neurons. The learning algorithm groups correlated synaptic inputs on the same dendritic branch. Since the learning results in modified connection patterns, it can be incorporated into current event-based neuromorphic systems with little overhead. This work also presents a branch-specific spike-based version of this structural plasticity rule. The proposed model is evaluated on benchmark binary classification problems, and its performance is compared against that achieved using support vector machine and extreme learning machine techniques. Our proposed method attains comparable performance while using 10% to 50% less in computational resource than the other reported techniques.