Memristive spiking neural networks are a promising emerging technology in the field of deep learning. These models can be implemented using neuromorphic hardware and therefore offer low power consumption and low latency, crucial to edge-computing applications. These systems, however, pose several challenges, including on-chip training and connectivity reduction. The latter is essential to ease the manufacturing complexity of the system. On-chip training can be realized using synaptic plasticity enabled by memristors. In this work, we compare two methods of connectivity reduction applicable to memristive spiking networks: an ensemble-based approach and a probabilistic sparse connectivity approach. We evaluate both of these methods in conjunction with a three-layer spiking neural network on the handwritten and spoken digits classification tasks using two memristive plasticity models and a classical time-dependent plasticity rule. On the handwritten digits recognition task, both methods achieve the F1-score of 0.89–0.93, and yield the 0.80–0.96 F1-score on the spoken digits recognition task.