Spike-Timing-Dependent Plasticity (STDP) is an unsupervised learning mechanism for Spiking Neural Networks (SNNs) that has received significant attention from the neuromorphic hardware community. However, scaling such local learning techniques to deeper networks and large-scale tasks has remained elusive. In this work, we investigate a Deep-STDP framework where a convolutional network is trained in tandem with pseudo-labels generated by the STDP clustering process on the network outputs. We achieve $24.56\%$ higher accuracy and $3.5\times$ faster convergence speed at iso-accuracy on a 10-class subset of the Tiny ImageNet dataset in contrast to a $k$-means clustering approach.